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Sponsored by the IEEE Magnetics Society and co-sponsored by:

Data Storage Systems Center (DSSC) - CMU Center for Magnetic Recording Research (CMRR) - UCSD

Center for Micromagnetics & Information Technologies (MINT) - U of MN Center for Materials for Information Technology (MINT) - U of AL

Center for Magnetic Nanotechnology - Stanford Computer Mechanics Laboratory (CML) – UCB

DIGEST OF THE

18th MAGNETIC RECORDING CONFERENCE

TMRC - 2007

Minneapolis, Minnesota

May 21 – 23, 2007

Heads & Systems

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May 21-23, 2007

THE MAGNETIC RECORDING CONFERENCE

2007 TMRC MAGNETIC RECORDING

HEADS & SYSTEMS

TMRC 2007

ON

MAGNETIC

RECORDING HEADS AND SYSTEMS

18th Annual Magnetic Recording Conference

PROGRAM & DIGEST

University of Minnesota – Minneapolis, MN

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Copyright © 2007 by the Institute of Electrical and Electronics Engineers, Inc. For copying, reprint, or republication, write to:

Manager, Rights and Permissions

IEEE Services Center P.O. Box 1331 445 Hoes Lane

Piscataway, NJ 08855-1331 (732) 562-3966

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May 21-23, 2007 Minneapolis, MinnesotaSponsored by the IEEE Magnetics Society

Co-sponsored by:

Data Storage Systems Center (DSSC) - CMUCenter for Magnetic Recording Research (CMRR) - UCSD

Center for Micromagnetics & Information Technologies (MINT) - U of MNCenter for Materials for Information Technology (MINT) - U of AL

Center for Magnetic Nanotechnology - StanfordComputer Mechanics Laboratory (CML) - UCB

THE MAGNETIC RECORDING CONFERENCE

2007 TMRC HEADS & SYSTEMS

Dear Colleagues:

I am pleased to announce that the 18th annual TMRC will be held May 21-23, 2007,on the campus of the University of Minnesota in Minneapolis, MN. The subjects forthis year's conference will be magnetic recording heads and systems. Particularemphasis will be given to the following topics: · Read and write head design and development · Advanced reader, assisted write technologies and write head dynamics · Head / media interface and reliability · Head testing, methods and apparatus · High data rate effects and advanced electrical interconnects · Recording systems and integration · Advanced recording channels and detection algorithms · Advanced coding and error-correction technologies · System reliability and mechanics

Dr. Klaas Klaassen, Dr. Dean Palmer and the Program Committee have put together awonderful program with 36 invited papers in the topics listed above. Authors andcontributors represent academia as well as a wide range of international companies. All papers are invited and there will be 30 minutes allowed for the presentations andquestions. There are no parallel sessions. Reviewed & accepted papers will bepublished in the IEEE Transactions on Magnetics by the end of 2007. The PosterSessions are organized by Mr. Scott Schaefer and will take place at the end of eachafternoon session on Monday and Tuesday. All the invited talks will also be presentedin one of the poster sessions. In addition, some selected work from other contributorswith an emphasis on student presentations will be included in the poster sessions.Posters will be presented concurrently with the Bierstube in an informal atmosphere atthe Northrop Auditorium lobby.

TMRC 2007 will be using the campus facilities of the University of Minnesota andruns Monday through Wednesday. Minneapolis and St. Paul are beautiful twin citiesand the area has many recreational and cultural attractions. I urge you to make yourreservations early. The conference banquet will be held Tuesday evening, May 22, atthe Weismann Art Museum. This museum is also located inside the University ofMinnesota next to the banks of the Mississippi River.

This year’s TMRC will be an outstanding conference. Please call anyone on thecommittee with questions. We look forward to seeing you in May.

Dr. Juan Fernandez-de-CastroConference Chairman, TMRC-2007

Poster Chairman Scott Schaefer Hutchinson Technology Inc. 40 West Highland Pk Hutchinson, MN 55350 Phone: 320-587-1956 Fax: 320-587-1496 scott.schaefer@hti.htch.com

Conference Chairman Dr. Juan Fernandez-de-Castro Seagate Technology 7801 Computer Ave. South Bloomington, MN 55435 Phone: 952-402-7216 Fax: 952-402-7848 juan.j.fernandez-de-castro@seagate.com

Program Co-chairmen Dr. Klaas Klaassen Hitachi San Jose Research 3403 Yerba Buena Road San Jose, CA 95135 Phone: 408-717-5108 Fax: 408-717-9068 klaas.klaassen@hgst.com

Dr. Dean Palmer Seagate Technology 7801 Computer Ave. South Bloomington, MN 55435 Phone: 952-402-7972 Fax: 952-402-5740 dean.palmer@seagate.com

Local Chairman Prof. Jian-Ping Wang University of Minnesota MINT Center, ECE Department EE/Esci 4-174, 200 Union St. Minneapolis, MN 55455 Phone: 612-625-9509 Fax: 612-625-4583 jpwang@umn.edu

Publications Co-chairmen Dr. Ned Tabat Seagate Technology One Disc Drive Bloomington, MN 55435 Phone: 952-402-8146 FAX: 952-402-8595 ned.tabat@seagate.com

Dr. Adam Torabi Western Digital 5863 Rue Ferrari San Jose, CA 95138 Phone: 408-363-4233 FAX: 408-363-5354 adam.torabi@wdc.com

Publicity Chair Dr. Sally Doherty Agere Systems 1230 Northland Drive Mendota Heights, MN 55120 Phone: 651-675-3335 Fax: 651-675-2940 sallydoherty@Agere.com

Treasurer Dr. Joost Mortelmans 12388 Priscilla Ln Los Altos Hills, CA 94022 mortelma@gmail.com

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TMRC - 2007 DAILY SCHEDULE

Mon 21st Tues 22nd Wed 23rd

Registration 7:30 AM – 2 PM 8 – 12 AM & 1 – 2 PM 8 – 10 AM

8:00 – 9:00 AM Continental Breakfast Continental Breakfast Continental Breakfast

9:00 – 12:00 AM Session A Session C Session E 12:00 – 1:30 PM Lunch Break Lunch Break Lunch Break 1:30 – 4:30 PM Session B Session D Session F

4:30 – 6:00 PM Posters & Bierstube Posters & Bierstube

6:00 – 9:00 PM Banquet

All Oral Sessions: Auditorium of the Tate Lab. of Physics (049)

Poster Sessions & Bierstube: Atrium of the Northrop Memorial Auditorium (053)

Breakfast & Lunch: Atrium of the Northrop Memorial Auditorium (053)

TMRC Banquet, May 22nd, 6:00 – 9:00 PM: Weisman Art Museum (172)

Banquet Speaker: Dr. Currie Munce, Vice President US Labs and WW Research & Ad Tech, Hitachi Global Storage Technologies

Last minute information may also be found at the TMRC Web-site:

http://www.ece.umn.edu/~MINT/TMRC2007

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TMRC-2007 Banquet Key Note Speaker: Dr. Currie Munce Vice President US Labs and WW Research & Ad Tech Hitachi Global Storage Technologies 5600 Cottle Road San Jose, California 95135 USA ABSTRACT: The magnetic hard disk drive (HDD) is now 50 years-old, but demand is still growing for larger capacities, faster performance and enhanced features. The recording density for data on the surface of the disk has increased 70,000,000-fold in those 50 years and placed tremendous challenges on all aspects of the drive design. The transition to perpendicular magnetic recording is about to enter its second generation of products. However, to continue this great progress and meet future demands, many more technological breakthroughs will be required over the next several years. The leaders in the industry will need support from leading-edge research teams, both internal to their companies and at universities. This talk will cover key technology directions for this research and discuss some of the most challenging issues ahead. ABOUT THE SPEAKER: Dr. Currie Munce is Vice President of US Labs and Worldwide Research and Advanced Technology for Hitachi Global Storage Technologies (Hitachi GST). In his position, Dr. Munce is responsible for all the HDD product development located in the US and for efforts in Research and Advanced Technology in both US and Japan. He has worked for Hitachi GST since its inception on January 1, 2003 when it was created from the merger of IBM’s and Hitachi’s HDD businesses. Prior to joining Hitachi GST, he worked for IBM Research for over 17 years. Dr. Currie Munce received his Bachelors degree in Applied Mechanics from UC San Diego, and his Masters and Ph.D. degree in Mechanical Engineering from Stanford University.

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Oral Sessions for Monday, May 21st 2007

Session A, Monday AM: Read Heads Chair: Janusz Nowack, IBM T. J. Watson Laboratory

A1 CPP-GMR Sensors for Narrow-Track Magnetic Recording

J.R. CHILDRESS, M.J. CAREY, S. MAAT, N. SMITH, R.E. FONTANA, D. DRUIST, K. CAREY, J.A. KATINE, N. ROBERTSON, M. ALEX, J. MOORE and C. TSANG San Jose Research Center, Hitachi Global Storage Technologies

A2

FeCo Nanocontact Magnetoresistance with Current- Cnfined-Path Structures in CPP Spin Valves

M. TAKAGISHI, H. N. FUKE, S. HASHIOMOTO, H. IWASAKI Corporate Research & Development Center, Toshiba Corporation S. KAWASAKI, K. MIYAKE, and M. SAHASHI Department of Electronic Engineering, Graduate School of Engineering, Tohoku University

A3 CPP-GMR Heads with a Current Screen Layer for 300 Gb/in2 Recording

K. NAKAMOTO, H. HOSHIYA, H. KATADA, K. HOSHINO, N. YOSHIDA, H. TAKEI, M. SHIIMOTO, M. HATATANI, and K. WATANABE Hitachi Central Research Lab.

A4 Ramping Square Pulses Breakdown Test for TMR Heads

Guifu WANG, Yu CHEN, Zhaoyu TENG, Luge YIN, Kaijie ZHANG, Qiuyu HUANG, Haiting LI, Chuanfang JIANG, Ge YAN, William LI and Sidney CHOU SAE Technologies Development (Dongguan) Co., Ltd

A5 An Analysis of Noise Occurrence in TMR Reader During Drive Reliability Test

Pak Kin WONG, Yi Mei TAM, Vincent M.F. CHIAH, and Tad SHIMIZU SAE Magnetics (H.K.) Ltd

A6

Anti-static Robustness Enhancement and High Frequency Noise Pickup Immunity by Internal Shunting on Tunneling Magnetoresistive Sensor

Anthony Wai Yuen LAI, Eric Cheuk Wing LEUNG, Pak Kin WONG, Tad SHIMIZU SAE Magnetics (HK) Ltd, Hong Kong Takeo KAGAMI, TDK Corporation Moris DOVEK, Headway Technologies, Inc

Session B, Monday PM: Write Heads Chair: Mourad Benakli, Seagate Research Center

B1 A Study of Media Dependence of Shielded Perpendicular Write Head Design Optimization

Lijie GUAN, Joe SMYTH, Moris DOVEK, Yue LIU, Kenichi TAKANO

Headway Technologies, Inc. Tatsuya SHIMITZU SAE Magnetics (H.K.) Ltd

B2 Dynamics in Integrated in Write-Read Heads

Thomas SCHREFL, Alexander GONCHAROV, Gino HRKAC, Simon BANCE University of Sheffield Manfred SCHABES, Hitachi Global Storage Technologies Otmar ERTL, and Dieter SUESS, Vienna University of Technology

B3 High Magnetic Saturation Poles for Advanced Perpendicular Writers

Mark KIEF, Venkat INTURI, Ibro TABAKOVIC, Ming SUN, Olle HEINONEN, Steve RIEMER, Vladyslav VAS’KO Recording Head Operations, Seagate Technology Mourad BENAKLI, Seagate Research Center

B4 Exact Solution of Magnetic Field and Spectral Response Function for Read Heads in Perpendicular Recording

Z. J. LIU Data Storage Institute

B5 Heat Assisted Magnetic Recording for Continued Scaling of Areal Density

Michael A. SEIGLER, William A. CHALLENER, Edward GAGE, Ganping JU, Bin LU, Kalman PELHOS, Chubing PENG, Robert E. ROTTMAYER, Xiaomin YANG, Hua ZHOU, Tim RAUSCH Seagate Research Center

B6 Microwave Assisted Magnetic Recording (MAMR)

Jian-Gang (Jimmy) ZHU and Xiaochun ZHU Data Storage Systems Center, Carnegie Mellon University

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Oral Sessions for Tuesday, May 22nd 2007

Session C, Tuesday AM: Head-Disc Interface Chair: James Bain, Carnegie Mellon University

C1 The Production and Performance of Si/SiO2 Magnetic Recording Head Sliders

Tim REILEY, Jeffrey LILLE, Tim STRAND, Ed LEE, Michael CHAW, Darrick SMITH, Mike SUK, Walt FONG, Bernhard KNIGGE Hitachi Global Storage Technologies, San Jose Kenji KUROKI, Hitachi Global Storage Technologies, Fujisawa Nicholas BUCHAN, Sitime Corp.

C2 Optimal Slider-Disk Surface Topography for Head-Disk Interface Stability in Hard Disk Drives

Vineet GUPTA and David B BOGY University of California, Berkeley

C3 Dynamic Flight Height Control Recording Head Design with System Considerations

Tao PAN, Suping SONG, Bill SUN, Victor RUDMAN, Kroum STOEV, Lanshi ZHENG, Vijay PRABHAKARAN, Saikumar BALASUBRAMANIYAM, Jagdeep BUTTAR, Eric SLADEK, and Francis LIU Western Digital Corporation

C4 Low Flying Height Slider with High Thermal Actuation Efficiency and Small Flying Height Modulation Caused …

Bo LIU, Shengkai YU, Weidong ZHOU, Chee-How WONG and Wei HUA Data Storage Insitute

C5 Head Slider Designs Considering Dynamic L/UL Systems for 1-Inch Disk Drives

Sang-Joon YOON and Dong-Hoon CHOI The Center of iDOT, Hanyang Univ Seok-Ho SON Department of Mechanical Engineering, Hanyang Univ

C6 Head Disk Interface Friction Measurements: Effects of Roughness, Lubricant, and Surface Energy

Chang-Dong YEO and Andreas A. POLYCARPOU Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign Michael SULLIVAN and Sung-Chang LEE, Samsung Information Systems America

Session D, Tuesday PM: Systems, Modeling and Interconnects Chair: Kaizhong Gao, Seagate Technology

D1 Nanoscale Fabrication of Discrete-Track and Patterned Bit Media: from Prototyping to Large Scale

Zvonimir Z. BANDIĆ, Bernhard KNIGGE, Paul VAN DER HEIJDEN, Dan KERCHER, Henry YANG, Tsai-Wei WU, Elizabeth DOBISZ and Thomas R. ALBRECHT Hitachi San Jose Research Center

D2 Study of Lithographically Defined Data Track and Servo Patterns on Conventional Perpendicular Media

Xiaodong CHE, Kiseok MOON, Yawshing TANG, Nayoung KIM, Hyung Jai LEE, Samsung Information Systems America Matthew MONECK and Jian-Gang ZHU, Carnegie Mellon University Nobuyuki TAKAHASHI, Fuji Electric Advanced Technology Co.

D3 Feasibility of Recording 1 Tb/in2 Areal Density

R. H. VICTORA, Xiao SHEN, and Stephanie HERNANDEZ Univ. of Minnesota

D4 System Modeling in Support of 345 Gb/in2 Areal Density

Byron LENGSFIELD, Terry OLSON, Paul Van der HEIJDEN, Walt WERESIN, Hoa DO, Ching TSANG, Michael ALEX, Andi MOSER, Bruce WILSON, Thomas THOMSON, Andreas BERGER, Manfred SCHABES, Yoshihiro IKEDA, Neal BERTRAM, Yimin HSU, Michael SALO, Hal ROSEN, Ken TAKANO and Kurt RUBIN Hitachi Global Storage Technologies

D5 Exploring Low-Loss Suspension Interconnects for High Data Rates in Hard Disk Drives

Reed HENTGES, John PRO, Michael ROEN, Gregory J. VANHECKE Hutchinson Technology, Inc. Gregory Kimball, Texas Instruments

D6 Advanced Interconnect Design for High Data Rate Perpendicular Magnetic Recording

W. Don HUBER, W. Curt TIPTON, and Leo C. HWANG Western Digital Corporation

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Oral Sessions for Wednesday, May 23rd 2007

Session E, Wednesday AM: Channels and Systems Chair: Jon Coker, Hitachi Global Storage Technologies

E1 Iterative Decoding Based on Error-Pattern Correction

Hakim ALHUSSIEN, Jihoon PARK and Jaekyun MOON University of Minnesota

E2 Microscopic and Macroscopic Approaches in Sector Failure Rate Estimation

Alexander KUZNETSOV and Raman VENKATARAMANI Seagate Research Center

E3 A New Read Head Model for Patterned Media Storage

Seyhan KARAKULAK, Paul H. SIEGEL, Jack K. WOLF and H. Neal BERTRAM Center for Magnetic Recording Research, University of California, San Diego

E4 Viterbi Detection Algorithm for Data-Dependent Non-Markov Read Channels

Sam GRATRIX, Robert JACKSON, Tom PARNELL and Oleg ZABORONSKI Arithmatica Ltd

E5 Role of Media Damping in a Recording System

Sharat BATRA, Thomas ROSCAMP, and Werner SCHOLZ Seagate Technology

Session F, Wednesday PM: Channels Chair: Jaekyun Moon, University of Minnesota

F1 Towards Maximum Likelihood Soft Decision Decoding of the (255,239) Reed Solomon Code

Wenyi JIN LSI Corporation

Marc FOSSORIER University of Hawaii at Manoa

F2 Performance and Decoding Complexity of Nonbinary LDPC Codes for Magnetic Recording

Wu CHANG and J. R. CRUZ The University of Oklahoma, Norman

F3 Error Correcting Codes for 4k-Byte Sectors

Toshio ITO and Toshihiko MORITA Fujitsu Laboratories Ltd

F4 Read Channel with Inner LDPC Codes

Weijun TAN LSI Corp

F5 Syndrome ECC Decoding Using Bit Reliabilities

Victor Y. KRACHKOVSKY, Jonathan J. ASHLEY, Clifton J. WILLIAMSON and German FEYH LSI Corporation

F6

Maximum a Posteriori Estimation with Vector Autoregressive Models for q-ary LDGM Coding Systems in Digital Magnetic Recording Channels

Hidetoshi SAITO Kogakuin University

Masayuki HAYASHI and Ryuji KOHNO Yokohama National University

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Additional Non-Oral Poster

Poster Presentations Included in the Digest

P1

Optimal Characteristic Impedance of Suspension Interconnect Considering Output Impedance of Write Driver and Signal Loss

Eunkyu JANG Samsung Information Systems America

P2

Measurement and Interpretation of the Transverse Field Dependence of Magnetic Fluctuation Noise in Tunneling Magnetoresistive Heads

Peter GEORGE

St. Cloud State University

Guchang HAN Data Storage Institute

P3 Exchange Coupling in Synthetic Antiferromagnetic Multilayers for Write Head

Yun-Hao XU and Jian-Ping WANG University of Minnesota

Hai JIANG, Kyusik SIN and Yingjian CHEN Western Digital Corporation

P4 Correlation of Noise Spectrum in GMR and TMR Head with Bias Field

Shengxian SHE and Dan WEI DMSE, Tsinghua University

P5 Effects of Laminated Layers on Rise Time of Writer Head

Liang QUAN and Dan WEI Tsinghua University

P6 Effect of Head Scaling on Initial Permeability of Pole-tip Driven Head

Sumei WANG, Liang QUAN and Dan WEI Tsinghua Univ

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Notes

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A1

CPP-GMR Sensors for Narrow-Track Magnetic Recording

J.R. CHILDRESS, M.J. CAREY, S. MAAT, N. SMITH, R.E. FONTANA, D. DRUIST, K. CAREY, J.A. KATINE, N. ROBERTSON, M. ALEX, J. MOORE and C. TSANG.

San Jose Research Center, Hitachi Global Storage Technologies 3404 Yerba Buena Rd, San Jose, CA 95135

I. INTRODUCTION

As commercial recording densities continue to increase well beyond 100 Gb/in2, the current-perpendicular-to-the plane (CPP) geometry for recording head sensors offers numerous advantages in term of fabrication, geometry, and sensor performance.[1] In particular, the removal of the insulating gap between sensor and shields (now used as electrical contacts) facilitates the continued scaling of the shield-to-shield (SS) spacing to dimensions < 50nm. In addition, the parasitic lead resistance is virtually eliminated, reducing overall noise, and inactive sensor stack layers such as antiferromagnet and seed layers no longer shunt the sense current. Among CPP sensors, tunneling magnetoresistance (TMR) sensors currently have a substantial advantage over CPP-giant magnetoresistance (GMR) sensor in terms of signal due to their large magnetoresistance (>20% and potentially > 100%). In addition the resistance-area (RA) product of practical TMR junction with high MR has been demonstrated as low as ~ 1 -m2

[2], which means that reasonable sensor impedances (a few hundred ohms) are achievable for sensors down to ~50 nm in lateral dimensions. Consequently, CPP-TMR sensors are currently the main sensor candidates for high areal densities to 300 Gb/in2 and beyond.[3]

Nevertheless, all-metal CPP-GMR sensors remain an attractive alternative as the sensor dimensions are reduced below 50nm. With typical RA products in the range 0.03-0.10 -m2, these CPP sensor have the potential to deliver low sensor impedance at the smallest conceivable dimensions, and therefore lower noise and higher bandwith performance.[4] Among the challenges that CPP-GMR sensors face are low signal levels due to their low resistance, low R/R for thin magnetic layers, as well as current-induced noise and instability due to the spin-torque effect.

Previously we have reported on the fabrication of CPP dual spin-valve (SV) head sensors with standard ferromagnetic electrodes.[5] Compared to single-SV’s, dual-SV’s provide a significant increase in R/R and substantial cancellation of the spin-torque effect due to the symmetric arrangement of the dual pinned layers. Their performance might, however, be limited by a relatively large shield-to-shield spacing and a complex stack structure requiring among other things the optimization of two separate antiferromagnetically-coupled pinned layer structures. On the other hand, with the use of alternative ferromagnetic alloys such as CoFeAl[6] and Heusler alloys[7], sizeable R/R might be achievable even with single-SV’s. In this work, therefore, we report on the investigation of simpler single-SV’s CPP-GMR sensors with ferromagnetic Heusler alloys in the free and reference layers to yield read heads with relatively narrow read gaps and sizeable signal levels. In particular, read heads with 45-nm magnetic trackwidth and 45nm shield-to-shield spacings have been fabricated and tested under high-density magnetic recording conditions.

Jeffrey R. Childress Hitachi San Jose Research Center 3403 Yerba Buena Rd, San Jose, CA 95135 Tel: (408) 717-5435 Fax: (408) 717-9065 E-mail: jeff.childress@hitachigst.com

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II. CPP-GMR FILM & HEAD SENSOR FABRICATION Single-SV with bottom-pinned sensor multilayers were deposited by DC magnetron sputtering. The antiparallel (AP)-coupled pinned layer structure consisted of a 7 nm-thick IrMn antiferromagnet, CoFe-based pinned layer and Heusler-alloy-based reference layer. The Heusler-alloy free layer had a magnetic thickness equivalent to 4.5nm of Ni80Fe20 and was separated from the pinned layer structure by a Cu spacer layer. A film-level CPP magnetoresistance of 5-6% for this sensor structure was measured on test devices fabricated by e-beam lithography. The magnetic properties of the Heusler based spin-valve was typical of standard head sensors films with free layer coercivity of about 5 Oe, and a coupling field of less than 20 Oe.

The read head sensor geometry was defined by a combination of optical lithography and e-beam lithography to achieve physical widths between 30nm and 60nm, as shown in Fig.1. The sensor was stabilized by CoPtCr hard magnet at the track-edges and was insulated from the hard magnet by a thin Al2O3 spacer. The final sensor height after lapping was around 50 nm, resulting in sensor resistances of 30-60 Ω.

Shield 2

Shield 1

Hard biasHard bias

Al2O3Al2O3 40 nm

Shield 2

Shield 1

Hard biasHard bias

Al2O3Al2O3 40 nm

Fig.1: SEM micrograph of the air-bearing surface (ABS) view of a completed 40nm-wide CPP-GMR head.

Fig.2: Microtrack profile of 40-nm wide CPP GMR head. The full width at half-maximum is about 45nm.

III. RECORDING RESULTS Transfer curves of suspended read heads showed the total R/R to be similar to the initial film level values of 5-6%.

Recording readback on perpendicular media showed that substantial operating bias voltages of 50-100mV could be applied before the onset of spin-torque induced instabilities, yielding signal amplitudes over 1mV (peak-to-peak) as well as head & electronics SNR around 30db for these narrow track read heads. More details of recording performance will be discussed in the full paper.

REFERENCES

1) J.R. Childress and R.E. Fontana, C.R. Physique 6 997-1012 (2005). 2) Y. Nagamine et al., Appl. Phys. Lett. 89, 162507 (2006). 3) T. Kagami et al., IEEE Trans. Magn. 42, 93-96 (2006). 4) M. Takagishi et al., IEEE Trans. Magn. 38, 2277 (2002). 5) J.R. Childress et al., IEEE Trans. Magn. 42, 2444-2446 (2006). 6) K. Nagasaka et al., Jujitsu Sci. Tech. J., 42, 149-157 (2006). 7) M. Saito et al., Digest FB-02, Intermag Asia 2005 Conference, Nagoya.

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A2

FeCo NANOCONTACT MAGNETORESISTANCE WITH CURRENT- CONFINED-PATH STRUCTURES IN CPP SPIN VALVES

M. Takagishi1, H. N. Fuke1, S. Hashiomoto1, H. Iwasaki1,

S. Kawasaki2, K. Miyake2, and M. Sahashi2 1) Corporate Research & Development Center, TOSHIBA CORPORATION,

1, Komukai Toshiba-cho, Saiwai-ku, Kawasaki 212-8582, Japan 2 ) Department of Electronic Engineering, Graduate School of Engineering, TOHOKU UNIVERSITY,

6-6-05, Aza-Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan

It is well known that current-perpendicular-to-plane giant magnetoresistance (CPP-GMR) is one of promising candidates for future high density recording, because of its lower area resistance (RA) required for high data rate recording, compared to tunneling magnetoresistance (TMR)[1]. It has been reported that CPP-GMR using current-confined-path (CCP) spin-valve (SV) structure and FeCo layers shows a high MR ratio of 7-9% at a low RA of 300-500mΩµm2[2][3]. These elements with CCP type structures require certain number of nanocontacts, because the distribution of the head resistances or some other performances becomes very wide in the case of smaller number of nanocontacts. That difficulty increases as the area density increases and as the element size decreases. Smaller nanocontact size is required in order to increase the number of nanocontact. We think domain wall MR[4][5] may be suitable to use in these high area density stage because of its higher MR ratio potential for smaller nanocontac size. In this paper, we report that FeCo nanocontact magnetoresistance with CCP structure in CPP spin valve shows a high MR ratio 10% at RA of 1-2 Ωµm2. What merit the domain wall MR has in the area density over 1Tbpsi is also discussed.

It depends on the system tolerance of HDD or performance margin of the heads how many nanocontacts are required in one

CCP type element. We estimated nanocontact size required when nanocontact number is 10 or 20pcs (Figure 1). If required element size is 30nm for area density of 1Tbpsi [6], the required nanocontact size is around 1-2 nm. In these high area density stage, domain wall MR may have the following merit, that is, it is predicted theoretically and experimentally that the smaller nanocontact size with the smaller domain wall increases MR ratio[4][5]. Figure 2 shows the MR ratio dependency on domain wall size by using the theory of reference [4]. This prediction indicates MR ratio more than 100% in 1 nm nanocontact size.

Ballistic magnetoresistance (MR) phenomena with high MR ratio above 200% were reported by using a nanocontact of the Ni nano-wires [7]. However, the ferromagnetic nanocontact MR with CPP-SV structure has not been reported yet. We have successfully achieved a stable and repeatable MR ratio of 10% at RA~1-2 Ωµm2 by ferromagnetic nanocontact MR with CPP-SV structure for the first time[8]. The CPP-SV structure was underlayer/PtMn15/CoFe3.3/Ru0.9/FeCo2.5/ Al-oxide/FeCo2.5/cappinglayer. The nano-oxide layer (NOL) of Al-oxide was formed by using ion assist oxidation (IAO) process [2]. MR performance was examined by fabricating test elements with 0.4 ~ 1µm size. A relation between MR and RA is shown in Figure 3. The relation can be classified into two groups. The open circle group with high RA shows TMR effect from R-V property, while the filled circle group shows ferromagnetic nanocontact MR of current confined path type from R-V property. It is confirmed by cross-sectional TEM observation and c-AFM analysis that the samples of the filled circle group have metallic channels below 5 nm diameter in NOL.This opens the new approach to study ferromagnetic nanocontact MR like BMR. Higher MR ratio and lower RA will be expected by realizing pure and well-controlled smaller-size ferromagnetic nanocontact structure.

Masayuki Takagishi

Corporate Research & Development Center, TOSHIBA CORPORATION, E-mail: masayuki.takagishi@toshiba.co.jp fax: +81-44-520-1802 tel: +81-44-549-2390 1, Komukai Toshiba-cho, Saiwai-ku, Kawasaki 212-8582, Japan

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REFERENCES

1) M.Takagishi, K.Koi, M.Yoshikawa, T.Funayama, H.Iwasaki and M.Sahashi, IEEE Trans Magn. 38, 2277 (2002) 2) H. Fukuzawa, H. Yuasa, S. Hashimoto, K. Koi, H. Iwasaki, M. Takagishi, Y. Tanaka and M Sahashi, IEEE Trans., Magn., 40, 2236(2004). 3) H. Fukuzawa, H. Yuasa, S. Hashimoto, H. Iwasaki and Y. Tanaka, Appl. Phys. Lett.87, 082507 (2005) 4) P. M. Levy and S. Zhang, Phys. Rev. Lett. 79, 5110 (1997) 5) Y. Ohsawa, Presented at the 2007MMM/Intermag joint conference, No. EW-08, to be published 6) H. J. Richter, A. Y. Dobin, O. Heinonen, K.Z. Gao, R. J. M. v.d. Veerdonk, R.T. Lynch, J. Xue, D. Weller, P. Asselin, M.F. Erden, and R. M. Brockie, IEEE Trans., Magn., 42, 2255(2006). 7) N. Garcia, M. Munoz and Y. –W. Zhao, Phys. Rev. Lett., 82, 2923(1999). 8) H. N. Fuke, S. Hashiomoto, M. Takagishi, H. Iwasaki, S. Kawasaki, K. Miyake and M. Sahashi, Presented at the 2007MMM/Intermag joint conference, No. HG-05, to be published

Fig.1 Relation between required nanocontact Fig.2 MR ratio and domin wall size

size and element size calculated by using reference[4] theory

Fig.3 MR ratio vs. RA(Ωµm2)

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A3

CPP-GMR HEADS WITH A CURRENT SCREEN LAYER FOR 300 Gb/in2 RECORDING

K. NAKAMOTO, H. HOSHIYA, H. KATADA, K. HOSHINO, N. YOSHIDA, H. TAKEI, M. SHIIMOTO,

M. HATATANI, and K. WATANABE Hitachi Central Research Lab., Odawara, Japan, kazuhiro.nakamoto.tx@hitachi.com

I. INTRODUCTION

A CPP-GMR head is one of the most promising candidate technologies to achieve areal densities of 300 Gb/in2 or higher, since the head resistance can be designed in an appropriate range of 50 - 200 Ω suitable for high data rate. Even with a low resistance TMR films with an RA (resistance area product) of 1 Ω µm2, sensor resistance becomes 400 Ω when the sensor size is 50 nm by 50 nm.

There are two types of CPP-GMR films: “all metallic”, and “current screen” where the spacer has a nm-thick oxide layer with controlled nano-holes which act as confined current paths. In the case of simple all metallic films, for example CoFe/Cu/CoFe/AF similar to those used in CIP-GMR heads, sensor resistance would be about 20 Ω when the size is 50 nm, which may not be a sufficiently large value compared to parasitic resistance from leads, interconnects, etc. The large sensing current necessary for a high output may also cause high head noise from the spin torque effect [1]. Thus, it is not easy to get a high enough SNR from the simple all metallic films. On the other hand, in the case of films with the current screen layer, we are able to design the sensor resistance to an appropriate value. We have previously fabricated 80-nm-wide heads with the screen layer, and confirmed reasonable values (25 – 30 dB) for the head-amp SNR [2]. We have also showed that the spin torque noise of the screen type heads can be eliminated when the peak asymmetry is within +/- 20% [3].

In this paper, we try to compare the SNR of the current screen CPP-GMR heads to that of all metallic ones. We also discuss a potential of the fabricated current screen CPP-GMR heads with 50-nm-wide.

II. EXPERIMENT We fabricated read-only CPP-GMR heads with a sensor width of 50 nm and a shield gap of 36 nm. The CPP-GMR film

has a current screen (CoFe oxide) layer in the Cu layer to form confined current paths. The MR ratio was about 4%, and the resistance-area (RA) product was 0.25 Ω µm2. A perpendicular medium was used for read-write testing. The head-to-medium spacing was about 8 nm. The positive direction of the sensing current was defined as the direction in which current flows from the pinned layer to the free layer.

III. RESULTS AND DISCUSSION Fig. 1 shows the calculated SNR of two types of the CPP-GMR heads as a function of the track width. We assumed an MR

ratio of 10% for both films, and RA of 0.25 Ω µm2 for the current screen film and 0.04 Ω µm2 for the all metallic film. The head noise is assumed to be a sum of the Johnson noise, mag-noise and spin torque noise. The spin torque noise was calculated using a micro-magnetic model. The current screen heads showed better SNR when the track width was 40 nm or wider, since the SNR of the all metallic heads was eliminated essentially by the huge spin torque noise. As is shown in Fig. 2, the magnetization configuration of the free layer is not uniform due to the large current induced field in the all metallic heads, even when the peak asymmetry is almost zero. In this case, the magnetization of the right part is anti-parallel to that of the pinned layer, and this part generates a high spin torque noise. However, the current screen heads showed negligibly small spin torque noise since the sensing current is about 1/5 of the all metallic ones, so they showed better SNR.

Kazuhiro NAKAMOTO

Central Research Lab., Hitachi, Ltd. E-mail: kazuhiro.nakamoto.tx@hitachi.com fax: +81-465-49-4811 tel: +81-465-48-1111 (ext 2403) 2880 Kozu, Odawara, Kanagawa 256-8510, Japan

17

A3

Fig. 3 shows the head-amp SNR vs. head resistance of the fabricated current screen CPP-GMR heads. The measured SNR was from 20 to 30 dB, which is quite high for a narrow track width of 50 nm. Higher MR ratio (e.g. 7%) and lower RA (e.g. 0.15) would give us higher SNR of 30 dB or more. Fig. 4 compares the measured head noise to the calculated mag-noise. The Johnson noise was subtracted from the measured noise. The FMR (ferromagnetic resonance) frequency was measured for all of the heads, and was used to calculate the mag-noise [4]. As is shown in Fig. 4, the measured noise well agreed with the calculated mag-noise. We are able to conclude that clear spin torque noise was not observed in the fabricated heads. We did not observe 1/f like noise, either. The CPP-GMR heads with a current screen layer was thus shown to be promising. Data on films and spin stand testing will be discussed in the conference.

REFERENCES

[1] N. Smith, et al., IEEE Trans. Magn., vol.41, p.2935, 2005. [2] K. Nakamoto, et al, IEEE Trans. Magn., vol.41, p.2914, 2005. [3] H. Katada, et al, IEEE Trans. Magn., vol.42, p.2450, 2006. [4] K. Klaassen, et al, IEEE Trans. Magn., vol.41, p.2307, 2005.

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Fig. 1 Calculated head and amp SNR vs. track width of the read head, where the stripe height equals to the track width.

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Fig. 2 Magnetization configuration of the free layer in the all metallic head with a track width of 80 nm.

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Fig. 3 Head and amp SNR vs. head resistance of the fabricated heads. Solid line denotes calculation with MR ratio of 4%.

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Fig. 4 Comparison of the measured noise to the calculated mag-noise. The Johnson noise was subtracted from the measured one.

18

A4

RAMPING SQUARE PULSES BREAKDOWN TEST FOR TMR HEADS

Guifu WANG, Yu CHEN, Zhaoyu TENG, Luge YIN, Kaijie ZHANG, Qiuyu HUANG, Haiting LI, Chuanfang JIANG, Ge YAN, William LI and Sidney CHOU

SAE Technologies Development (Dongguan) Co., Ltd., Guangdong, P.R. China, ge_yan@sae.com.hk

The breakdown test is a quick evaluation technique for the analysis of the failure mechanisms and the estimation of the reliability for the thin oxide. In the magnetic tunnel junctions with an ultrathin barrier, the intrinsic breakdown and the extrinsic breakdown were observed. The intrinsic breakdown was believed to occur in a well-formed oxide and was explained by the E model, which was based on the field-enhanced thermal bond-breakage[1]. The anode hole injection (1/E) model was also developed to explain the gate oxide dielectric breakdown[2]. Even though there wasn’t any indication the 1/E model was applicable to the magnetic tunnel junction, good fitting was also possible for the experimental data within a limited field interval[3]. The extrinsic breakdown was suggested to be interpreted by the pinhole enlargement in the barrier due to the thermal dissipation and/or the electric field at the pinhole[4,5]. In order to describe the breakdown voltage dependence on the voltage ramping speed for the intrinsic breakdown, a general statistical model based on E and 1/E model was developed, but only for the E model the analytical expression could be given[3]. In this paper, the TMR heads were subjected to ramping square pulses while the pulse width was same, the analytical forms for the breakdown voltage dependence on the pulse width will be gotten for both E and 1/E model, the lifetime extrapolation to the lower bias voltage for the TMR heads will also be discussed.

Following the analysis done by Oepts et al[3], if the breakdown probability density p is time independent, the fraction of failed junction at time t can be expressed as: F =1-exp(-pt). If the head fails at a specific failure probability Fs, then the time to failure (TTF) of this head can be defined as:

TTF =- ln(1-Fs)/p (1) In the E and 1/E models, p is given as:

p = A exp(V/B) (2) and

p = C exp(-D/V) (3) respectively. Where V is the breakdown voltage, A is arbitrary scale factor which depends upon materials and process, if taking into account of the acceleration effect of temperature, A can be replace by an Arrhenius factor: A0exp(-Ea/kT), where A0 is arbitrary scale factor and Ea is the activation energy for dielectric breakdown, and C, B, D are constants.

For the ramping square pulse breakdown test, if the breakdown probability density is only dependent on the voltage and independent of the voltage-time history of the heads, then the pulses width is TTF at breakdown voltage VBD. TTF is same for all the heads which was broken down at the same pulse width, so the mean TTF (MTTF) equals to TTF, and ln(MTFF) = mean ln(TTF). For E and 1/E models, from Eq.(1), the MTTF can be expressed as:

ln(MTTF) = ln(-ln(1-Fs)/A) – Mean(VBD)/B (4) and

ln(MTTF) = ln(-ln(1-Fs)/C) + D*Mean(1/VBD) (5) respectively. The equation (4) is equivalent to the equation (9) derived by W. Oepts et al in the reference 3. In our experiment, the ramping speed is ∆V/pulse width, ∆V is the ramping pulse step. Comparing Eq.(4) with W. Opets’ equation, the specific failure probability in Eq.(1) can be given by:

Fs= 1-exp(-∆V/B) (6) So, our MTTF has a little difference from W. Opets’ mean lifetime which was defined as the time at which 50% of the junctions have experienced breakdown.

Fig. 1 shows an example of the change of the normalized resistance (MRR) for TMR heads during the ramping square pulses breakdown test, both the intrinsic breakdown which showed abrupt MRR change and extrinsic breakdown which showed gradual MRR change were observed also. We set the voltage at which MRR decrease 50% as the breakdown voltage VBD, for all intrinsic breakdown, this was the dielectric breakdown voltage. For both intrinsic and extrinsic breakdown, Fig. 2 shows the plots of MTTF at 1008C against the mean VBD and mean 1/ VBD , respectively. Both E model and 1/E model could describe the intrinsic breakdown, but the extrapolated lifetimes at a low bias voltage showed large difference. At 150mV bias voltage and 50% duty cycle, the estimated Ge YAN SAE Technologies Development (Dongguan) Co., Ltd. E-mail: ge_yan@sae.com.hk Fax: +86-769-2281 1524 Tel: +86-769-2281 0033 Ext:6808 Winnerway Industrial Area, Nancheng, Dongguan City, Guangdong, P.R. China 523087.

19

A4

lifetimes were about 2.6×1016years and 2.6×1068years, respectively, it suggested that our intrinsic TMR heads have no short lifetime concern even working at as high as 1008C.

For the extrinsic breakdown, MRR showed large change prior to VBD, the structure of the barrier and barrier/electrode interface was changed, the breakdown probability density supposed to be dependent on the voltage-time history, it means that Eq. 4 and 5 are not applicable to the extrinsic breakdown. But surprisingly, the fitting for the experimental data was very well, as shown in Fig 2. The reason for this is not clear yet. Again, both models showed a large difference of the extrapolated lifetimes at lower bias voltage. At 150mV bias voltage and 50% duty cycle, the estimated lifetime was about 1.1×106years according to 1/E model while it was only about 1year according to E model.

In order to verify the reliability of those extrapolated lifetimes, constant voltage stress (CVS) was conducted at 100°C, and the TTF was defined as the time at which the MRR dropped 50%, so that the data could be compared with that of the breakdown test. For the lower constant voltage stress, the early failed heads were thought to be extrinsic failure, the intrinsic heads and part of the extrinsic heads would be survived. For the higher constant voltage stress, all the extrinsic heads would show very early breakdown, and intrinsic breakdown would come more later, and all those data for CVS were showed in Fig. 2. The CVS data for the intrinsic heads stayed on the fitting lines while all the CVS data for the extrinsic heads were upper than the fitting lines, these results indicated that above extrapolated lifetimes for the extrinsic heads were underestimated due to the accumulated MRR drop prior to VBD during the ramping pulse breakdown test.

Eq.(4) also shows the temperature acceleration effect on the breakdown, the intercept ln(-ln(1-Fs)/A) should have linear relation with 1/T according to the Arrhenius factor. Fig. 3 gives the experimental data at the temperature from 35°C to 120°C and a very good fitting could be found for both intrinsic and extrinsic breakdown.

REFERENCES [1] J. W. Mcpherson and H. C. Mogul, J. Appl. Phus. 84, 1513(1998). [2] I. C. Chen, S. E. Holland and C. Hu, IEEE Trans. Electron Devices 32, 413(1985). [3] W.Oepts and H.J.Verhagen, Journal of Applied Physics, 86, 3863 (1999) [4] Bryan Oliver, Journal of Applied Physics, 95, 1315 (2004) [5] Pak-Kin Wong, IEEE Transactions Magn. 42, 232 (2006)

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20

A5

AN ANALYSIS OF NOISE OCCURRENCE IN TMR READER DURING DRIVE RELIABILITY TEST

PAK KIN WONG, YI MEI TAM, VINCENT M. F. CHIAH and TAD SHIMIZU

SAE Magnetics (H.K.) Ltd, SAE Technology Center, 6 Science Park East Avenue, Hong Kong Science

Park, Shatin, Hong Kong, pakkinwong@sae.com.hk

I. INTRODUCTION

Tunneling MR (TMR) reader head has been widely adopted in the mass production of hard disk drives with recording density >100 Gb/in2. With AlOx tunneling barrier, failure in drive reliability test due to barrier breakdown and pinhole development is rarely reported. We have observed that the major failure mode in drive reliability test is increase in noise after a few to hundreds of hours of drive operation. After the failure, the readers were checked with quasi-static tests (QST) and were found to have noise increased, indicating degradation in reader quality. In this article, we report our analysis on the source of such reader noise, implying which part of reader is degraded. Moreover, we report our search of possible triggers in drive causing the degradation.

II. FAILURE ANALYSIS

In our production, all readers have their magnetic alignments set by a longitudinal field of 6k Oe applied along the designed direction of hard magnet (HM) magnetization. This sets the expected magnetic alignment of heads unchanged in drives. To search for the part of the reader degraded in drive reliability tests, we realign the degraded heads by a sweeping field along the HM direction, ranging from 400 Oe to 6k Oe. The response of reader during field sweeping is captured by a high field QST tester (HFQST). After each field sweeping, the reader noise is checked. We have observed that a small portion of the failure population have reader noise eliminated after such field sweeping, implying a non-permanent distortion of magnetic alignments causing the noise. In such cases, the magnitude of the sweeping field needed to recover the failed heads from noise falls between the saturation of the reader shields and that of the HM. The reader response captured by the HFQST during field sweeping suggests a distortion of HM magnetization. The possible causes of HM distortion in drives will be discussed

21

A5 In most of the failed readers, noise cannot be eliminated by the sweeping field. We have applied field in HM direction of increasing magnitude to check at what field magnitude the noise can be suppressed. We have found that the field required to suppress the noise falls between the field of reader shield saturation and HM saturation. After removing the field, the noise comes back. We conclude that the noise comes from the degradation of HM property, but in this case, it is not a non-permanent distortion in HM. To search for the reason of HM degradation, we put the failed heads at elevated temperature (140C) and observed a reduction in noise level, and in many cases, the noise is eliminated. Firstly, this indicates that the noise is not resulted from a degradation of HM remanence with thermal energy. Secondly, the recovery from noise hints a link between the noise and the mechanical stress which can possibly be relaxed or changed at elevated temperature. We have further investigated the effect of stress on the noisy heads. Mechanical deformations on the heads surface covering the whole reader is made by nano-indentation technique with a round-topped tip of 5um diameter. The deformation depth ranges from 3~6 nm, about 5% of the reader strip height. After such deformation, the noise level is significantly lowered and in most cases, the noise level comes down to be same as normal readers. The investigation is followed by a serious of studies with ion milling (~4nm depth removal) and head-media touch-down, for the effect of surface quality.

III. CONCLUSIONS We conclude that the noise occurred in drive reliability test is likely caused by a modification of surface stress and morphology of the readers, instead of the intrinsic degradation of the HM. Detailed results of the studies and a discussion on the possible mechanism of surface stress and morphology change in drive will be made in the article.

PAK KIN WONG SAE Magnetics (H.K.) Ltd. Email: pakkinwong@sae.com.hk fax: (852)-2480-4757 tel: (852)-2612-8442 SAE Technology Center, 6 Science Park East Avenue, Hong Kong Science Park, Shatin, Hong Kong Preferred category: #

22

A6 Anti-static Robustness Enhancement and High Frequency Noise Pickup Immunity by

Internal Shunting on Tunneling Magnetoresistive Sensor

Anthony Wai Yuen LAI1, Eric Cheuk Wing LEUNG1, Pak Kin WONG1, Tad SHIMIZU1 , Takeo KAGAMI2 and Moris DOVEK3

1) SAE Magnetics (HK) Ltd, Hong Kong, Anthony_lai@sae.com.hk 2) TDK Corporation, Nagano, Japan, tkagmi@mb1.tdk.co.jp

3) Headway Technologies, Inc, Milpitus, US, Moris.Dovek@headway.com

I. ABSTRACT Tunneling magnetoresistive (TMR) head are promising device for high storage density of 100Gbit/in magnetic recording head1. Due to ultra thin barrier quality, very low dielectric breakdown voltage of insulating barrier and conductive path in insulating barrier provided by presence of pinholes is a concern on TMR sensor anti-static robustness. Many reports show that TMR sensor performance will be degraded2-4 by electrostatic discharge (ESD). Internal shunting is an option to improve TMR sensor anti-static robustness for better reliability. In addition, we have observed external noise current which may come from media or system ground being pickup by TMR sensor. Avoid noise injection into TMR sensor is very difficult. In this paper, we will introduce how to minimize external high frequency noise current pickup by internal shunting design and grounding system.

II. Anti-static robustness of Internal shunted TMR sensor In TMR sensor, there are a lot of capacitors around the sensor which can accumulate charge and so sensor will be damaged during discharge.(Fig.1) Sensor resistance and output will drop if charging voltage on head is higher enough. (Fig.2) Internal shunted TMR sensor is with two high resistance resistors which are connected to both top shield and bottom shield to minimize the capacitance between writer shield-to-top shield and substrate-to-bottom shield respectively.(Fig.3) Then charge can be drained out thru shunting resistor to substrate and then suspension ground or system ground. Due to charge no longer accumulate around sensor, no discharge current will be induced with probing on reader pad by small resistance path connect. Anti-static robustness of TMR sensor can be improved. For the ESD direct charged device model (DCDM) event of TMR sensor with internal shunting, even charging voltage up to 20V, head resistance and output do not change. (Fig.4) Comparing with TMR sensor without internal shunting, ESD threshold voltage can be enhanced more than 10 times. So less latent damage can be expected in TMR sensor with internal shunting due to ESD event in production line.

III. Noise Immunity by Internal shunted If noise frequency is higher enough, noise current from substrate can be injected into TMR sensor due to different level of coupling by top and bottom shield.(Fig.5) Low shunting resistance from substrate to writer shield is used to shunt part of noise current to writer shield. If capacitance between writer shield-to-top shield and substrate-to-bottom shield is same, noise injection on both top shield and bottom shield will be same amplitude and phase. Therefore noise signal is compensated by the differential read back signal.(Fig.6) In order to further enhance high frequency noise immunity by internal shunting, grounded substrate is recommended. Anthony Wai Yuen, LAI

SAE Magnetics (HK) Ltd E-mail: anthony_lai@sae.com.hk fax: +852-2480-4757 tel: +852-2612-8669 SAE Technology Centre, 6 Science Park East Avenue, Hong Kong Science Park, Shatin, N.T., Hong Kong

23

A6 REFERENCES [1] K. Shimazawa et al., Appl. Phys. Lett. 73, 2363, (1998). [2] A. Wallash et al., EOS/ESD Symposium Proceedings, 470, (2000). [3] L.Baril, IEEE Trans. Magn., 38, 2283, (2002). [4] Z.Y.Teng et al., EOS/ESD Symposium Proceedings, 346, (2004).

Fig.1 Schematic diagram of TMR sensor

ESD (DCDM) Threshold Voltage (V)S

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Fig.3 Schematic diagram of TMR sensor with internal shunting

Fig.5 Noise Spectrum of TMR sensor

Fig.4 ESD DCDM profile for TMR sensor with internal shunting

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24

B1

A Study of Media Dependence of Shielded Perpendicular Write Head Design Optimization

Lijie GUAN1, Tatsuya SHIMIZU2, Joe SMYTH1, Moris DOVEK1, Yue LIU1, Kenichi TAKANO1

1) Headway Technologies, Inc., 678 S. Hillview Drive, Milpitas, CA 95138, USA 2) SAE Magnetics (H.K.) Ltd, 6 Science Park East Ave, Hong Kong, China

I. INTRODUCTION

Head-media integration has been increasingly important for improving PMR recording density. A double layer PMR media with soft magnetic underlayer (SUL) is essentially a component of the recording head. In spite of the different recording geometry arrangement than longitudinal recording, the fundamental requirements for PMR writer design remain the same: provide sufficient writability and good field gradient at the correct track pitch. In today’s commercial PMR products, trailing shield PMR writer design has been widely used. In this work, Finite Element Analysis (FEA) and experimental study are used to investigate media dependence of two shielded PMR designs: double coil and single coil.

II. MODELING AND EXPERIMENTS

For double coil design, the current fields in read/write shields are canceled, while they are not cancelled for single coil design. Therefore, there is more flux flow from the shields to SUL for single coil design. If SUL thickness is thin or saturation Bs is low, SUL can be partially saturated. Fig. 1 shows the perpendicular field Hy, in-plane field Hx, and field magnitude |H|, as function of write current Iw for single coil and double coil designs. SUL with Bs = 16 kOe and thickness of 50nm is assumed. At low current, the field components of both designs are almost identical. With further increasing current, single coil design shows a decrease of perpendicular field and an increase of in-plane field, as compared to double coil design, which improves field gradient with a tradeoff with less field magnitude. The current dependence of two designs strongly depends on the SUL properties and will be discussed in details. Both single coil and double coil are fabricated on the same wafer with similar dimensions of write pole and trailing shield. Spin-stand dynamic performance (DP) tests are done on two different media. A brief summary of media’s H-M loop properties is listed in Table I. To understand the performance for different disk/media combination, reverse DC noise measurement is carried out. Fig. 2 shows a typical result of noise profile as a function of sweeping current. The write head used here has a physical width of 1.5um. In this case, the head field is large enough to fully saturate the media and the noise floor is equal head system noise. This is confirmed by measuring noise amplitude on a non-magnetic disk. The obtained noise amplitude matches the floor of reverse DC noise. The curve shown in Fig. 2 is basically the derivative of dynamic ‘H-M loop’, where the write current at noise onset/peak/fall locations correspond to nucleation field Hn, corercity Hc, and saturation field Hs, respectively.

Ljiie Guan, Headway Technologies, Inc. E-mail: Lijie.guan@headway.com fax: 408-934-5353 tel: 408-934-3222 678 S. Hillview Drive, Milpitas, CA95035, USA

Fig. 1 Iw dependence of single coil and double coil Fig. 2 Reverse DC noise on a generic magnetic media and a non-magnetic media.

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III. RESULTS AND DISCUSSIONS

Parametrics of spin-stand DP testing results are listed in Table II. Write current is fixed at 30mA. While double coil performs similarly on both media, single coil shows 0.7dB better SNR on media A and 0.7dB lower SNR on media B, as compared to double coil. From the magnetic properties listed in Table I alone, it is not possible to explain such performance difference. In fact, the measured MWW suggests media A has slightly higher Hc than media B, opposite to Hc values in Table I.

The reverse DC noise profiles of two media are measured with wide track width head and are shown in Fig. 3. It can be seen that media A has larger Hn and Hc, but smaller Hs than media B, indicating larger squareness of the dynamic H-M loop. Media A also has lower noise peak than media B. Without knowing the details of the media microstructures, media A is conjectured to have stronger inter-granular exchange coupling.

We also measured the reverse DC noise with single coil and double coil samples used in DP testing. The results are plotted in Fig 4. A previous study on reverse DC noise had found good correlation between noise peak and SNR performance [1]. In our case, it can be seen that single coil reduces noise peak consistently on both media, which indicates field gradient improvements by single coil. It is also worthwhile to note that there is more reduction of noise peak by single coil on media A than on media B, possibly due to different inter-granular exchange coupling [2].

To explain the SNR dependence on media, the tradeoff between writability and field gradient needs to be considered. The level of saturated reverse DC noise agrees with tested OVW for the head/media combinations. On both media, single coil shows poorer writability than double coil. For media A with smaller Hs, both single coil and double coil have reasonably good writability. In this case, single coil has better SNR, due to better field gradient. For media B with larger Hs, the writability requirement is tougher. As OVW becomes marginal, the tradeoff between field gradient and writability favors the latter. In this case, single coil shows poor SNR.

The simplicity of single coil design may have additional advantage in head fabrication and in head-media integration. However, one potential issue with single coil design is wide range adjacent erasure (WATE). A new structure of single coil write shield design for WATE improvement will be discussed in the article.

REFERENCES

[1] Y. Sonobe, N. Supper, K. Takano, K. Yen, H. Do, H. Muraoka, and Y. Nakamura, “Reverse DC erase medium noise analysis on exchange-coupling effect in coupled granular/continuous perpendicular recording media”, J. Appl. Phys., 93, 7855(2003) [2] E. N. Abarra, P. Gill, B. R. Acharya, J. Zhou, M. Zheng, G. Choe, and B. Demczyk, “Bulk AC-Erasure Technique for Perpendicular Recording Media: Effect of Exchange Coupling”, IEEE Trans. Magn. 41, 3127 (2005)

Table I Magnetic disk properties of tested media Table II. Summary of DP results of single coil and double coil.

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Fig. 3 Reverse DC noise of testing media using wide track width head.

Fig. 4 reverse DC noise of testing media using DP tested single coil and double coil heads.

26

B2

DYNAMICS IN INTEGRATED WRITE-READ HEADS

Thomas SCHREFL1, Alexander GONCHAROV1, Manfred SCHABES2, Gino HRKAC1, Simon BANCE1, Otmar ERTL3, and Dieter SUESS3

1) University of Sheffield, Sheffield, UK, t.schrefl@sheffield.ac.uk 2) Hitachi Global Storage Technologies, San Jose, CA, USA, Manfred.Schabes@HitachiGST.com

3) Vienna University of Technology, Vienna, Austria, suess@magnet.atp.tuwien.ac.at

I. MICROMAGNETIC AND NUMERICAL BACKGROUND

Multiscale finite element micromagnetics resolve the dynamic magnetization processes in write-reads heads for perpendicular recording. The Landau-Lifshitz equation is solved simultaneously with the quasi-static Maxwell equations taking into account non-uniform drive currents as well as eddy currents. The total effective field in the yoke is augmented by the magnetic field generated by the time dependent coil current and by the magnetic field arising from eddy currents. The magnetic fields are calculated from a magnetic vector potential [1] using hybrid finite element boundary method [2] that is accelerated using hierarchical matrices [3]. This novel combination of different methods enables the full micromagnetic simulation of an integrated write-read head consisting of the coil, the yoke, the main pole, the return pole, the soft underlayer (SUL), the GMR read sensor, and the shields of the reader. A graded finite element mesh is used in order to resolve the magnetization distribution at a length of 5 nm in the write pole, in the SUL below the write pole, and in the read sensor stack. Fig. 1 shows the finite element model of the write-read head. Fig. 2 gives the flux closure state in the shields of the reader.

II. RESULTS

The write field rise time of single pole heads will be discussed as function of pole tip shape, Gilbert damping, exchange stiffness, and conductivity. The reversal speed of the magnetization in pole tip determines the head field rise time. Fig. 3 compares the write current and the write field as a function of time. The delay between zero crossing of the current and reaching the maximum write field is about 0.8 ns. The time profile of the write field is governed by two characteristic time scales: (1) reversal of the pole tip by vortex motion and (2) saturation of the pole tip and alignment of the SUL magnetization. Fig. 4 shows the pole tip magnetization (top) and the corresponding write field (bottom) 0.3 ns, 0.65 ns, and 0.8 ns after zero crossing of the current. The pole tip reversal occurs by vortex motion. After annihilation of the vortex an end domain which reduces the surface charges remains for about 0.2 ns. Finally, the maximum write field of 1.2 T is reached. Tapering the pole tip decreases the time required to develop a certain field gradient by more than one half. The write field is the superposition of the magnetostatic field generated by the head magnetization and magnetostatic field from the soft underlayer (SUL) magnetization. In conventional perpendicular media the spacing between the media and SUL can be optimized for most effective media switching by increasing the angle between applied head-field and media magnetization. A moderate magneto-crystalline anisotropy in the SUL reduces the domain wall width which leads to a well defined magnetization pattern in the SUL. Therefore a tailored magnetocrystalline anisotropy in the SUL can significantly increase the write field gradient. Eddy currents increase the effective Gilbert damping. The effective damping constant is proportional to the σL2, where σ and L are the conductivity and the extension of the soft magnetic yoke, respectively.

Write currents and magnetization processes in the yoke and the soft underlayer generates magnetic fields that considerably change the magnetization configuration of the magneto-resistive reader stack. This interaction is of concern for reader stability. Furthermore the required delay between writing and reading is affected by the time needed for the magnetization in the reader to relax to its equilibrium state. The readback signal is calculated micromagnetically. The self-consistent scheme takes into account the change of the read current density and the Oersted field due to the change of the local resistivity of the sensor elements.

27

B2

REFERENCES

1) S. Kurz, J. Fetzer, G. Lehner, W. M. Rucker, "A novel formulation for 3D eddy current problems with moving bodies using a Lagrangian description and BEM-FEM couping," IEEE Trans. Magn.. 34, 3068-3073, (1998).

2) D. R. Fredkin and T. R. Koehler, "Hybrid Method for Computing Demagnetizing Fields," IEEE Trans. Magn. 26, 415-417, 1990.

3) L. Grasedyck and W. Hackbusch, "Construction and arithmetics of H-matrices," Computing 70, 295-334, 2003.

Fig. 1. Finite element model of an integrated write-read head.

Fig. 2. Magnetization distribution in the reader at zero write current and zero read current.

Fig. 3. The typical time to develop the maximum head field is about 0.8 ns. The field rise time is limited by the gyromagnetic precession of the magnetization.

Fig. 4. Pole tip magnetization and perpendicular write field as function of time.

Fig. 5. Different write pole shapes. Fig. 6. Contour plot of the perpendicular write field, which is

generated from the magnetic charges is the pole tip and from magnetic charges in the SUL.

Thomas SCHREFL University of Sheffield, Dept. of Engineering MaterialsE-mail: t.schrefl@sheffield.ac.uk fax: +44-114-222-5943 tel: +44-114-222-5965 Sir Robert Hadfield Building, Mappin Street, Sheffield, S1 3JD, UK

28

B3

Mark KIEF 1, Venkat INTURI 1, Mourad BENAKLI 2, Ibro TABAKOVIC 1, Ming SUN 1, Olle HEINONEN

1, Steve RIEMER 1, Vladyslav VAS’KO 1 1) Recording Head Operations, Seagate Technology, Minneapolis, MN 55435

2) Seagate Research Center, Seagate Technology, Pittsburgh, PA 15222

I. ABSTRACT

Advanced perpendicular writers continue to demand maximum write fields, fast rise times at ever vanishing head-media spacing and strict reliability standards. This means that the asymptotic progression to a 2.4T pole with nearly ideal magnetic response continues. At the same time we must control critical pole dimensions, fabricate at a reasonable cost while protecting against corrosion and erasure risks. We will review progress made to meet these challenges in a discussion of high moment materials utilizing electroplating and sputter deposition for single layer films and laminates. Concerns for corrosion will be assessed and minimized by controls on key contaminants. Micromagnetic modeling will be used to study the phenomenology and expected performance impacts of these various materials and structures. Results will be used to provide a better insight into the potential materials/design trade-offs that must be made. In conclusion, performance and reliability will be assessed through head electrical testing.

II. DISCUSSION

It is generally understood that the magnetic properties of polycrystalline thin films are strongly dependent upon the microstructure and grain size. High moment compositions of FeCo alloys are no exception to this rule. FeCo35-40 are particularly important alloys since they exhibit the highest known saturation magnetization. The importance of grain size can qualitatively be explained as arising from the exchange averaging of local anisotropies when the grain size is well below the magnetic exchange length. We will briefly review the origin of these phenomena then demonstrate how it can be applied to the case of high saturation magnetization writer poles. We will show the resulting quasi-static and dynamic magnetic properties of sputtered and electroplated FeCo alloy materials.

Although high saturation magnetization with low coercivity and soft magnetics are desirable for the main pole material, these are not sufficient. The small dimensions, ≤ 200 nm, of the main pole and the close proximity of the media SUL can produce conditions favorable for a vortex magnetization state and perpendicular remanence (i.e. in the direction out of the ABS). These conditions may impede with the high speed switching behavior of the pole and can cause on-track erasure of recorded data. One solution to this problem is to control the main pole remanence by introduction of magnetic/ nonmagnetic laminations in the main pole. These laminations can effectively utilize the demagnetization energy to control remanence rather than contribute to its cause. We further show how the laminations can also facilitate material grain size and texture control to provide low coercivity, soft magnetic materials for writer pole applications. Figures 1 and 2 illustrate the microstructural and resulting magnetic properties for both sputtered and electroplated FeCo and laminated FeCo materials. This is the first demonstration that the lamination approach can be applied to electroplated materials as well as vacuum deposited materials. Another important reliability concern, in addition to erasure, is corrosion of the FeCo materials at the air-bearing surface. We will show that these corrosion properties can be significantly improved by the proper control of material preparation and composition.

High Magnetic Saturation Poles for Advanced Perpendicular Writers

Mark KIEF Recording Head Operations, Seagate TechnologyE-mail: Mark.T.Kief@Seagate.Com fax: 952-402-8349 tel: 952-402-7842 7801 Computer Ave, Minneapolis, MN, USA 55435

29

B3 To better understand the role and limitations of laminate materials, we apply a simple energetic model. This

model can provide insight into the laminate layer thickness requirements and the key importance of top pole width to erasure control. We then examine a more accurate micromagnetic simulation of the remanent state and switching behavior. In particular the effect of the exchange coupling mediated by the lamination was studied using large-scale micromagnetic simulation. It has been reported in the literature, and indeed it is common practice in current commercial perpendicular writers, to use an antiferromagnetic coupling (AFC) in order to control the remanent state of the writer pole tip. A sufficiently strong AFC forces the poletip into a scissor-like remanent state, in which the magnetization in consecutive layers is anti-parallel and largely in the ABS plane. Such a state has low magnetic charge density on the ABS and therefore smaller stray fields that the vortex state that is common with no or ferromagnetic lamination. However, a concern is that a strong AFC will make it more difficult to saturate the top pole and the available write field will suffer, as a consequence. In addition, the field rise time may be affected by the strength of the coupling. We will report the effects of exchange coupling strengths mediated by the laminates from +1.0 to –5.0 erg/cm2 and the resulting impact upon writer pole efficiency, rise time and remanence.

In conclusion, these materials and concepts presented will be evaluated by head performance and erasure testing.

Fig. 1 TEM and B(H) Loops for Sputtered FeCo with seedlayer and with laminations Fig. 2 TEM and B(H) Loops for Electroplated FeCo with seedlayer and with laminations

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30

B4

EXACT SOLUTION OF MAGNETIC FIELD AND SPECTRAL RESPONSE FUNCTION FOR READ HEADS IN PERPENDICULAR RECORDING

Z. J. LIU

Data Storage Institute, Singapore, dsiliuzj@dsi.a-star.edu.sg

I. DIGEST

This paper discussed the playback performance of perpendicular magnetic recording (PMR) systems, in particular the solution of the read sensor sensitivity field, the spectral response function and the effects of various parameters of head-medium combinations. Quantitative investigation of the playback process may be carried out using finite element methods (FEM) by solving the Maxwell equations numerically. Results obtained using numerical analyses were reported in the literature [1,2]. Though, the numerical methods are not very effective to gain insight into the interdependence of the read sensor characteristics and the various recording system parameters [3], and they also demand considerable computing power when playback waveforms resulted from a large number of recorded transitions need to be constructed. In the past, two dimensional (2D) analytical models [4,5] were developed for theoretical understanding of the playback physics, and three dimensional solutions were also reported recently [6,7]. The limitations of 2D solutions due to the flux paths in the cross-track direction were noted by several researchers [e.g. 1]. In addition, three dimensional modeling is required for studying some other effects, for example, the influence of mechanical disturbances on the positioning of the read sensor and thus the playback waveforms.

In this paper, an analytical solution of 2D magnetic field for perpendicular read heads is presented. The magnetic scalar potential of the field is expressed in form of Fourier series, i.e. using sinusoidal base functions, such that it can be conveniently applied in both time and frequency domain analysis. The method is then extended to solve the 3D head sensitivity field and the results are verified using FEM simulations. The boundary value problem being solved includes the following effects: the softmagnetic underlayer (SUL) with finite permeability, the recoding medium with non-unity relative permeability, and the spacing between the medium layer and SUL, in addition to the other read head parameters. The magnetic field distribution in all sub-regions including the medium layer, softmagnetic underlayer and the shield gaps can be obtained. This is in contrast to the previously available solutions in that the effect of SUL is considered by introducing an magnetic image of the reader head (equivalent to assuming infinitely large permeability of the SUL), and thus the image of the magnetization distribution in the medium layer when calculating the response to given recorded patterns. As the calculation of the Fourier coefficients are not obtained by using numerical approximations, for example the numerical inversion of a conformal mapping solution or Fourier integrals, the field solution in the region near the air-bearing surface (ABS) is more reliable when compared to the previously available analytical models [4-6] (which may provide approximations of the Fourier coefficients up to some harmonic orders). The spectral response function is calculated by applying Fourier transform of the field intensity at the read sensor ABS. The playback profile in response to the recorded transitions in the medium layer is evaluated using the reciprocity principal. Z. J.LIU Data Storage Institute, Singapore E-mail: dsiliuzj@dsi.a-star.edu.sg fax: +65-67771349 tel: +65-68748510 5, Engineering Drive 1, National University of Singapore, Singapore 117608

31

B4

Fig. 1 shows the model of the read sensor of symmetrical structure. The origin of the coordinates is set at the center of the sensor ABS. It is shown that the magnetic medium spacing and the medium permeability values affect the scalar potential distribution at the ABS which in turn impact on spectral response function of the read head. The predicted effects agree with those reported in the literature. The roll-off curves computed under the condition of idealized transition of magnetization show that the SUL boosts the playback amplitudes at low frequency signals. In Fig. 2, the influence of the shield-to-shield spacing length on the roll-off property of the read sensor is illustrated. The output of the read sensor is normalized to the value corresponding to the case when the shield-to-shield spacing is 30 nm. For the given setting of the read sensor parameters, the output amplitude decreases as the shield-to-shield spacing decreases, but in general, the output amplitude decays faster when the shield-to-shield spacing is large. More results will be given and discussed in the full paper.

REFERENCES

1) M. K. Bhattacharyya, G. J. Tarnopolsky, and L. T. Tran, 3D analysis of MR readback on perpendicular medium, IEEE Trans Magn,27, 6, 4707, (1991).

2) T. A. Roscamp, E. D. Boerner, and G. J. Parker, Three-dimensional modeling of perpendicular reading with a soft underlayer, Journal of Applied Physics, 91, 10, 8366, (2002).

3) D. Litvinov, and S. Khizroev, Perpendicular magnetic recording: playback, Journal of Applied Physics, 97, 7, 1101, (2005).

4) E. Champion, and H. N. Bertram, The effect of MR head geometry on playback pulse shape and spectra, IEEE TRANS MAGN, 31, 4, 2461 (1995)

5) D. T. Wilton, H. A. Shute, and D. J. Mapps, Accurate approximation of fields and spectral response functions for perpendicular recording heads, IEEE TRANS MAGN, 35, 4, 2172 (1999).

6) Y. Suzuki, and Y. Nishida, “Exact calculation method for medium field from a perpendicular medium”, IEEE Trans. Magn. 39, 5, 2633-2635, (2003).

7) H. A. Shute, D. T. Wilton, D. M. McKirdy, P. M. Jermey, and J. C. Mallinson, Analytic Three-Dimensional Response Function of a Double-Shielded Magnetoresistive or Giant Magnetoresistive Perpendicular Head, IEEE TRANS MAGN, 42, 5, 1661, (2006).

Fig. 1 Schematic view of read sensor geometry Fig.2 Roll-off curves vs. shield-shield gap length

shield

shield

x

y

z

Sensor element

SUL Spacing

Medium Magnetization

32

B5

Heat Assisted Magnetic Recording for Continued Scaling of Areal Density

Michael A. SEIGLER, William A. CHALLENER, Edward GAGE, Ganping JU, Bin LU, Kalman PELHOS, Chubing PENG, Robert E. ROTTMAYER, Xiaomin YANG, Hua ZHOU, Tim RAUSCH

Seagate Research Center, 1251 Waterfront Place, Pittsburgh, Pennsylvania, USA 15222

I. DISCUSSION

One of the difficulties in magnetic recording is balancing the media signal-to-noise, thermal stability and writability. Scaling the areal density, while maintaining a proper balance between these three parameters, will require an alternative technology. One potential technology is Heat Assisted Magnetic Recording (HAMR). HAMR uses heat to decrease the intrinsic magnetic properties, such as the magnetic anisotropy and saturation magnetization, to nearly zero [1]. HAMR heats the media to a temperature where the coercivity is below the magnetic field applied by the write head. The heated region is then rapidly cooled to ambient temperature while the head field is applied. As long as the head field is larger than the local demagnetization fields from the nearby media, the magnetization of the media grains will be oriented in the direction of the applied head field. A sketch illustrating the HAMR writing process is shown in Fig. 1(a). There are three major challenges for the HAMR head design and process: 1) Apply a large magnetic field confined to a spatially small area; 2) Form an intense and spatially small optical spot on the media; 3) Integration of the magnetic and optical field delivery systems into one head with a reader. The first challenge can be addressed with a magnetic recording head field delivery system very similar to today’s magnetic recording writer, see Fig. 1(b). The second challenge can be addressed using a Planar Solid Immersion Mirror (PSIM) to form a diffraction limited focal spot, see Fig. 1(c) [1-5]. The PSIM consists of a planar waveguide (WG), which is a high index of refraction (n) layer sandwiched between two low n layers. The WG is then patterned into the shape of a parabola and gratings are formed in the WG to couple light from a laser into the WG. When the light strikes the edge of the parabola, the light is reflected and focused at the focal point of the parabola. The width of the spot in the plane of the WG determines the data track width. If alumina (n~1.67) and tantala (n~2.25) are used for the cladding and core layers respectively, an NA of ~1.9 and spot width of ~λ / 4 can be achieved. Since the NA > 1, the high spatial frequency components of the light that gives the small spot, do not propagate in air. Therefore, the PSIM needs to be held in close proximity to the media so that the evanescent waves can couple from the PSIM to the media before they decay. This can be achieved with the standard magnetic recording slider that flies above the media and keeps the head-to-media spacing < 30nm. The third challenge is difficult, due to the generalities that good magnetic materials are poor optical materials, good optical materials are non-magnetic. Fig. 1(b & c) show a proposed design for integrating the magnetic writer and PSIM

Coe

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Coils WG Core WG Cladding Magnetic Poles Substrate

(a) (b) (c) Fig. 1. Diagram showing the HAMR writing process. The laser heats the media to a temperature where the media coercivity is lower than the magnetic field applied by the write head. The media is then allowed to quickly cool while the field is still applied.(b) Cross-sectional and (c) top down diagrams of a HAMR head that combines a planar solid immersion mirror (PSIM) with an input coupling grating and a magnetic recording ring head [4].

Corresponding author: Mike A. Seigler Seagate Technology LLC, Seagate Research Center E-mail: mike.a.seigler@seagate.com fax: +81-22-217-5496 tel: +81-22-217-5494 1251 Waterfront Place, Pittsburgh, PA 15222

33

B5 This asymmetric writer allows for the magnetic field to be applied to the media where it is being heated, yet the pole is not in close proximity to the WG core for a very long distance. If certain material and design parameters are assumed, such as standard optical properties for the alumina, tantala and CoFe alloy pole, a core thickness of 100 nm, λ=488nm, and either a TE or TM mode, the WG has a loss of <1 dB/cm when the pole is >1µm from the core and a loss of 1000’s of dB/cm when the pole is <100 nm from the core. Thus, it is very important to keep the magnetic pole material away from the WG core whenever possible. In order for the light to propagate from the grating coupler to the ABS without losing too much optical power, the k of the WG materials needs to be <10-4. Large n materials (core & cladding) can be used to decrease the lateral spot size, and a small n cladding or large n core can be used to reduce the down track optical spot size. Thousands of HAMR heads as shown in Fig. 1(b & c) were fabricated using standard wafer processing similar to that used to build magnetic recording heads, except for the processes used for the WG materials. Some of these heads were then built into sliders and lapped such that the focal point of the PSIM was located at the ABS. Fig. 2(a) shows an SEM image of the ABS of one of the heads. These sliders were then fabricated into HGAs. 488 nm light was coupled into the PSIM via the grating coupler, and the focal spot width (in the cross-track direction) was measured using a Scanning Near Field Optical Microscope. The central spot width was found to have a full width at the half maximum of 124 nm, see Fig. 2(b). Modeling and HAMR spin-stand testing of optical only [5] and integrated HAMR heads will be discussed further during the presentation. To achieve a spot size smaller than the diffraction limited spot formed by the PSIM, a near-field transducer using surface plasmon resonance may be employed. Some near-field transducer designs and their projected performance and processability will be discussed during the talk.

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Fig. 2. (a) SEM image of the ABS of a HAMR head. (b) SNOM image of the ABS of a HAMR head.

III. CONCLUSIONS

The reason for an alternative magnetic recording scheme was introduced, along with the HAMR recording concept. The challenges for designing a HAMR head were discussed. A fully integrated HAMR head design was introduced, and an ABS SEM and SNOM characterization was shown from a head that was fabricated. These heads were modeled and also tested on a HAMR spin-stand, and these results will be discussed further during the presentation.

REFERENCES

[1] R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, “Heat-Assisted Magnetic Recording,” IEEE Trans. Magn. Vol. 42, No. 10, (2006)

[2] W. Challener, C. Mihalcea, C. Peng, and K. Pelhos, “Miniature planar solid immersion mirror with focused spot less than a quarter wavelength,” Opt. Exp., vol. 13, no. 18, pp. 7189–7197, (2005).

[3] C. Mihalcea, K. Pelhos, T. Rausch, C. Peng, W. A. Challener, E. Gage, K. Mountfield, and M. A. Seigler, “Fabrication of dielectric optical waveguides on AlTiC sliders for heat assisted magnetic recording,” Proc. of SPIE, Vol. 5380, Optical Data Storage 2004, pp. 34-39 (2004).

[4] M. A. Seigler, T. W. Clinton, M. W. Covington, and C. D. Mihalcea, “Data writing with plasmon resonator,” US Patent Application 20050289577 [5] T. Rausch, C. D. Mihalcea, K. Pelhos, C. Peng, E. C. Gage, K. Mountfield, M. A. Seigler, and W. A. Challener, “Spin stand characterization of dielectric

optical waveguides fabricated on AlTiC sliders for heat assisted magnetic recording,” Proc. of SPIE, Vol. 5380, Optical Data Storage 2004, pp. 40-46 (2004).

34

B6

Microwave Assisted Magnetic Recording (MAMR)

Jian-Gang (Jimmy) Zhu and Xiaochun Zhu Data Storage Systems Center, Carnegie Mellon University, jzhu@ece.cmu.edu

I. INTRODUCTION

In this paper, we present a micromagnetic analysis of the microwave assisted magnetic recording scheme that enables recording at a recording field significantly below medium coercivity. The scheme utilizes a high frequency ac field, applied transversely to the magnetic easy axis of the medium grain, in addition to the recording head field. If the frequency of ac field matches the ferromagnetic resonance frequency of the magnetic grain in the recording medium, the amplitude of the magnetization gyromagnetic motion would increases rapidly, leading to a magnetization reversal at the recording head fields significantly below the normal switching fields of the medium grains. This scheme enables recording with write field significantly below medium coercivity. To generate the ac field, an oscillator structure utilizing spin momentum transfer (SMT) is proposed. Micromagnetic modeling with inclusion of SMT shows that the generated ac field can reach frequency 40 GHz or higher with amplitude at order of thousands of oersteds.

II. MODELING AND RESULTS

The magnetic switching of a cubic shaped grain of a size 6 x 6 x 6 nm3 is modeled via micromagnetic simulation. Cubic mesh cells with each cell size 1 x 1 x 1 nm3 are used for the modeling. The Gilbert gyromagnetic equation

(1)

is converted into the Landau-Lifshitz equation form before solved numerically, where γ is the electron spin gyromagnetic coefficient and α is the damping constant. Throughout the paper, α=0.02 is used unless mentioned otherwise. A variable order and variable time step method is used for the dynamic equation integration with maximum time step not exceeding one picosecond. The magnetic grain is assumed to have a uniaxial anisotropy with the anisotropy energy constant K = 9x106 erg/cm3 and the easy axis is along one of the cube edges. The saturation magnetization of the grain is assumed to be Ms=900 emu/cm3. The ac transverse magnetic field is applied orthogonal to the easy axis and its frequency is varied. The magnetic field for reversing the magnetization of the grain, referred to as reversal field, is a single pulse field with a pulse duration 1 ns and a rise time 0.2 ns. For all the results presented in this paper, the initial magnetization orientation is at 10o angle with respect to the easy axis and along the initial direction of the ac field.

Figure 1 shows the trajectory of the volume averaged magnetization of the grain during a magnetization reversal with the presence of a continuous ac transverse field of an amplitude Hac=0.1Hk and an angular frequency ω=0.34γHk. The reversal dc field Either without the presence of the ac transverse field, or the ac field is at a significantly different frequency, the observed reversal will not occur. Obviously, this resonance assisted magnetization reversal is a strong function of the medium damping constant α. A sufficiently small damping constant is necessary for the reversal below medium coercivity. Figure 2 shows the calculated reversal field threshold as a function of the ac transverse field angular frequency for three different directions of the reversal field. As the reversal field angle with respect to the easy axis increases from 2o to 30o, the minimum reversal field threshold decreases from 0.43Hk to 0.17Hk. In the figure, the symbols are actual calculation results and the solid curves are the results of five-point average smooth.

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35

Fig. 3. A schematic drawing of the spin torque driven oscillator with the field generating layer made of FeCo high moment material and having a thickness of 10nm. The picture on the right shows the trajectory of the magnetization in FGL and the perpendicular anisotropy layer.

Fig. 1 Magnetization trajectory during a magnetization reversal with the reversal field significantly below the normal switching field threshold .

Fig. 2. Switching field with an ac transverse field as a function of the ac field frequency.

Fig. 4. The frequency of spin torque driven ac magnetic field as a function of injected current level for a oscillator with lateral dimension 35nm x 35 nm. The generated ac field at 38GHz has an amplitude exceeding 2kOe inside the

di

B6

Figure 3 shows a scheme that utilizes a perpendicular spin torque driven oscillator to generate a localized ac field at microwave frequencies, placed next to the write pole of a perpendicular recording head. The oscillator consists of two perpendicularly magnetized magnetic multilayer structure sandwiching a normal metal layer. The oscillating multilayer stack consists of two ferromagnetic exchange coupled layers: one with strong perpendicular anisotropy and the other with high saturation moment for generating the ac magnetic field. With sufficiently high perpendicular anisotropy, the field generating layer thickness can be thicker than 10nm while still oscillating coherently at frequency as high as 40 GHz. In the paper, a full detailed analysis of the characteristics of the ac field oscillator and recording simulation on a full scale media model will be presented.

Reference [1] X. Zhu and J.-G. Zhu, “Bias-Field-Free Microwave Oscillator Driven by Perpendicularly Polarized Spin Current,” IEEE Trans. Magn. Vol. 42, p.2670 (2006).

Jian-Gang (Jimmy) Zhu Data Storage Systems Center, Carnegie Mellon University E-mail: jzhu@ece.cmu.edu Fax: +1-412-268-8554, Tel: +1-412-268-8373 Address: Department of Electrical and Computer Engineering, Carnegie Mellon University Pittsburgh, PA 15213-3890, U.S.A.

36

C1

THE PRODUCTION AND PERFORMANCE OF Si/SiO2 MAGNETIC RECORDING HEAD SLIDERS

Tim REILEY1, Jeffrey LILLE1, Tim STRAND1, Kenji KUROKI2, Nicholas BUCHAN3, Ed LEE, Michael

CHAW1, Darrick SMITH1, Mike SUK1, Walt FONG1, Bernhard KNIGGE1 1Hitachi Global Storage Technologies, San Jose, CA, First.Last@HitachiGST.com

2Hitachi Global Storage Technologies, Fujisawa, Japan, Kenji.Kuroki@HitachiGST.com 3Sitime Corp., Sunnyvale, CA, NB@Sitime.com

An alternative has been sought for the very hard Al2O3/TiC (AlTiC) two-phase ceramic material used as the substrate for magnetic recording heads. Its extreme hardness was useful in reducing head wear against particulate media in the early disk drives, but in subsequent drives with thin film media, its application has historically been problematical, either because of direct damage to the recording media or through the shedding of particles which can then cause disk damage and drive failure. The work described here replaces AlTiC with silicon as the substrate and slider body material, with the primary insulator enclosing the recording head being made of SiO2. We show performance enhancements of silicon over AlTiC, which are expected from the lower hardness and modulus and larger thermal conductivity; see Table I. Silicon was also selected because it makes possible the addition of active electronics on the slider, including diode protection or advanced recording sensors. This work includes the fabrication of recording heads similar to conventional heads and building of Head-Gimbal Assemblies (HGA’s), which were then evaluated in test stands and in functional disk drives. Wafers with conventional writer and GMR reader were prepared with conventional lithography. Care was taken so that no material other than SiO2 extended into the kerf at the edge of each slider. The means by which the Si slider bodies were produced was a two-step plasma etching process, rather than a diamond sawing process. The first etch is a Reactive Ion Etching (RIE) step to remove the SiO2 overcoat between the sliders. The second and primary etching process, is known as Deep Reactive Ion Etching (DRIE), and was initially developed specifically to allow very high aspect ratio etching in Si. In our work we have demonstrated the ability to etch through pico (1.25 mm) wafers or femto (0.85 mm) wafers with slider-to-slider spacing less than a standard diamond saw blade thickness. Also, since no saw damage is generated in the sliders, less material removal is required in the lapping process. This allows a notable decrease in the allowable spacing between sliders and an associated increase in the number of heads per wafer. Fig. 1 shows a group of partially etched sliders. In this case, these are femto sliders placed on a pico layout, thereby requiring that an individual kerf be removed around each slider. Fig. 2 shows the skeleton of a quarter wafer completely etched through, with the sliders removed. One major deviation from normal slider fabrication was to form the separate sliders from the wafers in one step without the intermediate state of a row of sliders. Lapping of the sliders was performed individually using an exploratory laboratory-scale process. The ability to form rows using the RIE/DRIE approach was also demonstrated. After lapping, conventional air bearings were etched into the sliders using standard etching techniques. HGA’s were prepared using conventional suspensions, with the pitch of the HGA requiring a small adjustment to compensate for the slightly trapezoidal etched shape of the DRIE’d sliders. One addition to the normal processing was the preparation of an ohmic contact (formed by metal deposition and laser annealing) on the suspension side of the slider. This allows the slider to be grounded through the suspension. The fly height and the magnetic characteristics of the Si HGA’s were similar to those of AlTiC ones.

Timothy C. REILEY Hitachi Global Storage Technologies San Jose Research Center Tim.Reiley@HGST.com Fax: 408 717 9073 Phone: 408 717 5798 3403 Yerba Buena Rd., San Jose, CA 95135

37

C1 A range of mechanical experiments was done using Si slider HGA’s and drives containing them. These included operational shock tests, disk slap tests (both static and dynamic) and load/unload tests directly onto pre-written data. A series of shock tests were performed on Microdrives which contained both an AlTiC and a Si HGA. The Si HGA showed a 3x improvement in operational shock over the AlTiC HGA, with the Si HGA withstanding more than 1000 G’s at 1 ms pulse length with no disk scratches or hard errors. Disk slap tests were nearly equally favorable. Load/unload experiments on data showed no loss of data. Pitch mode vibration frequencies were measured and showed an increase consistent with the 45% lower density of Si vis-à-vis AlTiC. Flyability experiments, in which slider disk contact was imposed by drive pressure reduction, showed a much extended lifetime for Si vs AlTiC sliders. One issue was observed in the drive experiments at high temperature, which is problematical. Given the low coefficient of thermal expansion of Si and sputtered SiO2 with respect to the poletip and shield materials, thermal protrusion of these elements caused head disk interaction which adversely affected servo stability. The head design of the Si slider has large shields, which is the primary contributor to the protrusion. Smaller shields and other design changes are likely to resolve the issue successfully. Overall, the project has demonstrated several potential mechanical advantages with Si/SiO2 sliders, as well as a new approach to their fabrication. Other advantages with Si contribute to the incentive for AlTiC slider replacement.

Fig. 1 Partially etched femto sliders on pico layout. Fig. 2 Wafer skeleton after etching.

Table I Some properties of Si, SiO2 and other recording head materials Coefficient Thermal Material Hardness(GPa) Modulus(GPa) of Exp.(ppm/K) Cond. (W/mK) Si 12.5 160 2.6 150 SiO2 (sputtered 9.5 70 2.6 Al2O3 (cryst.) 20 TiC (bulk) 33 AlTiC 400 6.9 20 Al2O3 (sputtered) 11 130 6.5 1.8 Ni-Fe (shields, poles) 6 12.8 35

38

C2

OPTIMAL SLIDER-DISK SURFACE TOPOGRAPHY FOR HEAD-DISK INTERFACE STABILITY IN HARD DISK DRIVES

Vineet GUPTA1 and David B BOGY2

1) University of California, Berkeley, USA, vineet@cml.me.berkeley.edu 2) University of California, Berkeley, USA, dbogy@cml.me.berkeley.edu

I. INTRODUCTION

With significant reduction in the allowable TMR and FHM limits in order to achieve higher areal densities, and the elevated excitation due to slider-disk topographies – smaller variations in slider positioning pose a potential threat of head-disk interface failure. At flying heights less than 5 nm, the slider-disk topographies will significantly effect the vibrations and stability of the slider at the head disk interface. On one hand the waviness (macro, micro and nano) will excite the structural modes of the HSA increasing the TMR and the FHM. And on the other hand the roughness will affect the magnitude of the adhesion forces and hence the stability of the slider at the head-disk interface. Consequently, effects that were formerly considered negligible are now becoming quite significant. This motivates our studying the dynamics of the slider at a higher level of complexity and proposing design improvements that can reduce the resulting slider vibrations and increase the head-disk interface stability.

II. THE HEAD DISK INTERFACE MODEL

Researchers in the past have made an attempt to predict the slider dynamics using a simple 3 degree of freedom slider model, which completely ignore the dynamics of the HSA [1-2]. Moreover in some of these investigations the slider-disk surface roughness was ignored while calculating the adhesion forces. It has been shown that the system dynamics predicted by these models is significantly different from the actual system response (measured experimentally) for sub-5nm flying sliders. In order to predict the slider behavior at low mechanical spacing we need a reliable model that captures the system dynamics accurately. Consequently a sophisticated solver was developed by the authors to study the slider vibrations and stability in the hard disk drive [3]. This solver not only includes the HSA and the disk model along with the usual 6 degree of freedom slider model but also the includes the effect of the slider-disk topographies while calculating the magnitude of the adhesion forces [4]. This solver, developed by the authors, can be used as a design tool to suggest optimal slider-disk topography that can minimize slider vibrations and improve the HDI stability. This model will be presented in detail at the conference.

III. THE EFFECT OF SLIDER-DISK TOPOGRAPHIES

In order to investigate the effect of slider and disk surface topographies we divided the features on the surface into three different categories: (a) Roughness – Surface features with wavelengths up to a few µm, (b) Waviness – Surface features with wavelength of the order of a few µm to a few mm, and (c) Large wavelength features like disk run-out – Surface features with wavelengths greater than a few mm’s. The roughness and the waviness wavelength domains are further sub-divided into smaller wavelength regimes. Different wavelength regimes are investigated separately to gain a better understanding of their effect on the slider vibrations and stability. In order to study the effect of roughness we have used a statistical approach. In this approach the heights of the asperities are assumed to be randomly distributed with a Gaussian density function. The parameters of this Gaussian density function are based on the experimental slider and disk surface measurements. The effect of waviness on slider dynamics is evaluated using an experimentally measured disk profile. These measurements of the disk profile are done using an LDV. And finally the effect of large wavelength disk features is evaluated by studying the effect of various circumferential disk modes on the slider dynamics.

39

C2

IV. CONCLUSIONS We found that the small wavelength disk features – with wavelength less than a few µm – significantly affect

the magnitude of the adhesion and the contact forces. We found that very smooth and very rough surfaces are undesirable because they increase the magnitude of the adhesion forces and the contact forces, respectively. Our results indicated that for maximum HDI stability we should not have extremely smooth slider and disk surfaces, but instead some amount of roughness is necessary. We also found that intermediate wavelength features – with wavelength more than a few µm but less than a few mm – excite some HSA modes and thus result in an increase in the amplitude of the slider vibration along all 6 degrees of freedom. Our results indicate that by selectively burnishing the wavelengths that can excite the critical modes of the HSA we can reduce the slider vibrations. Further we found that the large wavelength disk features – with wavelength more than a few mm – does not significantly effect the slider vibrations as the slider can easily follow these features. Fig 2 summarizes all these results in a single chart. It shows the plot of the wavelength and the amplitude range of the disk features that effect the vibration and the stability of the slider at the HDI.

IV. ACKNOWLEDGEMENTS This work was supported by the Computer Mechanics Laboratory at the University of California, Berkeley and

the Information Storage Industry Consortium’s EHDR Servo program.

REFERENCES

1) Lin Wu, D.B. Bogy, “Effect of the Intermolecular Forces on the Flying Attitude of Sub-5 nm Flying Height Air Bearing Sliders in Hard Disk Drives”, ASME J of Tribology, 124(3), 562-567, (2002).

2) B.H. Thornton, D.B. Bogy, “Head-Disk Interface Dynamic Instability due to Intermolecular Forces”, IEEE Transactions on Magnetics, 39(5), 2420-2422, (2003).

3) V. Gupta and D.B. Bogy, “Slider Disk Head-Stack-Assembly Modeling in Hard Disk Drives Using Model Order Reduction Technique”, submitted to Journal of Sound and Vibration.

4) W.R. Chang, I. Etsion and D.B. Bogy, “An Elastic-Plastic Model for the Contact of Rough Surfaces”, ASME J of Tribology, 109, 257-263 (1987).

Fig. 1 Pico slider design used in head-disk interface simulations. The suspension pre load is 1.5 gm. The crown & camber are 25.4 nm and 2.5 nm, respectively.

Fig. 2 The amplitude and wavelength range of features on the disk surface that affect the vibrations and the stability of the slider at the head-disk interface.

Corresponding AUTHOR Computer Mechanics Laboratory, UC Berkeley E-mail: vineet@cml.me.berkeley.edu fax: +1-510-643-9786 tel: +1-510-642-4975 5146 Etcheverry Hall, Dept of Mechanical Eng, University of California, Berkeley, USA

40

C3

Tao Pan, Suping Song, Bill Sun, Victor Rudman, Kroum Stoev, Lanshi Zheng, Vijay Prabhakaran,

Saikumar Balasubramaniyam, Jagdeep Buttar, Eric Sladek, Francis Liu Western Digital, 44100 Osgood Road, Fremont, CA 94539

I. INTRODUCTION

Magnetic hard disk drive industry has been going though two major technology transitions from longitudinal magnetic recording to perpendicular magnetic recording, and from current in plane giant magneto-resistance (CIP GMR) sensor to tunnel giant magneto-resistance(TuGMR) sensor. These two transitions are widely believed to be the key enablers to sustain the areal density growth at a rapid pace. However, both new write and read head technology success still heavily rely on recording spacing reduction due to extremely sensitive write and read spacing loss[1-3]. Remarkable recording head flying height(FH) or clearance reduction in the last several decades has been slowed down in recent years partly due to several factors: inevitable FH distribution, thermal pole tip protrusion(TPTP) and write induced pole tip protrusion(WPTP). As in recent areal density demonstrations, the recording clearance, which could be much smaller than the combination of TPTP and WPTP, and FH distribution, were required be below a couple of nanometers[4-6]. In this paper, a recording head design with a heated device inside as dynamic flight height(DFH) control to compensate TPTP and WPTP and reduce FH distribution will be reviewed with component and system perspectives.

II. DFH SYSTEM DESIGN REQUIREMENTS

The goal of a DFH system is to achieve low operating clearance during writing and reading processes. Typical FH budget needs to consider TPTP, WPTP, FH sigma, altitude clearance and other head and media variation as shown in Fig. 1. The average clearance of pole tip is the approximately sum of TPTP, WPTP, three sigma of FH and clearance budget for altitude margin. With a DFH system capable to detecting touch down[1], The pole tip only need to back off from touch down to the height of clearance budget as indicated by the long dashed line. Therefore, average clearance of a DFH head system and sigma of clearance are much smaller than those of a non DFH head system.

Fig. 1: DFH System Scheme

Dynamic Flight Height Control Recording Head Design with System Considerations

Clearance Budget TPTP Glide Height

Glide Height PTR 1.5

High Tem

perature DFH

off

Flying Height

WPTP

Room

Temperature D

FH off

FH 3σ

DFH

on at all temperature

Touch Dow

n surface

41

C3 A DFH system design is bound by a lot of stringent system requirements: (1)100% touch down, (2)power efficiency, (3) reliable heater, (4)acceptable reader temperature rise for all the FH distribution of heads, (5) good protrusion profile, (6) enough tunable spacing resolution, (7)adjust DFH power compensation according to temperature, (8) touch down and back off by certain amount of head media spacing, (9) fast enough dynamic DFH response, (10) reliable air bearing design matched with system requirements.

III. DFH HEAD DESIGN Any overweight on one of above requirements without considering other factors could impact system performance. For instance, DFH power efficiency can be easily improved by moving heater closer to ABS. However, the reader temperature due to DFH will be higher. A figure of merit of a DFH system is introduced: amount of PTP for each degree of reader temperature rise due to DFH: DFH Figure of Merit=PTP(nm)/reader temperature rise degree Eq. [1]. As shown in Table 1, as the heater is moving away from ABS, this DFH figure of merit is better. However, if the heater is too far away from ABS, the power efficiency will be too low. 100% touch down may not be achieved. The interaction [7] between ABS push back effect and heater should be optimized to meet system power efficiency requirements as shown in table 1. Protrusion profile[5] can be adjusted by inserting the heater at different locations inside the slider as shown in Fig. 2.

Heater Recess from ABS

Power Efficiency(nm/mW)

Reader Temperature Rise ºC/mW

DFH Figure of Merit nm/ºC

Large 0.054 0.34 0.16Small 0.064 0.48 0.13

ABS Push Back65% 0.06 0.3 0.255% 0.086 0.43 0.245% 0.12 0.5 0.24

0

1

2

3

4

5

6

7

8

9

-20 -15 -10 -5 0 5 10

Distance from write gap (um)

Hea

ter A

ctua

tion

(nm

)

vp3UCS2/P1

Table 1 Fig. 2: DFH protrusion profiles

References

[1] Y. Tang, S. Hong, N. Kim and X. Che, “Overview of Flight Control Applications in Perpendicular Magnetic Recording”, IEEE Magn. Trans. Vol.43, No. 2, Feb 2007

[2] S. Gebredingle, S. Gider and R. Wood, “Magnetic spacing sensitivity of perpendicular recording”, IEEE Trans.on Magn. Vol. 42, No.10, Oct, 2006

[3] D. Guarisco, B.E. Higgins, Z. Li, Y. Wu, K. Kaito, and A. LeFebve, “ Drive integration in Perpendicular Recording” in Proc. MMM, San Jose, CA Nov. 2005, Paper GC-13

[4] S. Mao, etc, “Commercial TMR heads for hard disk drives characterization and extendibility”, IEEE, Trans. On Magn, Vol. 42, No.2, 2006

[5] P. Ryan, “ Recording heads for next generation perpendicular recording”, A1, TMRC, 2006 [6] Y. Hsu, etc, “Challenges for perpendicular write heads at high recording density”, IEEE. Trans. On Magn.

Vol. 43, No. 2, Feb. 2007 [7] J. Juang, “Flight control sliders with piezoelectric and thermal nanoactuator for ultrahigh density magnetic recording”, Ph.

D. Thesis, 2006, CML

Corresponding author: Tao Pan Western Digital Corp. E-mail: tao.pan@wdc.com Fax: 1-510-683-7666 Tel: 1-510-683-7476 44100 Osgood Road, Fremont, CA94539

42

C4 Low Flying Height Slider with High Thermal Actuation Efficiency and Small Flying

Height Modulation Caused By Disk Waviness Bo LIU, Shengkai YU, Weidong ZHOU, Chee-How Wong & Wei HUA

Data Storage Insitute, Singapore, liu_bo@dsi.a-star.edu.sg

I. INTRODUCTION

The increasing demand for higher areal density in magnetic recording continues to push the mechanical spacing (or flying height, FH) between the read/write head element and the disk surface to below 5 nm. At such low spacing, even nanoscale FH loss will greatly impact the stability and reliability of the head-disk interface (HDI). The FH loss includes the static loss induced by manufacturing tolerances, environmental variations and operation conditions, etc; and the dynamic loss caused by the flying height modulation (FHM) due to disk waviness, shock and vibrations, etc. These FH losses can cause the slider head disk contact, resulting in failure of head and media, and data loss.

Recently, a novel active FH control technology has been used to reduce these FH losses. The thermal flying height control (TFC) slider was first demonstrated by Meyer, et al. [1] and has been applied in the latest generations of hard disk drives. It uses a thermal heating device to produce a localized thermal protrusion in the region of the read/write head elements to control the FH. However, as the thermal actuator works at the low frequency (<10 kHz), it is almost impossible to active control the dynamic losses of FH, such as FHM due to disk waviness.

One important criterion for TFC slider design is its thermal actuation efficiency. The high actuation efficiency, i.e. large FH reduction with small applied power, is desirable so that the TFC slider has a large enough stroke for FH adjustment. It can usually be achieved by optimizing the TFC slider structure such as the shape and position of heaters, and optimizing the air bearing surface (ABS) design of the TFC sliders. Another crucial criterion is that the TFC slider must have enough capability in following disk waviness so as to minimize the FHM caused by the disk waviness. However, it is not easy to achieve these two design objectives simultaneously, because there are inherent relations between these two criteria.

This paper investigates the effects of air bearings on the thermal actuation efficiency and the capability in following disk waviness of the TFC sliders, and explores their inherent relations. The ABS design strategies and concepts for TFC sliders are proposed and investigated by simulations. The results show that both excellent thermal actuation efficiency and strong capability in following disk waviness can be achieved through proper arrangements of the air bearing pressure distribution on ABS of TFC sliders.

II. THERMAL ACTUATION EFFICIENCY AND FHM

A simulation platform is developed for the TFC sliders in DSI which consists of the FE model of TFC slider, the air bearing model and the heat transfer model. A coupled-field analysis scheme is used to solve the interactions among the aerodynamic, thermal and structural fields. In this study, two types of sliders, Panda 3 and Design A, as shown in Fig. 1, are compared by simulations to explore the air bearing effects on the thermal actuation efficiency and FHM. Panda 3 slider is designed for the conventional slider with low FH. It has high air pressure concentrated on the region of read/write element. Design A adopts the isolated read/write pad concept [2] where the air pressure around the region of read/write head elements is low, as shown in Fig. 2.

Fig. 3 compares their thermal actuation efficiency, i.e. FH reduction per milli-watt of power applied to the heater. It is found that Design A has significantly higher actuation efficiency (0.27 nm/mw) than Panda 3 (0.12 nm/mw). There are two mechanisms which cause the difference. One is the cooling effect of air bearing which reflects the heat being dissipated to the disk through the air bearing. The air bearing cooling is a very complicated heat transfer process which is dependent on both the FH and air pressure. Design A has lower air pressure around the heater region, and therefore, lower heat flux (Fig. 4), higher temperature and thermal protrusion at the same heating power. The thermal protrusion for Design A is 10.1 nm at 25 mw heating power, while it is 7.2 nm for Panda 3. The other mechanism for improving actuation efficiency is the protrusion compensation effect due to lift force of air bearing. Design A has a higher ratio of FH reduction to protrusion (0.695) than Panda 3 (0.425) due to the lower air pressure around the region of read/write element of Design A.

43

Fig. 1 ABS design (a) Panda 3; (b) Design A

Fig. 2 Air pressure profile (a) Panda 3; (b)

Design A

FH Change v.s. Protrusion

y = -0.121x + 7.870

y = -0.269x + 10.453

0

5

10

0 10 20 30 40Heating Power (mw)

FH (n

m)

Panda 3

Design A

Fig. 3 Thermal actuation efficiency FHM

0.0

0.5

1.0

1.5

2.0

0.0 0.5 1.0 1.5 2.0 2.5Wavelength of waviness (mm)

FHM

/ w

avin

ess

Rat

io Panda 3

Design A

Fig. 5 FHM due to disk waviness

C4

However, when their FHMs due to disk waviness are compared, it is found that Design A has much higher FHM-to-waviness ratios than Panda 3. It is because the air bearing pressure is not concentrated on the region of read/write element in Design A, which results in an increase of the distance between the head position and the nodal line. It will cause a larger lag phase between the motions of slider and disk, and result in a larger FHM [3]. Therefore, it needs to rearrange the ABS design of the TFC slider to consider both thermal actuation efficiency and FHM.

III. NEW ABS DESIGN AND DISCUSSION

Based on the above understanding, several ABS design strategies to achieve both high thermal actuation efficiency and high capability in following disk waviness are proposed, and a new ABS design has been developed with excellent performance on both criteria. They will be discussed in more details in the full paper.

REFERENCES

1) D.W. Meyer, P.E. Kupinski, and J.C. Liu, “Slider with temperature responsive transducer positioning,” U.S. Patent 5 991 113, (1999)

2) J.H. Li, B. Liu, W. Hua and Y.S. Ma, “Effects of casimir and van der force in sub-10nm spaced head-disk interface,” IEEE Trans. on Magn. 38(5), 2141-2143, (2002)

3) S.K. Yu, B. Liu and J. Liu, “Analysis and optimization of dynamic response of air bearing sliders to disk waviness”, Tribology International, 38(6-7), 542-553, 2005.

Bo LIU Data Storage Institute E-mail: liu_Bo@dsi.a-star.edu.sg fax: +65-6777-2406 tel: +65-6874-8507 5 Engineering Drive 1, Singapore 117608

44

C5

HEAD SLIDER DESIGNS CONSIDERING DYNAMIC L/UL SYSTEMS FOR 1-INCH DISK DRIVES

Sang-Joon YOON1, Seok-Ho SON2 and Dong-Hoon CHOI3

1) The Center of iDOT, Hanyang Univ., Seoul, Korea, ysjyoon@hanyang.ac.kr 2) Department of Mechanical Engineering, Hanyang Univ., Seoul, Korea, raptorz4@ihanyang.ac.kr

3) The Center of iDOT, Hanyang Univ., Seoul, Korea, dhchoi@hanyang.ac.kr

I. APPROXIMATE DESIGN OPTIMIZATION FOR L/UL APPLICATIONS

The L/UL applications, which are necessary for small form factor disk drives as well as mobile and server ones, have increased the possibility of slider-disk contact during L/UL operations. As a way to prevent the flying slider from contacting on the disk, this paper suggests the ABS design optimizations for L/UL applications using an efficient approximate model of the dynamic unloading performance.

For a good L/UL application, the lift-off force of the slider should be reduced during unloading process. The important parameters which affect the lift-off force are known to be the negative pressure force as well as the flying attitude of the slider including pitch angle in steady state. In this study, a design optimization problem is formulated to minimize the amplitude of lift-off force during the unloading process while keeping the flying height, pitch and roll angles within suitable ranges over the entire recording band as well as reducing the possibility of slider-disk contact in steady state as follows:

Minimize ),,,(~ βαmFF hnL (1)

Satisfying hODh hhh γγ +≤≤− ** , hIDh hhh γγ +≤≤− ** (2)

UOD

L ααα ≤≤ , UID

L ααα ≤≤ (3) U

ODL βββ ≤≤ , U

IDL βββ ≤≤ (4)

OD

L hh )( minmin ≤ , ID

L hh )( minmin ≤ (5) nixxx U

iiLi ,...,2,1, =≤≤ (6)

where a simplified lift-off force model with respect to air-bearing suction force and flying attitudes is created by the kriging method [1] because it takes a huge amount of computational time in solving time-dependent dynamic L/UL equations. To effectively reduce the number of computer experiments, the optimal Latin-hypercube design [2] is introduced as a design of experiment (DOE), which is to select the best Latin-hypercube design which optimizes a given maximin criterion. To wrap and connect the kriging model and static air bearing solver, the FRAMAX [3] is utilized as a design framework.

II. COMPUTATIONAL RESULTS

From the conventional CSS and L/UL types of negative pressure slider models, the optimally designed sliders were automatically obtained for an 1-inch disk drive with L/UL system. As shown in Figs. 1 and 2, their dynamic L/UL simulation results revealed that the optimally designed sliders had the small ramp forces (pico is 21% off and femto is 1.2% off) as well as the small lift-off forces (pico is 62% off and femto is 10% off) in comparison with the initial ones, respectively, while keeping the desired static characteristics over the entire recording band. It was demonstrated that the designed slider incorporated with the suspension was not only properly unloaded onto the ramp without rebounding problems, but also smoothly loaded onto the rotating disk. As a result, the proposed design approach is believed to work efficiently in slider air-bearing designs for L/UL applications because it uses only the static analysis instead of the time-dependent dynamic L/UL analysis during the iterative optimization process.

45

C5

ACKNOWLEDGMENT

This research was supported by the Center of Innovative Design Optimization Technology (iDOT), Korea Science and Engineering Foundations.

REFERENCES

1) Ryu, J. S., Kim, M. S., Cha, K. J., Lee, T. H. and Choi, D. H., “Kriging Interpolation Methods in Geostatistics and DACE Model,” KSME International Journal, Vol. 16, No. 5, pp. 619-632, (2002).

2) Morris, M. D. and Mitchell, T. J., “Exploratory Design for Computational Experiments,” Journal of Statistical Planning and Inference, Vol. 43, pp.281-402, (1995).

3) FRAMAX [Online]. Available: http://iframax.com

(a) Initial design (b) Optimum design Fig. 1 Unloading performances of the pico slider model

(a) Initial design (b) Optimum design Fig. 2 Unloading performances of the femto slider model

- 10

0

10

20

30

0 1 2 3 4Time [ms]

Forc

e [m

N]

Air bearing forceSuspension forceL/UL ramp force

0

10

20

0 1 2 3 4Time [ms]

min

. FH

[um

]

0.0

0.2

0.4

0.6

0.8

1.5 2 2.5

- 10

0

10

20

30

0 1 2 3 4Time [ms]

Forc

e [m

N]

Air bearing forceSuspension forceL/UL ramp force

0

10

20

0 1 2 3 4Time [ms]

min

. FH

[um

]

0.0

0.2

0.4

0.6

0.8

2 2.5 3

- 10

0

10

20

30

0 1 2 3 4Time [ms]

Forc

e [m

N]

Air bearing forceSuspension forceL/UL ramp force

0

10

20

0 1 2 3 4Time [ms]

min

. FH

[um

]

0.0

0.2

0.4

0.6

0.8

1.5 2 2.5

- 10

0

10

20

30

0 1 2 3 4Time [ms]

Forc

e [m

N]

Air bearing forceSuspension forceL/UL ramp force

0

10

20

0 1 2 3 4Time [ms]

min

. FH

[um

]

0.0

0.2

0.4

0.6

0.8

2 2.5 3

- 30

- 20

- 10

0

10

20

30

0 0.5 1 1.5

Time [ms]

Forc

e [m

N]

Air bearing forceSuspension forceL/UL ramp force

0

50

100

0 0.5 1 1.5Time [ms]

min

. FH

[um

]

- 0.2

- 0.1

0.0

0.1

0.2

0 0.5 1

- 30

- 20

- 10

0

10

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Dong-Hoon CHOI The Center of Innovative Design Optimization Technology, Hanyang University E-mail: dhchoi@hanyang.ac.kr fax: +82-2-2291-4070 tel: +82-2-2220-0443 #312 HIT, Hanyang University, 17 Haengdang-dong, Sungdong-gu, Seoul 133-791, Korea

46

C6

HEAD DISK INTERFACE FRICTION MEASUREMENTS: EFFECTS OF ROUGHNESS, LUBRICANT, AND SURFACE ENERGY

Chang-Dong Yeo1, Michael Sullivan2, Sung-Chang Lee2, Andreas A. Polycarpou1

1) Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, USA, cyeo2@uiuc.edu / polycarp@uiuc.edu

2) Samsung Information Systems America, San Jose, CA 95134, USA, msullivan@sisa.samsung.com / sungc.lee@sisa.samsung.com

I. ABSTRACT

The frictional force in head disk interfaces (HDIs) was investigated considering the surface energy of the lubricant and carbon overcoat (COC). Perfluoropolyether (PFPE) Z-Tetraol with an additive (A20H) was applied onto two types of COC (Type-A and Type-B), and the lubricant thickness was controlled to be in the range of 11 – 19 Å. The polar and dispersive components of the surface energy were determined from contact angle measurements as a function of lubricant thickness. For each disk sample, the frictional forces were measured using actual hard disk drives (HDD), and they were compared to the measured surface energy values. As the lubricant thickness increases, it was observed that the surface energy values of the lubricated disks decreased, and accordingly the frictional forces of the HDI also decreased. Comparing the frictional force and surface energy for the two types of disks, type-A disks showed lower surface energy but higher frictional force at all lubricant thickness, which could be attributed to the surface roughness parameters, surface energy of the underlying carbon film, and lubricant interactions.

II. INTRODUCTION

The measurement and modeling of frictional forces in HDI is very important and researchers have focused on PFPE lubricant design such as chemical composition, physical thickness, and other factors [1-2]. However, in HDI rough surface contacts, the surface asperities of the head slider can penetrate the lubricant film and thus contact the underlying carbon surface [3-4]. Under such contact conditions, the solid asperity contacts between head and disk can also affect the tangential movement of the contacting surfaces. In this paper, a representative PFPE lubricant (Z-Tetraol) combined with an additive (A20H) was applied onto two types of carbon films. The dispersive and polar surface energies of the lubricated disks were measured from contact angle measurements with respect to lubricant thickness. For the specified lubricated disks, the frictional forces in actual HDD were measured and compared to the surface energy values. Also, the contribution of surface energy, roughness parameters, and lubricant interactions to the frictional force were discussed.

III. EXPERIMENTS

Z-Tetraol lubricant with an additive (A20H) was applied on two types (Type-A and Type-B) of carbon overcoat (COC) used in magnetic recording media. Type-A and Type-B COC films were made of amorphous-hydrogenated carbon (a-C:H-N) with different nitrogen content (%). The COC thicknesses were 25 Å and 27 Å for Type-A and Type-B, respectively. The applied lubricant thickness was in the range of 11 Å – 19 Å. The dispersive and polar surface energy of the lubricated disks were measured from contact angle measurements using VCA-OptimaTM (AST products Inc.). As reference liquids for the surface energy measurements, DI water and hexadecane were used for the lubricated disks, and DI water and methylene iodide were used for bare carbon (no lubricant) disks. Using the measured contact angles from the two combinations of reference liquids, the dispersive and polar surface energy of the disk samples could be determined. In order to measure the frictional forces for the specified lubricated disks, actual HDDs were built using exactly the same assembly parts except for the disks. Under static HDI contact conditions with a prescribed gram-load, the motor driving current (in amperes) increased from zero to the value needed to initiate disk motion (step size of 2 mA). This spin-up motor current value was used as a qualitative measure of the HDI frictional force. The measurements were performed in both ambient (25 °C) and hot (70 °C) environments to investigate the temperature effects on the HDI frictional forces. For each specified lubricated disk, four HDDs were manufactured and used to measure the spin-up motor current.

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C6

IV. RESULTS AND DISCUSSION

The polar and dispersive surface energies of the lubricated disks as obtained from contact angle measurements showed that type-A lubricated disks had lower surface energy than type-B lubricated disks at all lubricant thickness as seen in Fig. 1 (a). The HDD friction experiments revealed that type-A lubricated disks had higher frictional force than type-B lubricated disks as seen in Fig. 1 (b). These results appear to be opposite to the surface energy measurements. In order to verify the higher frictional force with lower surface energy of type-A disks, the effects of surface roughness, lubricant interactions, and surface energy of carbon film on the frictional behavior in HDI were investigated. First, based on the results of an improved sub-boundary lubrication (ISBL) friction model, HDI-A (type-A disk) showed higher adhesive and frictional forces due to the larger asperity radius. Second, type-A lubricated disks had stronger polar end groups bonding to the underlying carbon film, which could cause higher frictional force. Third, type-A carbon film had larger surface energy than type-B carbon film. Since the static HDI contact has considerable solid asperity contacts, the higher surface energy of type-A carbon film can cause higher HDI frictional force. Therefore, the higher frictional force with lower surface energy of type-A lubricated disk in this study could be attributed to the above three factors, which need to be accounted for the accurate analysis and control of HDI frictional behavior.

REFERENCES

1) Zhao, Z., Bhushan, B., “Tribological performance of PFPE and X-1P lubricants athead–disk interface. Part I. Experimental results,” Tribol. Lett., 6, 129-139 (1999). 2) Kim,Y. –S., Chung, K. –H., Kim, D. –E., “Micro-tribological Characteristics of PFPE Zdol Lubricant Coated on Silicon,” IEEE APMRC 2004, 94-94 (2004). 3) Stanley, H. M., Etsion, I., Bogy, D. B., “Adhesion of Contacting Rough Surfaces in the Presence of Sub-Boundary Lubrication,” ASME J. Tribol., 112, 98-104 (1990). 4) Lee, S. –C., Polycarpou, A. A., “Adhesion Forces for Sub-10 nm Flying-Height Magnetic Storage Head Disk Interfaces,” ASME J. Tribol., 126, 334-341 (2004). Fig. 1 (a) Surface energy measurements of lubricated disks, (b) HDI friction measurements in actual HDDs

0 5 10 15 2010

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Corresponding AUTHOR Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign E-mail: polycarp@uiuc.edu fax: 1-217-244-6534 tel: 1-217-244-1970

48

D1

NANOSCALE FABRICATION OF DISCRETE-TRACK AND PATTERNED BIT MEDIA: FROM PROTOTYPING TO LARGE SCALE

Zvonimir Z. BANDIĆ, Bernhard KNIGGE, Paul VAN DER HEIJDEN, Dan KERCHER, Henry YANG,

Tsai-wei WU, Elizabeth DOBISZ and Thomas R. ALBRECHT Hitachi San Jose Research Center, 3403 Yerba Buena Rd, San Jose, CA 95135

I. INTRODUCTION

As the superparamagnetic limit continues to make scaling of conventional magnetic recording technology to higher densities and larger capacities more difficult, novel concepts such as discrete-track and patterned magnetic bit media are being considered as likely routes to terabit per square inch densities and beyond. Discrete track media is currently being studied to understand its potential to improve signal to noise ratio and adjacent track erasure compared to conventional perpendicular media, while patterned bit media overcomes the thermal stability problems of conventional magnetic media by implementing single domain magnetic islands for each bit of recorded information.

II. LARGE SCALE FABRICATION

Large scale fabrication of patterned media requires the application of emerging technologies, such as nanoimprint lithography for volume fabrication of patterned media disks, and advanced electron beam lithography for master mold fabrication. Figure 1 shows principal schematics of the steps involved in the fabrication of patterned media disks. One or a small number of masters are fabricated employing e-beam lithography, while nanoimprinting lithography is used to fabricate large number of individual patterned media disks. [1]

Fig. 0 a) Resist coated disk in the e-beam lithography tool b) SEM images of the patterned disk c) AFM images of the magnetic patterned disk.

Figure 0 Large scale fabrication of patterned media disks

49

D1

III. PROTOTYPING OF FLYABLE PATTERNED MEDIA DISKS

At the same time, media development and magnetic recording testing effort requires prototyping fabrication of flyable magnetic disks. Some of the challenges in both prototyping and large scale fabrication of patterned media disks are creation and high fidelity replication of nm-scale pattern features, the development of robust processes for electron beam lithography on non-conductive substrates, implementation of circular-symmetry patterns in Cartesian e-beam lithography tools, and design, fabrication and testing of pre-patterned servo patterns. Figure 2 shows some of the steps in prototyping of flyable magnetic recording disks, starting from (Fig.2a) direct e-beam lithography on disks coated with resist, SEM image of etched SiNx layer on the top of the disk using resist as a mask (Fig. 2b) and AFM of the patterned disk coated with magnetic media, overcoat and lubricant (Fig. 2c).

IV. SPINSTAND STUDIES OF DISCRETE TRACK MEDIA DISKS

Fig. 3a) shows the low magnification image of 100 µm wide band of the 100 ktpi discrete track media prototype disk with the 120 MHz servo pattern. Fig. 3b) shows the results of the Laser Doppler Velocimetry (LDV) measurements of the air bearing slider flying in the vicinity of the patterned band. Figure 4 shows phase diagrams of the position error signal (PES) patterns. Fig. 4a) shows the phase diagram of the PES measured on a spinstand, while Fig. 4b) shows simulated data that takes into account position errors introduced in the e-beam lithography process.

REFERENCES

1) Z.Z. Bandic et al, “Patterned magnetic media: impact of nanoscale patterning on hard disk drives”, Solid State Technology S7, S (2006). Zvonimir BANDIĆ

Hitachi San Jose Research Center E-mail: Zvonimir.Bandic@hitachigst.com fax: +1-408-717-9066 tel: +1-408-717-5483 3403 Yerba Buena Rd, San Jose, CA 95135

Fig. 3 a) SEM image of the 100 micron wide band of discrete track media with servo pattern on the disk b) results of the LDV measurements on the slider.

Fig. 4 Phase diagram of PES signal: a) measured b) simulated

50

D2

STUDY OF LITHOGRAPHICALLY DEFINED DATA TRACK AND SERVO PATTERNS ON CONVENTIONAL PERPENDICULAR MEDIA

Xiaodong CHE1, Kiseok MOON1, Yawshing TANG1, Nayoung KIM1, Hyung Jai LEE1, Matthew

MONECK2, Jian-Gang ZHU2, Nobuyuki TAKAHASHI3 1) Samsung Information Systems America, 75 W Plumeria Drive, San Jose, CA 95134, USA, carl.che@samsung.com

2) ECE Department, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA, mmoneck@andrew.cmu.edu 3) Fuji Electric Advanced Technology Co., Ltd. 4-18-1 Tsukama, Matsumoto, Nagano 390-0821, Japan, takahashi-

nobuyuki@fujielectric.co.jp

I. INTRODUCTION

Nano-imprinting technology has been utilized for fabrication of discrete track media (DTM) [1][2]. The recording performance advantage of such media, especially in reducing adjacent track erasure (ATE), has been studied and demonstrated [1][3]. As nano-imprinting lithography (NIL) technology advances, discrete track media is viewed as one of the next promising technologies to support areal density increase.

We study discrete track media recording (DTR) technology through E-Beam fabricated recording tracks and servo features on conventional PMR media. This approach offers us several benefits: first, it requires shorter discrete track process time and is flexible to design and change in patterning features. Since the features are localized, we can directly compare discrete track performance with conventional PMR media on one single recording track.

This paper will be arranged with the following three topics: 1) DTM adjacent track erasure study, 2) DTR servo pattern fabrication and characterization, 3) A geometrical TPI model for DTM.

II. DTM ADJACENT TRACK ERASURE STUDY

Comparing with conventional media, it is found that ATE is much less for DTR media. To understand the mechanism, we measure the location of the erased edge as an adjacent track is recorded. The two dimensional playback signal mappings, one example of which is shown in Figure 1, are used to calculate the erased edge difference between DTR media and continuous media. The difference, labeled as d in Figure 1, is found to be approximately 20nm and does not change with center track data pattern frequency. This difference cannot be simply explained by the physical features of the DTR media. The magnetic writing process has to be considered.

This finding also indicates that granular magnetic properties (including inter-granular coupling) may be optimized differently for DTR media since we may have less trade-off concern between on track SNR improvement and write width reduction.

III. DTR SERVO PATTERN FABRICATION AND CHARACTREIZATION

Future DTM for HDD integration should have discrete recording tracks along with some disk format features. Among them, servo information can be included in the disks during the NIL process. Current HDD manufacturing requires the servo information be written with recording heads. DTM allows more flexible servo schemes, some of which cannot be easily written with any servo write/copy method.

51

D2

Using E-beam lithographic fabrication, we systematically studied several servo schemes for DTM. Some of the schemes are designed to generate identical servo signals as current servo patterns. At 250ktpi, the quality of the DTM servo bursts is studied and compared with conventional servo bursts written on continuous media. As shown in Figure 2, the edge definition of each servo burst for DTM is very sharp. The variation of PES signal is mainly due to the fluctuation of the physical edge location. We also studied several alternative servo schemes that can be generated by the NIL process. The playback waveforms and PES signals for these approaches are analyzed as well.

A two dimensional linear playback model is developed using SEM images to obtain the DTM physical configuration, which is then used to calculate playback signals. The model shows good agreement with measurement; it also gives more statistical information of the servo signals from DTR media.

IV. A GEOMETRIC TPI MODEL FOR DTM

In this section, we will introduce a general formula estimating DTR media TPI gain over conventional media. As shown in the following equation, the total TPI gain for DTR media is a product of two factors: physical feature factor β and magnetic side erasure factor γ :

MediaContDTR TPITPI .)1)(1( γβ ++≈

The definition of these two factors will be given in the paper. Both factors can be quantitatively measured. This equation gives a good estimation of TPI gain with DTR media over continuous media.

For HDD application, the ultimate measure of a new recording technology is the areal density increase, assuming similar linear density can be achieved by DTM and continuous media, this TPI estimation is also a first order estimation of areal density gain with DTM.

REFERENCES

1) Y. Soeno, M. Moriya, A. Kaizu, and M. Takai, “Performance Evaluation of Discrete Track Perpendicular Media for High Recording Density,” IEEE Trans. Magn., vol. 41, no. 10, pp. 3220-3222, Oct. 2005.

2) D. Wachenschwanz, W. Jiang, E. Roddick, A. Homola, P. Dorsey, B. Harper, D. Treves, and C. Bajorek, “Design of a manufacturable discrete track recording (DTR) medium,” IEEE Trans. Magn., vol. 41, no. 2, pp. 670–675, Feb. 2005.

3) X. Che, Y. Tang, H. Lee, S. Zhang, K. Moon, N. Kim, S.Hong, N.Takahashi, M. Moneck, J.Zhu, “Recording Performance Study of PMR Media with Patterned Tracks,” to be published on IEEE Trans. Mag., Inermag 2007.

Fig. 2. Magnetic signal map for the servo bursts. The top map is on DTR media, and the bottom map is on continuous media. For continuous media, the bottom edge of the track is formed as the track is written, whereas the top edge is formedby positioning the head 100nm offtrack and writing with an AC frequency. This simulates the “trimming” process used when the servo bursts are written.

Fig. 1. Magnetic signal map of DTR and continuous media regions. (a) Before adjacent track writing; (b) after adjacent track writing with HF. The edge erased by the adjacent track writing is measured. d is the offset between the track edges for DTM and continuous media.

Pattern (dc erased)

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52

D3

Feasibility of Recording 1 Tb/in2 Areal Density

R. H. Victora1, Xiao Shen2, and Stephanie Hernandez3 1) Univ. of Minnesota, Minneapolis, USA, victora@ece.umn.edu

2) Univ. of Minnesota, Minneapolis, USA, shenxiao@ece.umn.edu 3) Univ. of Minnesota, Minneapolis, USA, herna095@umn.edu

I. Introduction

Exchange coupled composite media [1] has been proposed as a possible solution for terabit per square inch magnetic recording owing to its advantage in writablity comparing with conventional perpendicular media at the same level of thermal stability. For example, synthetic antiferromagnet exchange coupled composite media [2] was reported to reduce the switching field by 60% comparing with its conventional counterpart without decrease in thermal stability. In this paper, we propose a specification, calculated micromagnetically, but using realistic constraints for those parts of the system outside the reach of our calculations. We allow 1909 emu/cc saturation Ms for the writer. Anisotropy field of the writer material is 10 Oe in plane (cross track direction). Jitter is calculated as in [3] and jitter to bit length ratio is limited to 13%. Skew effect is minimized by making the foot print of the head to be a square. A reasonable seed layer (5 nm) is inserted between the media and the soft under layer (SUL). The magnetic fly height is also 5 nm. We require the media to be archival against thermal fluctuations for 10 years. Adjacent track erasure does not occur for up to 107 passes of the writer. A non-magnetic grain boundary of 1 nm is included. We also implement lamination in the write pole to minimize remnant write field. For read back, T50 of the read back pulse is estimated using a typical CPP GMR reader and its magnetization noise [4] is calculated.

II. Synthetic Antiferromagnet Exchange Coupled Composite Media

The synthetic antiferromagnet exchange coupled composite media has a three layer (two hard layer and one soft layer) structure as described in [2]. The saturation magnetizations of the hard and soft layers are 500 and 1650 emu/cc, respectively. The average magnetization of the media is 550 emu/cc. Thicknesses of the three layers are all 3.3 nm thus the total thickness is about 10 nm. Antiferromagnetic exchange between the two hard layers is -8×10-6 erg/cc. Ferromagnetic exchange between the hard and soft layer is 107 erg/cc. Switching field distribution of the media is 5%. Grain diameter is about 6 nm. The synthetic antiferromagnet exchange coupled composite media has its ratio of energy barrier to switching field, defined as ξ=2∆E/(MsHsV), equal 2.5. This means that, at the same thermal stability, the switching field can be reduced by 60%. We notice that exchange spring media with graded anisotropy [5] can also reach this ratio. However, it requires thicker media, which reduces the head field gradient, or very low exchange, which lowers the Curie temperature.

III. Writer Design and Results

The geometry of the writer is shown in figure 1. PW denotes the pole width. The writer pole is square shaped at the ABS to minimize skew effect. H0, H1 and H2 are height of down track and cross track flares as shown in figure 1. The cross track flare slope is 45 degree. The down track flare slope is denoted as θ1 and θ2. SG, SW, SL and ST are side shield gap, width, length and thickness, respectively.

Randall Victora The Center for Micromagnetics and Information Technologies (MINT), Electrical and Computer Engineering, University of Minnesota, 200 Union Street SE, Minneapolis, Minnesota 55455 E-mail: victora@ece.umn.edu tel: +1-612-625-1825

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The method we use to estimate the areal density that can be achieved by each writer is the same as discussed in [3] except that this time we include realistic grain boundaries and increase the guard band to allow for head skew. For skew effect, we assume that the maximum skew angle of the writer is 15°. Thus skew effect will force us to increase the track pitch by PW*sin(15) because the pole length equals the pole width PW in our design. Our optimized writer has H0, H1 and H2 equal 60, 80 and 40 nm respectively. Pole width PW is 40 nm. θ1 and θ2 both equal 45°. SG, SW, SL and ST are 20, 160, 200 and 20 nm respectively. The achieved areal density is 1.0 Tb/in2. In the pole tip region, along the cross-track direction, the pole is laminated into two layers magnetically decoupled from each other. This reduces the remnant field by a factor of two but leaves the write field almost unchanged. Table I summarizes the results for the optimized system and the effect of fluctuations in fly height d, media thickness t and seed layer thickness s. Among them, fluctuation of the fly height has the largest effect on areal density. In contrast, fluctuation of H0, H1 and H2 by ±20 nm has little effect. There is great sensitivity to the down track flare angle θ1. Increasing θ1 from 45°to 60° substantially decreases the areal density owing to a loss of write field. Side shield Ms is 800 emu/cc. A value between 600 to 800 emu/cc is acceptable but further increase in side shield Ms will dramatically decrease the areal density because it induces too much side fringe field. The side shield gap is most effective between 20 and 30 nm and the side shield width can have a ±40 nm fluctuation. The free layer of the CPP GMR reader has dimensions 9×30×30 nm3. The gap between free layer and reader shield is 6 nm. We use equation (23) in [6] to estimate T50 and the result is shown in Table I. For the optimized design T50 is 9.2 nm. This is slightly less than the 10.1 nm bit length, and thus the ratio is roughly comparable to current values. The signal to magnetization noise ratio of this reader is estimated to be 35 dB.

REFERENCES

1) R. H. Victora and X. Shen, "Composite media for perpendicular magnetic recording," IEEE Trans. Magn,.41, 537, (2005). 2) S. Hernandez, M. Kapoor and R. H. Victora, “Synthetic antiferromagnet for hard layer of exchange coupled composite

media,” Applied Phys. Letters., 90, 132505, (2007) 3) X. Shen, M. Kapoor, R. Field and R. H. Victora, “Issues in recording exchange coupled composite media”, IEEE Tran.

Magn., 43, 676 (2007) 4) N. Smith and P. Arnett, “White-noise magnetization fluctuations in magnetoresistive heads”, Applied Phys. Letters., 78,

10, 1448, (2001) 5) A. Dobin and H. J. Richter, GA-02 MMM/Intermag Joint Conference, 2006 6) B. Valcu, T. Roscamp and H. Neal Bertram, “Pulse shape, resolution, and signal-to-noise ratio in perpendicular

recording”, IEEE Tran. Magn., 38, 288, (2002)

Fig. 1 Writer geometry

Table 1

Fly height (nm)

Media thickness (nm)

Seed thickness (nm)

Hc (Oe) dH/dx (Oe/nm)

D (nm)

TW (nm)

TP (nm)

BL (nm)

Density (Tb/in2)

BAR T50 (nm)

5 10 5 10300 315 5.9 36 62 10.1 1.0 6.1 9.2

7 10 5 9700 260 6.2 34 62 11.5 0.87 5.4 11.8

10 10 5 9200 180 6.4 30 62 14.7 0.69 4.2 15.3

5 12 5 9800 280 5.6 36 63 9.9 1.0 6.4 9.5

5 15 5 9200 230 5.2 34 63 10.3 0.97 6.1 10.1

5 10 7 10000 300 6.0 36 62 10.4 0.96 6.0 7.6

5 10 10 9300 280 6.3 38 63 10.5 0.94 6.0 ---

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D4

System Modeling in Support of 345 Gb/in2 Areal Density

Byron LENGSFIELD1, Terry OLSON, Paul Van derHEIJDEN, Walt WERESIN, Hoa DO, Ching TSANG, Michael ALEX, Andi MOSER, Bruce WILSON, Thomas THOMSON,

Andreas BERGER, Manfred SCHABES, Yoshihiro IKEDA, Neal BERTRAM, Yimin HSU2, Michael SALO2, Hal ROSEN, Ken TAKANO and Kurt RUBIN.

1) Hitachi GST San Jose Research Center., San Jose, CA 95193, USA 2) Hitachi Global Storage Technologies, San Jose CA 95193, USA

I. INTRODUCTION

The design of a perpendicular recording system involves a complex multidimensional optimization process. The goal of this work is to employ modeling tools in conjunction with parametric and spin-stand experiments to facilitate this task. The system design of the 345 Gb/in2 demonstration first proceeded by developing an understanding of the noise mechanism governing the performance of the current generation of capped media. A hierarchy of micromagnetic models was developed in which the media was first discretized into layers and then into smaller cells. Simulations were compared to measurements of high-resolution MFM domain patterns, hard and easy axis loops. Accelerated Dynamics was used in the simulations of the easy axis loops. The ability to fit the shape of both the hard axis and easy axis loops were found to provide a good set of media parameters which were later refined by fitting spin-stand recording data taken at a modest areal density. Recording simulations were then undertaken using FEM write fields for which head dimensions were obtained by SEM analysis of the write poles employed in the experiments. In the simulations, jitter, T50 and low-frequency MWW were monitored. Squeeze tracks were then simulated in order to insure the on-track jitter and off-track jitter degradation were in accord with experiment. The micromagnetic media models were then used to examine 345Gb/in2 head and media designs. A simple-channel-model (SCM) was used to predict on-track performance and a geometrical 747 model was used to estimate off-track performance in this survey. Both simulations using our SCM and subsequent spin-stand experiments highlighted the importance of reader performance in the optimization of the recording system. The system designs were centered at a bit-aspect-ratio of 5. At the track pitch needed to attain the areal density target, narrow write poles were considered and transition curvature was a major concern. To address this issue, high-resolution MFM studies of recorded transitions resulting from different head designs were compared to simulations.

II. MODELING

In accord with TEM experiments, media with an average core grain diameter of 7.8 nm, a grain size distribution sigma of 21% and grain boundary of 0.8 nm were employed in the micromagnetic simulations. The media consisted of a hard magnetic oxide layer, 14nm thick and a ferromagnetic capping layer, 6nm thick. Each layer was initially discretized into two units. The anisotropy, intergranular exchange and interlayer exchange were varied until a reasonable fit of the hard and easy axis loops was obtained, as can be seen in Figs 1 and 2. The anisotropy field in the capping layer is small but non-zero, a Hk of 5000 Oe and Ms of 450 emu/cm3 provided a reasonable fit to the data. The media parameters were refined by comparing jitter, T50 and particularly MWW to spin-stand experiments. MWW provided a sensitive test of the exchange coupling strength employed in the model. The trends seen in BER measurements were described by our simple-channel-model, for which the resulting BER is a function of three variables: T50/T, jitter/T and head-electronics SNR (HdSNR). The importance of HdSNR is clearly seen in Fig. 3 where T50/T and jitter/T are fixed and HdSNR varied. The micromagnetic model was then used to assess write pole designs. A key concern at this areal density is the optimal control of the track pitch and adjacent-track-erasure.

Dr. Byron H. Lengsfield III Hitachi GST San Jose Research Center E-mail: byron.lengsfieldiii@hitachigst.com fax: 408-717-9065 tel: 408-717-5160 3403 Yerba Buena Rd San Jose, CA 95135, USA

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Fig. 1 Normalized Hard Axis Loop Fig. 2 Normalized Easy Axis Loop

Fig. 3 Simple Channel Model Fig. 4 Experimental 747 Curve at 343 Gb/in2

III SPIN-STAND RESULTS

A number of write head designs employing wrap-around-shields (WAS) were found capable of producing areal densities in the 330-345 Gb/in2 regime. One example [1,2] is shown in Fig. 4 where a narrow read-gap, high performance (HdSNR > 34 dB at bandwidth) TMR reader was employed. Linear densities in the 1300 to 1540 kbpi regime were obtained using different WAS designs in accord with early modeling targets of 1350 kbpi. The largest linear densities were obtained at near contact recording.

REFERENCES

[1] Y. Hsu, et al., “Challenges for Perpendicular Write Heads at High Recording Density”, TMRC 2006, A-04

[2] M. Ho, et al.,“TMR Read Head for High Areal Density Perpendicular Recording Applications”, TMRC 2006, C-03

00.1

0.20.3

0.40.50.6

0.70.8

0.91

3 4 5 6 7Adjacent track pitch (µin)

OTC

( µin

)Linear density: 1536 kbpiData rate: 729.4 Mb/sec

15% OTC

Track pitch: 4.47 µin (113.5 nm)Track density: 223.5 ktpi

56

D5

Exploring Low-Loss Suspension Interconnects for High Data Rates in Hard Disk Drives

1) Reed HENTGES, Hutchinson Technology Inc., reed.hentges@hti.htch.com 2) John PRO, Hutchinson Technology Inc., john.pro@hti.htch.com

3) Michael ROEN, Hutchinson Technology Inc., michael.roen@hti.htch.com 4) Gregory J. VANHECKE, Hutchinson Technology Inc., gregory.vanhecke@hti.htch.com

5) Gregory H. KIMBALL, Texas Instruments, Longmont, CO The introduction of perpendicular recording has placed demands on the preamp-head suspension interconnect on three fronts. Perpendicular recording has allowed the linear density to increase at a constant rate, thereby driving up data rates. The need for higher write over-shoot currents over time has initially slowed with the introduction of PMR, however, the need is likely to grow as magnetic shielding on PMR poles is enhanced along with increases in data rate and media coercivity. Preamplifier power supply voltage limitations, peak write current overshoot requirements and overall preamplifier/interconnect/writer power is already resulting in a trend towards lower impedance interconnects. The suspension interconnect used today is a differentially-driven microstrip transmission line connecting the hard disk drive preamplifier to the magnetic recording head. Low-conductivity stainless steel and significant characteristic impedance discontinuities, inherent with these interconnect designs, present a challenge in delivering large peak overshoot currents at faster rise times through the interconnect. Future suspension interconnect design/technology will need to provide low characteristic impedance at high electrical bandwidth, in part by providing a continuous characteristic impedance in areas that require low mechanical stiffness., while maintaining a small footprint size and low cost of manufacturability. Copper overlayer [1], broadside traces and multi-lead “inter-leaved” interconnects are evaluated on these premises, as potential technologies that achieve low impedance and high bandwidth. Today’s interconnects are made up of a copper, dielectric and stainless steel layer. The stainless steel layer serves as the key structural element as well as the interconnect ground plane. The use of stainless steel as a ground plane leads to significant high frequency losses. This effect is depicted in Fig. 1 a). Removal of this coupling plane (Fig. 1 b)) from below the differentially-driven traces reduces the ohmic loss, but also reduces capacitance significantly. This results in an increase in differential impedance. Combining the two structures from Fig. 1 in various percentages of unbacked to backed (i.e. windowing [2]) produces the electrical design space [3] plotted in Fig. 2. It becomes increasingly difficult to achieve high bandwidth and low impedance due to the increasing trace width and total footprint. A commercial preamplifier model capable of delivering a 100ps (10% -ss to 90% +pk) write current risetime was used to explore a measured set of 66 Ohm interconnects at a fixed overshoot preamplifier setting. These interconnects were of variable bandwidths and were terminated in a generic PMR writer. Results are plotted in Figure 3.

Reed HENTGES Hutchinson Technology Incorporated E-mail: reed.hentges@hti.htch.com fax: (320) 587-1955 tel: (320) 587-3797 x5057 40 West Highland Park Dr. NE, Hutchinson, MN 55350

Fig. 2 Design space for 50mm coupon (interconnect characteristic impedance vs. bandwidth) of structure depicted in figure 1.

Fig. 1a Cross-section E-field plots of a fully backedcovercoat-copper-polyimide stainless steel structure. 1b Fig. 1a with stainless steel removed below traces .

Low Zdiff High BW

57

D5

Fig. 3 Overshoot portion of writer current vs. interconnect bandwidth. A macro model of this preamplifier was used to simulate the same measured set of interconnects to investigate interconnect required voltage, resulting current rise time, and total power consumed by the head and interconnect. The peak overshoot current was fixed at 100mA. The direct benefits of larger interconnect bandwidth can be seen in Table I. These benefits include lower launch voltage, less power consumption and minimal impact to signal rise time. The same preamp macro model setup was then simulated with a measured set of interconnects all having 8 GHz of bandwidth and variable impedances to investigate interconnect power loss after the preamp and relative overshoot. The direct benefits of lower impedances, when bandwidths are equivalent, are increases in peak current overshoot and decreased power consumption by the head/interconnect circuitry. Three different structures, depicted in Figure 4, were used to achieve low impedance and high bandwidth. Figure 5 shows the electrical design space of structures from figures 1 and 4. Electro-magnetic fields generated by structure 4a and 4b are mainly oriented in the vertical direction and adjustments in this direction are used to vary bandwidth. Fields of structure 4c, mainly oriented in the horizontal direction, allow for single-layer circuitry leading to minimized stiffness and manufacturing complexity. Added circuit layers generally lead to increased stiffness and manufacturing complexity.

REFERENCES

1) K. B. Klaassen, J. T. Contreras, J. C. L. van Peppen, “Read/Write Electronics Front-End Systems for Hard Disk Drives,” IEEE Trans. Magn., vol. 40, no. 1, pp.263-268, Jan. 2004. 2) L. Webb, “Controlled Impedance Interconnect Design and Measurements,” TMRC 2000 Digest, Paper A5. 3) J. D. Pro, M. E. Roen, “Characteristic Impedance and Signal Loss Measurements of Head-to-Preamplifier Interconnects,” IEEE Trans. Magn., vol. 42, no. 2, pp. 261-265, Feb. 2006.

T-Line BW V(pk-pk) t_rise Power 1.3 GHz 7.4 V 137ps 112mW 2.0 GHz 6.4 V 132ps 84 mW 3.25 GHz 6.1 V 123ps 76mW 6.0 GHz 5.9 V 115ps 62mW 8.5 GHz 5.7 V 114ps 60mW Ideal 5.3V 114ps 52mW

Table I Required launch voltage, writer current rise time and total power vs. interconnect bandwidth.

Fig. 4 Interconnect structures investigated.Fig. 5 Design space of structures from figures 1 and 4. Structures from Fig. 1, Fig. 4a and Fig. 4c are windowed 0 to 99%. Fig. 4b traces are 99% windowed.

58

D6

Advanced Interconnect Design for High Data Rate Perpendicular Magnetic Recording

W. Don HUBER, W. Curt TIPTON, and Leo C. HWANG

I. INTRODUCTION A change is proposed in the write current waveform for PMR (perpendicular magnetic recording) that halves the presently required bandwidth of the writer interconnects for a given data rate, but requires design changes in the writer amplifier. In the past much attention has been given to maximizing the bandwidth efficiency, η = data rate (bps) / bandwidth (Hz), in the playback or read channel. In general PRML (partial response maximum likelihood) read channels have bandwidth efficiency, η = 2 bps/Hz [1]. In contrast little attention has been given to the bandwidth efficiency of the record or write channel. The focus of this study is to consider maximization of bandwidth efficiency of the writer as the first phase of the task to preserve signal integrity in transferring read and write signals to the magnetic recording head of a disk drive. At increasingly higher data rates achievement of adequate bandwidth in the electrical interconnect becomes an issue in integrating the electrical design with mechanical constraints at low cost. The approach taken is first to review the bandwidth requirements of the PRML read channel particularly for PMR (perpendicular magnetic recording). Next, the write current, IW, waveforms are similarly constructed to those in the read channel from minimal bandwidth constituents that likewise demonstrate the minimum writer bandwidth requirements. Present write current waveforms are asymmetric about the zero-crossing following the method of Ambrico [2] which places a post-cursive overshoot in the direction of the transition; this results in a writer bandwidth efficiency of 1/2 bps/Hz which slightly exceeds the 2/5 bps/Hz due to the less accurate approximation that one should pass the 5th harmonic of the square wave whose half-period is equal to one coded channel bit period. Alternatively, it is shown that by choosing the anti-symmetric case of Best [3] with pre-cursive and post-cursive overshoots one may double the bandwidth efficiency to 1 bps/Hz. Moreover, the rate of change of write current, /WdI dt , at the zero-crossing is approximately 160% higher than that of the present asymmetric case when overshoot is 300% of steady state. Adequately, large /WdI dt and no inter-symbol interference are the main requirements for successful PMR (perpendicular magnetic recording) [4]. PMR writer designs have been investigated for the asymmetric but not the anti-symmetric write current waveform [5]. Another more subtle advantage (not yet shown) may be a reduction of even harmonic distortion in the PMR playback signal due to the pure anti-symmetric write current at the transition. No increase in writer output voltage range (head-room) or bandwidth is required; just the addition of an anticipatory delay to enable the creation of the anti-symmetric overshoots in the vicinity of the write current transition’s zero-crossing.

II. MINIMUM BANDWIDTH CONSTRUCTION OF WRITE CURRENT WAVEFORMS

As was the case in constructing PRML targets from sinc functions one may simply compose the write current waveform by adding PR(½,1,½) pulses (itself a sum of weighted sinc functions) and delayed by ½ the channel bit period, T/2. It has low, relatively non-interactive, side lobes and a finite cutoff frequency 1/T. The weight sequences are taken arbitrarily to approximate the desired waveform. The Fourier transform is simply calculated by

( ) ( ) 2

0,k

W

nj x

I P kk

H H w e πξξ ξ −

=

⎛ ⎞= ⎜ ⎟⎝ ⎠∑ (1)

where ( )PH ξ is the Fourier transform of the PR(½,1,½) pulse with T/2 delay between elements, and .fTξ =

Corresponding AUTHOR W. Don Huber, Western Digital Corporation E-mail: don.huber@wdc.com Fax: 1-408-363-5258 Tel: 1-408-284-7984 5863 Rue Ferrari, San Jose, CA 95138, USA

59

D6 The present day write current waveform as typified in Fig. 1 has an asymmetric transition; there exists neither odd nor even symmetry about the zero-crossing. The dashed lines in Fig. 1(a) show the individual PR(½,1,½) pulses that are superimposed to produce a conventional write current waveform (solid line) where the zero-crossings have channel bit period separations of (1,1,2,3,4) coded channel bit periods; the bit period is two seconds for a 1Hz truncation bandwidth. The overshoot in the direction of the transition produces an asymmetric transition following Ambrico [2]. Because of their asymmetry the zero crossings are shifted forward of the midpoint between the peak locations of the underlying PR(½,1,½) pulses that are indicated by x’s placed on the abscissa. The resulting asymmetric eye pattern shown in Fig. 1(b) has a useful open eye with asymmetric eye heights near transitions. For this asymmetric transition two seconds between transitions are required to preserve a fully open eye; this results in a bandwidth efficiency of ½ bps per Hertz. The eye itself is not symmetric indicating potential weakness of this waveform design. As shown in Fig. 1(c) the normalized truncation bandwidth of the magnitude response is 1/T. The dot on the normalized magnitude response curve indicates the highest frequency -3dB point.

III. DISCUSSION

At a bandwidth efficiency of ½ bps/Hz the asymmetric transition requires 2Hz bandwidth per 1bps data rate. It will be shown that the anti-symmetric transition enables a factor of two improvement in bandwidth efficiency; thus reducing by ½ the required interconnect bandwidth for the same data rate, reducing its cost, and complexity.

REFERENCES

[1] E. R. KRETZMER, “Generalization of a Technique for Binary Data Communication,” IEEE Trans. Comm., Vol. 14, No. 1, Feb-1966, pp. 67-68.

[2] LOUIS E. AMBRICO, “Pulse Crowding Compensation for Magnetic Recording,” U.S. Patent 3,503,059, 24-Mar-1970.

[3] DONALD T. BEST, “Precedent and Subsequent Minor Transitions to Alleviate Pulse Crowding,” U.S. Patent 4,167,761, 11-Sep-1979.

[4] ALEXANDER M. TARATORIN, and KLAAS B. KLAASSEN, “Write Current Rise Time in Perpendicular Recording: An Experimental Study,” IEEE Trans. Magnetics, Vol. 43, No. 2, Feb-2007, pp. 750-755.

[5] WERNER SHOLZ and SHARAT BATRA, “Effect of Write Current Waveform on Magnetization and Head-Field Dynamics of Perpendicular Recording Heads,” IEEE Trans. Magnetics, Vol. 42, No. 10, Oct-2006, pp. 2264-2266.

0 5 10 15 20 25Normalized Time tT 3

2

1

0

1

2

3

edutilpm

A

(a) Asymmetric Write Current at η = ½

0.25 0.5 0.75 1 1.25 1.5 1.75 2Normalized Time tT 3

2

1

0

1

2

3

edutilpm

A

Eye Width Eye Height(+ transition)

Eye Height(- transition)

0.25 0.5 0.75 1 1.25 1.5 1.75 2Normalized Time tT 3

2

1

0

1

2

3

edutilpm

A

Eye Width Eye Height(+ transition)

Eye Height(- transition)

(b) Eye Pattern at η = ½

0.2 0.4 0.6 0.8 1Normalized Frequency fT

60

50

40

30

20

10

0

dezilamro

Nsedutinga

MBd

(c) Normalized magnitude response

Fig. 1 – A (1,1,2,3,4) transition sequence;

asymmetric write current, resultant eye pattern, and magnitude response

60

E1

ITERATIVE DECODING BASED ON ERROR-PATTERN CORRECTION

Hakim ALHUSSIEN, Jihoon PARK and Jaekyun MOON University of Minnesota, Minneapolis, MN,USA

hakimh@umn.edu; jhpark@umn.edu; moon@umn.edu.

I. MOTIVATION AND SYSTEM DESCRIPTION

The bit error rate (BER) cliff of turbo equalizer (TE) systems approaches the capacity of partial response (PR) channels in the low signal-to-noise (SNR) region, but at higher SNRs the TE reaches an error floor well above the standard target sector error rate of recording systems [1]. An outer Reed-Solomon (RS) code can be used to reduce the SER if the TE output symbol error statistics are not bursty in nature.

The turbo equalizer is typically employed with channel precoding that makes the inner channel appear recursive. This results in a reduced error floor and an increased iterative gain in lower BER regions. However, the major drawback of channel precoding is that precoders tend to increase the burstiness of the inner turbo system and thus decrease the potential SER gain promised by the outer RS code. In this paper, we investigate a novel TE setup incorporating a non-interleaved inner high-rate error-pattern-correcting code (EPCC) tailored to the PR channel in addition to an interleaved outer convolutional code. Our objective is to enhance the iterative gain of the non-precoded TE without getting into the error burst issue, in hopes of employing an outer RS code to be able to enhance the overall system performance.

The EPCC proposed in [2] and [3] has been designed such that for a given set of L dominant error cluster pattern polynomials, ei(x), i = 1, …, L, inherent in a PR channel, any single dominant error pattern as well as a significant portion of their multiple occurrences can be corrected. While the high-rate linear block EPCC code has poor minimum distance, it is effective at targeting a relatively small set of known, dominant error patterns for the PR channel, utilizing not only algebraic information of the captured syndrome but also soft information available at the channel detector.

While a single dominant error-pattern event is completely identified by the captured syndrome, a list of likely multiple-error-pattern events can be established based on both the captured syndrome and the error-pattern-based local correlator that makes use of the distance metric as well as the a priori probability generated from the outer convolutional decoder [2]. Among the generated list of multiple-error-pattern events and corresponding error positions, the maximum likelihood error-pattern event is then determined. Based on the decision of the EPCC-based list decoder, the reliability measures at the output of the channel detector are updated to generate the extrinsic information of the channel-detector matched decoder which serves as a priori information for the convolutional decoder. See Fig.1.

BCJRdetector EPCC-based List Decoderrk

Channel-detector matched decoder

∏-1 Convolutionaldecoder

∏

−

+

−

+

Fig. 1: Turbo equalizer based on EPCC list decoder

JAEKYUN MOON

Electrical and Computer Engineering, University of Minnesota E-mail: moon@umn.edu fax: 1-612-626-1050, tel: +1-612-625-7322 Minneapolis, MN 55455, USA Preferred category: #

61

E1

II. NUMERICAL RESULTS

We compare the BER performance of the TE-EPCC system and the non-precoded TE in a PR channel response 5+6D−D3 corrupted by additive white Gaussian noise. The interleaver size is 4301 for both cases, where seven (630,616) EPCC codewords are bit-interleaved to form one sector. An outer (7,5)8 RSC with punctured rate 8/9 is used for the TE. The TE-EPCC operates at the same rate but divides the correction power between a punctured 10/11 outer RSC and an inner 616/630 EPCC. For the simulation results presented here, the code rate penalty is proportional to the inverse of the code rate.

Simulation results show that the conventional TE BER saturates by the second iteration and does not improve henceforth, while the TE-EPCC improves its BER through the fourth iteration. The results also show that at a BER of 10-4, TE-EPCC is 3.5 dB better than the uncoded system, outperforms the conventional TE by 0.5 dB, and is 2 dB away from the uniformly and independently distributed input capacity CUID of the 5+6D−D3 channel. Also, investigation of the symbol burst statistics of the TE-EPCC shows that there exist no significantly long symbol error bursts.

Fig. 2: BER comparison of the TE-EPCC and unprecoded TE

III. CONCLUSION

We enhanced the performance of TE by reallocating a small portion of the outer convolutional code redundancy to an inner high rate EPCC code that is tailored to the channel. The inner EPCC code attempts to correct any single dominant error pattern and a considerable portion of their multiple occurrences. As a result, saturation of iterative turbo gain is delayed to further improve the BER cliff region.

REFERENCES

[1] T. V. Souvignier, M. Öberg, P. H. Siegel, R. E. Swanson, and J. K. Wolf, “Turbo decoding for partial response channels,” IEEE Trans. Commun., vol. 48, pp. 1297–1308, Aug. 2000.

[2] J. Park and J. Moon, “High-Rate Error-Pattern-Correcting Cyclic Code,” IEEE Trans. Inform. Theory, submitted.

[3] J. Park and J. Moon, “A New Class of Error-Pattern-Correcting Codes Capable of Handling Multiple Error Occurrences,” IEEE Trans. Magn., Jun. 2007, to be published.

62

E2

MICROSCOPIC AND MACROSCOPIC APPROACHES IN SECTOR FAILURE RATE ESTIMATION

Alexander KUZNETSOV1 and Raman VENKATARAMANI2

1) Seagate Research, 1251 Waterfront Place, Pittsburgh, PA, Alexander.V.Kuznetsov@Seagate.com 2) Seagate Research, 1251 Waterfront Place, Pittsburgh, PA, Raman.C.Venkataramani@Seagate.com

I. INTRODUCTION

The sector failure rate (SFR) is extremely small at normal operating conditions of hard disc drives. In practice it cannot be obtained by counting as that would require numerous simulations. Therefore, appropriate statistical models are applied for the distribution of error symbols in a sector to estimate the SFR. In this paper we look at the underlying philosophy of existing estimation methods and classify them into macroscopic and microscopic types. We show how to estimate the model parameters optimally from a library of sample error indicator vectors. We observe that the microscopic models are well suited for certain iterative channels.

II. MACROSCOPIC AND MICROSCOPIC MODELS

Fundamentally, all models for error vectors may be classified as either microscopic or macroscopic models. A microscopic model captures the precise correlation between symbol errors locations while a macroscopic model captures the weight of the error indicator vectors alone ignoring the actual bit or symbol error locations. In general, precise microscopic models are difficult to find for iterative coded channels with interleavers due to the complex long range correlations present in the symbol errors. In contrast, macroscopic models are also simpler to analyze and are generally universal in the sense that it can work well for a variety of codes but they require larger training data sets.

An example of the macroscopic model is the multinomial model in which (a) an error indicator vector consists of N independent error events, and (b) a single error event is of a string of up to L symbols in error. The resulting error vector weight has the multinomial distribution. This is evidently a macroscopic model. Sometimes, the symbol errors are modeled as a Markov random process. An example is the Gilbert model [1, 2] or the generalized Gilbert model [3]. These models are microscopic because they explicitly model the error locations, not the error weight. An example of a slightly richer model than the Gilbert model is shown in Figure 1. According to this model, the probability of seeing a symbol error is 1mq + where m is the run-length of preceding symbol errors leading in that error event. For reduced model complexity we let m Mq q= for all m≥M where M is a fixed parameter. When the chain returns to the zero state from the nonzero state m, the generation of an error event E(m) is completed by attaching the final “0” to the run of m consecutive ones. This is a microscopic model because it characterizes the symbol error locations.

Having chosen any model (microscopic or macroscopic) its parameters can be estimated from the library of actual error vectors as follows. Let the data set consists of K error indicator vectors. Let kr and kr denote the histogram of the error vector weights and the modeled weight distribution respectively. The optimal estimate of the model parameters is the so called minimum relative entropy (MRE) solution where we minimize the Kullback-Liebler distance between the two weight distributions [4].

ˆ ˆ ˆmin ( || ( )) log( ( ) / )n n nn

D r r p r r p r= ∑

Alexander KUZNETSOV Seagate Research E-mail: Alexander.V.Kuznetsov@Seagate.com fax: +1-412-918-7111 tel: +1-412-918-7157 1251 Waterfront Place, Pittsburgh, PA

63

E2

III. MICROSCOPIC MODEL WITH TWO COMPONENT TYPES

We shall now extend multinomial model to SFR estimation of iterative channels as well. Let E(m) denote an error event (EE) of length m: it consists of m≥1 ones followed by a zero, e.g., E(3)=1110. A sequence of n≥1 consecutive zeros I(n) is called an error-free run of length n. Thus, we can always parse an error indicator vector into a unique sequence of interlacing error events and error free runs as follows: 1 1 2 2( , , , , , , )L LE I E I E Iξ = L .

Main Assumptions: The events are independent identically distributed random objects and the number of such error events in a sector is an independent random variable. Assume that Ei are described by the microscopic model described in Section III-B. Estimation of the parameters of the Markov model described above of can be done using the minimum relative entropy method described in Section III-C. We do not assume that PDFs of error events and error free runs are identical.

The word failure rate is ( ) ( ) ( , )W Wk

T Q k T kρ ρ= ∑ where ( )Q k and ( , )W T kρ are the distribution of number of

error events per word and the conditional word failure rate given k error events in the word. The latter quantity is computed using the MRE method described in Section II. The PDF Q(k) is estimated from statistics obtained from real or simulated data however its tail is extrapolated using a pre-specified distribution. Numerically, iterative channels using TPC and LDPC codes have exponential tails ( ( ) kQ k e λ−= ) and iterative channels using SPC have tails with a Poisson distribution ( ( ) / !kQ k e kλλ −= ). The parameter λ is estimated to fit the observed tails.

IV. SIMULATIONS

In the following example we evaluate the performance of the descriptive and predictive capabilities of various SFR estimation methods for a TPC system operating at 24dB. Each sector consists of 500 symbols including the ECC parity symbols. The full data set contains 79111 sectors and the partial data set contains 4% of this data. Figure 5 shows the SFR estimates sing several methods from the partial data and counted values from full data set. These methods appear to be consistent with each other and match the extrapolated counted values well.

Figure 1: Model for error event

Figure 2: SFR estimates for the TPC system

REFERENCES

1) J. R. Yee and E. J. Weldon, “Evaluation of the performance of error-correcting codes on a Gilbert channel,” IEEE Trans. Comm., vol. 43, pp. 2316–23, Aug. 1995. 2) E. N. Gilbert, “Capacity of burst noise channel,” Bell Systems Tech. J., vol. 39, pp. 1253–66, Sept. 1960. 3) J. K. Wolf, “ECC performance of interleaved RS codes with burst errors,” IEEE Trans. Magnetics, vol. 34, pp. 75–79, Jan. 1998. 4) T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991.

64

E3

A NEW READ HEAD MODEL FOR PATTERNED MEDIA STORAGE

Seyhan KARAKULAK, Paul H. SIEGEL, Jack K. WOLF and H. Neal BERTRAM Center for Magnetic Recording Research, University of California, San Diego, La Jolla, CA 92093, USA

It is conceivable that early generations of patterned media will utilize read heads whose dimensions are several times larger than an “island” of magnetization. For such a scenario, we propose a “3 islands per read head” model where the output from the read head is a function of the magnetization from three independently written tracks of islands. The readback signal is determined from a finite track-width magnetoresistive (MR) head model using reciprocity calculations [1], and two noise sources island position jitter and AWGN electronics noise are considered. By sampling the noisy signal at intervals corresponding to the down-track island separation, we obtain a discrete-time readback channel model whose performance, under partial-response equalization and maximum-likelihood sequence detection, is compared to that of a single island per read head model [2], [3], [4].

The magnetized islands are assumed to be configured in a square grid, with each island representing a single bit. Islands are assumed to be square, with side length s. A track consists of three parallel sub-tracks, and the read head, when centered over the middle sub-track, spans a specified fraction of the outer sub-tracks, as shown schematically in Fig. 1. The readback signal linearly combines contributions from each island in a 3×3 array, reflecting the geometry of the read head and properties of the recording medium. We can control the inter-island interference in the cross-track direction by varying W and in the down-track direction by varying g. For example, Fig. 3 shows the surface plot of the head potential distribution versus down-track and cross-track distance for a shielded MR head with infinitely wide shields, assuming width W=70nm, thickness t=3nm, and gap length g=35nm, with effective flying height 5nm. We ignore interference from adjacent tracks.

The discrete-time readback model assumes a center-to-center island spacing B=2s in both directions, and it can be represented by a 3×3 channel response matrix, H=[h1,h2,h3], where each hi is a 3-tuple of real numbers. The assumed symmetries of the head-medium geometries yield a channel response matrix of the form

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

rprtqtrpr

H . (1)

Each cross-track triplet of islands represents a recorded binary 3-vector, or “symbol” x. The discrete-time readback model then takes the form of a one-dimensional linear channel with symbols xi as inputs and a scalar y as the output, with input-output relationship determined by the channel response matrix, as depicted in Fig. 3.

If the bits on the islands can be written and read independently, there will be eight possible recorded symbols. However, symmetries of the channel response matrix can reduce the number of distinguishable symbols. For example, in (2), we show three channel response matrices for a head with a gap small enough to eliminate down-track inter-island interference. The matrix H1 corresponds to a head width slightly larger than the island width, in other words, a single island per read-head model. The matrix H2 represents a head that fully spans islands in all three subtracks, while H3 characterizes a head that only partially spans the islands in the outer sub-tracks.

Fig. 1. “3 islands per read head” model. Fig. 2. Head potential distribution versus down-track and cross-track

Track

Sub track 1

Sub track 2

Sub track 3

-100-50

050

100

-100-50

0

50100

0

0.2

0.4

0.6

0.8

down-trackcross-track

W=70nm, t=3nm, g=35nm, y=5nm

65

E3

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

000048.0000

1H ⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

048.0048.0048.0

2H ⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

016.0048.0016.0

3H (2)

The symmetries of H2 and H3 reduce the number of distinguishable symbols to four and six, respectively. The three matrices therefore correspond to recording densities of 1 bit/island, 2/3 bit/island and log2(6)/3 ≈ 0.86 bit/island, respectively.

We assume that the dominant component of the medium noise arises from the random variations in the island locations. This “island jitter noise” is non-stationary and characterized by the jitter noise variance, σj

2. The jitter noise and AWGN are assumed to be independent and additive. Fig. 4 compares the symbol error rates for the three channel response matrices in (2) in the absence of jitter noise, as a function of σ, the standard deviation of the AWGN. Since these cases involve no down-track inter-island interference, the probability of symbol error is given exactly by a formula similar to that used to characterize the performance of a pulse amplitude modulation (PAM) communication system. Since the minimum Euclidean distance between noiseless readback signals corresponding to distinct symbols is smaller for H3 than for H1 and H2, the probability of a symbol error is largest for H3. Fig. 5 shows the symbol error rate for H1 and H2 as a function of the normalized jitter noise standard deviation, σj/B, in the presence of AWGN with σ =0.08. Results for channel response matrices that include the effects of down-track interference will also be presented.

REFERENCES

1) Samuel W. Yuan and H. Neal Bertram, “Off-Track Spacing Loss of Shielded MR Heads,” IEEE Trans. Magn., vol. 30, no. 3, pp. 1267-1273, May 1994.

2) Paul W. Nutter, Ioannis T. Ntokas and Barry K. Middleton, “An Investigation of the Effects of Media Characteristics on Read Channel Performance for Patterned Media Storage,” IEEE Trans. Magn., vol. 41, no. 11, Nov. 2005.

3) Paul W. Nutter, , Ioannis T. Ntokas and Barry K. Middleton and David T. Wilton, “Effect of Island Distribution on Error Rate Performance in Patterned Media,” IEEE Trans. Magn., vol. 41 no. 10, Oct. 2005.

4) J. Richter, A. Y. Dobin, O. Heinonen, K. Z. Gao, R. J. M. v. d. Veerdonk, R. T. Lynch, J. Xue, D. Weller, P. Asselin, M. F. Erden, and R. M. Brockie, “Recording on Bit-Patterned Media at Densities of 1Tb/in2 and Beyond,” IEEE Trans. Magn., vol. 42, no. 10, Oct. 2006.

Fig. 5. Probability of a symbol error for H1 and H2 versus normalized jitter noise (σj/B), in the presence of AWGN with σ =0.08.

Seyhan KARAKULAK, Center for Magnetic Recording Research, University of California, San Diego 9500 Gilman Drive, La Jolla, CA 92093-0401, USA Fax: +1-858-534-2720, Tel: +1-858-534-6216, E-mail: skarakul@ucsd.edu

xi+1 . h3y

xi xi-1

D

h2

h1

xi . h2

xi-1. h1

xi+1 h3+

D

0.075 0.08 0.085 0.09 0.095 0.110-10

10-8

10-6

10-4

10-2

100

σ

Pro

babi

lity

of a

Sym

bol E

rror

H1

H2

H3

0 0.02 0.04 0.06 0.08 0.110-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

σj/B

Pro

babi

lity

of a

Sym

bol E

rror

H2

H1

Fig. 4. Probability of a symbol error for H1, H2 and H3 as a function of AWGN.

Fig. 3. Discrete-time read-head channel model.

66

E4

VITERBI DETECTION ALGORITHM FOR DATA-DEPENDENT NON-MARKOV READ CHANNELS

Sam Gratrix2, Robert Jackson1,2, Tom Parnell1,2 and Oleg Zaboronski1,2

1. Department of Mathematics, University of Warwick. Gibbet Hill Road, Coventry CV4 7AL, UK oleg.zaboronski@arithmatica.com

2. Arithmatica Ltd, Haseley Business Centre, Warwick UK. It is commonly accepted that in perpendicular magnetic read channel noise is both correlated and data dependent. For example, up to 90 percent of channel noise is caused by phase jitter which is data dependent in nature and leads, via inter-symbol interference (ISI), to correlations between consecutive noise samples. The current state-of-the-art Viterbi detectors are built on the assumption that channel noise is Markov with Markov length L and that the statistics of noise depends on D+1 data bits, where D is called data-dependent length. The corresponding Viterbi detector has 2L+D states. The analysis of several industrial perpendicular channel models shows that L+D is close to 8. This value is expected to grow further with density. It is clearly impossible to afford detectors with 256 or more states inside the read channel. Our analysis of the perpendicular channel with strong jitter shows that the best model for the corresponding noise is conditionally Gaussian with data-dependent banded correlation matrices. This model is not Markov (L is infinite). In the paper below we derive a new type of Viterbi detector for such a channel and analyse its performance. At the heart of the new detector is the module performing on-the-fly Cholesky factorization of banded correlation matrices conditioned on the surviving paths.

Assuming that channel noise is Gaussian, one can write the following probability distribution function (PDF) of noisy samples

),...,,( 11 nnnn NN −=r

conditional on data sequence ),...,,( 11 xxxx NN −=r

:

(1) where )(xCN

ris data-dependent correlation matrix, ( ) ,|

0,, ≥−−=jijNiNijN xnnEC r

and )()( 1 xCxV NNrr −= is data-

dependent variance matrix. As written, PDF (1) is not suitable for the search of the most likely data sequence using a Viterbi algorithm (VA). An alternative representation of (1) is obtained by using a product rule and the Matrix Inversion Lemma :

(2) ( )( )

,)()(2

1exp2| 22

12 ⎟

⎟⎠

⎞⎜⎜⎝

⎛−= ∏

=

xxx

xnP kk

N

k kN

rrr

rr ησσ

π

where we used the following notations :

(3) ( ))(det

)(det

1

2

xCxC

xk

kr

rr

−

=σ ,

(4) ( ) ( )∑ > −−=0 , ,

m mkmkkk nxbnx rrη

(5) ),()(1 xUxVb kkkrrrr

−=

(6) ( ) ( ) .0,)()( , >= − mxCxU mkkkmkrrr

It follows from (2) that ( ) .

2 )(| kllk xxE δσηη rr= Therefore, (2) represents a statement of whitening theorem for a

general data-dependent Gaussian process .nr The problem of finding the most likely data sequence can be now solved by employing the Viterbi algorithm with branch metric

(7) ).(log)()(2

1)( 222 xx

xxBM kk

kk

rrr

r σησ

+=

,)(21exp

)(det)2(

)|( ⎟⎠⎞

⎜⎝⎛−= nxVn

xCxnP N

N

N

Nrrr

rrr π

67

E4 As the sum in the right hand side of (4) has O(N) terms, Viterbi detector equipped with branch metric (7) has infinitely many states. To arrive at an implementable detector with finitely many states, the sum in (4) has to be truncated using an appropriate optimality criterion. Such a truncation will provide a realistic approximation of the original channel noise process only if coefficients )(, xb mk

r decay quickly enough as index m increases, i. e. if channel noise process is close to Markov. The green

curve in Fig. 1 shows the decay of these coefficients for a model perpendicular channel characterized by a tanh isolated pulse shape, jitter mixture equal to 90% and normalized channel density 2.50. One can see the decay of b-coefficients is quite slow and it is necessary to retain about ten terms of expansion (4) in order to faithfully represent channel noise correlations. The corresponding optimal Viterbi detector will need at least 210 states, which is clearly unrealistic. We conclude that perpendicular channel noise is essentially non-Markov. An alternative representation of whitened noise variables )(xk

rη which does not rely on Markovian nature of channel noise can be obtained by treating relations (4) as a lower triangular system of linear equations with respect to original noise variables kn . This system has a unique solution:

(8) ∑>

−+=0

, ),()()(m

mkmkkk xxnx rrr ηκη

where explicit expressions for coefficients κ can be obtained using an orthogonality relation between η ’s. The most important property of coefficients κ is that there are finitely many terms in expansion (8) for a strictly banded correlation matrix of channel noise. As it turns out, correlations in a perpendicular magnetic channel are well approximated by banded correlation matrices with the number of bands determined by ISI length. As a result, coefficients mk ,κ quickly decay as index m increases, c. f. the red curve in Fig. 1.

We conclude that Viterbi detector equipped with data-dependent IIR whitening filters whose taps are chosen according to an optimal truncation of (8) should outperform a Viterbi detector with data-dependent FIR whitening filters with the same number of taps chosen according to an optimal truncation of (4). This conclusion is supported by numerical simulations for the model channel described above. Here the Viterbi detector with 3-tap IIR whitening filters outperforms Viterbi detector with 3-tap FIR whitening filters by more than 0.6 dB at BER=10-4, see Fig. 2.

Fig. 1 Fig. 2

Dr. Oleg Zaboronski, Department of Mathematics, University of Warwick and Arithmatica LTD; Tel: +441926484024; Fax: +442476537028; e-mail: oleg.zaboronski@arithmatica.com and olegz@maths.warwick.ac.uk

68

E5

ROLE OF MEDIA DAMPING IN A RECORDING SYSTEM

Sharat Batra, Thomas Roscamp, Werner Scholz Seagate Technology, 1251 Waterfront Place, Pittsburgh, Pennsylvania 15222-4215, USA.

Dynamical effects in recording system are becoming important as data rates are increased above 2 – 3 Gbit/s. The system needs to be designed such that the media is stable at room temperature and is writeable at high data rates and high areal density. High areal density requires that SNR be improved by going to smaller grain size that requires an increase in the medium anisotropy to provide adequate thermal stability for data storage. We believe that understanding the role of media damping and its optimization is critical for future recording systems. We have used a micromagnetic model [1] that simulates recording on a Stoner-Wohlfarth (SW) type perpendicular recording media. The model includes demagnetization, inter-granular exchange, applied field and the thermal fluctuations fields. We use a FEM head field to record a footprint on a stationary media over a range of pulse widths from 50 ps up to 100 ns. This range can be extended and is limited only by the computation time. In figure 1, we show our results for recording footprint for pulse durations in the range of 100 ps to 10 ns for a given head field. The maximum effective field (Heff) for this head at a distance of 10 nm from the ABS at the trailing edge of the pole is calculated to be 1.3 T. The relevant media parameters are 4πMs of 259 emu/cm3, thickness of 15 nm, and grain size of 7 nm. Anisotropy field HK of 15 kOe and Gilbert damping constant (a) of 0.1. In addition, a log-normal grain size distribution of 20%, a log-normal distribution in the crystalline anisotropy field of 10% in magnitude and a Gaussian distribution for its orientation of 3.5 degree is assumed. As the pulse duration is reduced from 1 ns to 100 ps for this media, an incomplete saturation of media is observed where grains in the middle of transition are not even switched. This will result in a very significant degradation of recording performance, as incomplete saturation of the media at small pulse duration will result in a large transition jitter and DC noise. We use the footprint approach with scaled head field as a function of pulse duration to plot the dynamical coercivity of the media. We see a large increase in the magnitude of the field to saturate the media (> 0.95 Ms) as defined by a average My of the grains in the footprint as a function of pulse duration. Figure 2 shows a plot of field magnitude as a function of pulse duration. As in previous works [2,3,4], we observe two distinct regions in the dynamical coercivity plot. The Neel-Arrhenius like model [4] can describe the long time behavior for thermal stability as well as the magnitude of the field needed to saturate the media. The region below 500 ps is the dynamical switching regime, where a significantly larger head field is needed to completely saturate the media. As field is increased to saturate the media, we find that the written width of the track increases significantly, which will result in a significant adjacent track erasure and correspondingly a lower track density. We believe that for a high data rate and high areal density recording system, the recording system must be maintained in a regime where dynamical effects do not significantly increase the head field required for saturated writing. We have looked at the fitting of our footprint data in the long time duration described by the Neel-Arrhenius model and observe that better fit is observed by the modified “increased” thermal stability factor which includes the demagnetization field. As the grains are switched in the process of footprint writing, it becomes harder to switch last few grains as they experience demagnetization field opposing the head field, thereby requiring additional head field. This behavior modifies the “dynamic coercivity” plot and results in a larger thermal stability factor. In order to confirm this observation, we have also modeled the remanent coercivity by applying a reverse uniform field as a function of pulse duration as is often done [3,5] to obtain thermal stability factor. We find that for same media, the long time behavior of remanent coercivity is defined by the thermal stability factor KuV/kBT. We have then looked at the dependence of dynamic coercivity as a function of media damping. This is plotted in figure 3 for three different values of damping. We observe that at higher damping values, the onset of dynamical effects occurs at shorter pulse duration. In other words, the media with higher damping will have lower dynamic coercivity at high data rates. We highlight that the onset of dynamical effects is related to a decrease in the attempt frequency, which is related to how fast the energy can be removed from the spin system. Within the context of LLG with critical damping value of 1, the system will reduce its spin energy faster with increasing value of damping up to a critical damping value of 1.

Sharat Batra 1251 Waterfront Place Pittsburgh, PA, 15222-4215 Sharat.Batra@Seagate.com

69

E5 We have also carefully looked at the effects of distribution in media magnetic properties such as HK, exchange and temperature and these effects will be discussed in detail in full paper. We observe that thermal effects vanish at T=0K as expected and gets worse as temperature is raised. This paper will also discuss the effect of damping on the transition noise and transition parameter “a” [1]. [1] Sharat Batra, Werner Scholz, Thomas Roscamp, “Effect of thermal fluctuations on the noise performance of a

perpendicular recording system”, J. Appl. Phys., vol. 99, 08E706 (2006) [2] H. N. Bertram, X. Wang and V. Safonov, “Dynamical-Thermal effects in Thin Film Media”, IEEE Trans. Magn., vol. 37,

no. 4, pp. 1521-1527, 2001. [3] D. Weller and A. Moser, “Thermal effect limits in Ultrahigh-density magnetic recording”, IEEE Trans. Magn., vol. 35, no.

6, pp. 4423-4439, 1999. [4] H. N. Bertram and Q. Peng “Numerical simulations of the effect of record field pulse length on medium coercivity at Finite

temperatures”, IEEE Trans. Magn., vol. 34, no. 4, pp. 1543-1545, 1998. [5] M.P.Sharrock, “Time dependence of switching fields in magnetic recording media”, J. Appl. Phys., vol. 76(10), 6413-6418

(1994)

Figure 2: Footprint writing as a function of pulse duration for a fixed head field. At short pulse duration, incomplete writing will result in poor transition jitter and a large DC noise.

Figure 2: Shows dynamic coercivity using thefootprint writing. For same media, we have modeledincrease in remanent coercivity as a function of pulseduration.

Figure 3: Dynamic coercivity plots for 3 differentvalues of damping for a media with HK = 15 kOe andMs = 400 emu/cm3.

10 ns 1 ns 500 ps 300 ps 100 ps10 ns 1 ns 500 ps 300 ps 100 ps

0

0.5

1

1.5

2

2.5

3

3.5

4

1 100 10000 1000000

pulse duration (log (ps))

Nor

mal

ized

Fie

ld (H

K) Footprint writing

Footprint data fitting Remanence CoercivityArrhenius fit*0.9

00.5

11.5

22.5

33.5

44.5

5

1 10 100 1000 10000 100000

Time (log (ps))

Hcr

/HK

Damping 0.1Damping 0.02Damping 0.5

70

F1

TOWARDS MAXIMUM LIKELIHOOD SOFT DECISION DECODING OF THE (255,239) REED SOLOMON CODE

Wenyi Jin1 and Marc Fossorier2

1) LSI Corporation, Milpitas, California, USA, wenyi.jin@lsi.com 2) University of Hawaii at Manoa, Honolulu, Hawaii, USA, marc@aravis.eng.hawaii.edu

I. INTRODUCTION

The (255,239) Reed Solomon code is one of the most popular channel codes used in practice. Traditional hard decision decoding algorithms are efficiently used for the decoding of this code. To achieve better performance, many efforts have been made to exploit efficient soft-decision decoding algorithms. However, the performance of the various proposed soft-decision decoding algorithms is still far away from that of maximum likelihood decoding (MLD). In this paper, we investigate a new method to efficiently improve the performance of the box and match algorithm (BMA)[1], which is one of the efficient most reliable basis (MRB) reprocessing algorithms. For 2≥i ,

),( ksiBMA − has time complexity )( 1+inO and space complexity )2( nO ks− , where i is the order of BMA, n is the length of the code, k is the code dimension and s is control band parameter used by BMA [1]. The proposed improved ),( ksiBMA − can approach or even outperform ),1( ksiBMA −+ without increasing the memory size. We denote this type of algorithm as enhanced ),( ksiBMA − . Simulation results shows that the decoding performance of enhanced ),( ksiBMA − can approach that of MLD.

II. BMA

BMA is an enhanced ordered statistic decoding (OSD) algorithm. The BMA roughly reduces the computational cost of the OSD algorithm [2] by its squared root at the expense of memory. In addition to considering all the codewords associated with error patterns of Hamming weight at most i on the MRB, the BMA with order i also considers all the codewords associated with error patterns of Hamming weight at most i2 on the s most reliable positions (MRPs).

BMA is a list decoding algorithm. Both the list size and the memory increase exponentially with the order i . The largest order for real time decoding of the (255,239) Reed Solomon code with BMA is 2. But ),2( ksBMA − is not enough to achieve a target WER 1210− at SNR=5.6dB (near MLD) for practical value of ks − . To achieve better performance, we introduce efficient methods to efficiently enhance the decoding capability of BMA.

III. ENHANCED BMA

Define the control band as the region from position k to position 1−s in the ordered sequence. The matching procedure of BMA is simplified by constructing a reliable control band that is error free with high probability. We denote it as zero matching. This reduced matching introduces a controlled error floor which we can tightly estimate analytically. Next we enhance the ),2( ksBMA − in an efficient way such that the decoding performance can approach that of ),3( ksBMA − with linear increase in complexity. The enhanced algorithm is denoted as ),2( ksEBMA − . Borrowing the concept of biasing introduced in [3], we further enhance the ),2( ksEBMA − by randomly biasing the MRB. The resultant algorithm is denoted as ),2( ksEBMABM −− , which has linearly increased complexity with respect to ),2( ksEBMA − (as based on the same Gaussian elimination).

),2( ksEBMABM −− can match the performance of ),3( ksBMA − . Both the number of processed candidates and the memory are much smaller than that of ),3( ksBMA − .

Marc Fossorier University of Hawaii at Manoa E-mail: marc@aravis.eng.hawaii.edu fax: 808-956-3507 tel: 808-956-9741 Post 205H, 1680 East-West Road, Honolulu, HI, 96822

71

F1

However it is still not enough as compared with the performance of MLD of the (255,239) Reed Solomon code at the WER of 1210− : 5.6dB is required for MLD, 6.8 dB is required for )22,2(BMA , 6.5 dB is required for

)22,2(EBMA and 6.25dB is required for )22,3(BMA .

We then further improve the decoding performance by biasing the entire block. The improved algorithm is denoted as biased block EBMA ( ),2( ksEBMABB −− ), which can push the performance towards that of MLD. The complexity of ),2( ksEBMABB −− is larger than that of ),2( ksEBMABM −− since multiple Gaussian eliminations are required. However ),2( ksEBMABB −− can outperform ),3( ksBMA − . The average decoding complexity of enhanced BMA can be efficiently reduced with a probabilistic sufficient condition (PSC) [4]. This PSC introduces another controlled error floor.

Figure 1 depicts the performance of )22,2(EBMABB − with PSC for the decoding of (255,239) Reed Solomon code. The error performance of all proposed algorithms can be tightly bounded analytically.

Figure 1. Performance of )22,2(EBMABB − for the decoding of (255,239) RS code

REFERENCES

1) A.Valembois and M.Fossorier, "Box and Match Techniques Applied to Soft Decision Decoding,'' IEEE Trans. Inform. Theory, vol. 50, pp. 796-810, May 2004.

2) M.Fossorier and S.Lin, ''Soft Decision Decoding of Linear Block Codes Based on Ordered Statistics,'' IEEE Trans. Inform. Theory, vol. 41, pp.~1379-1396, Sept. 1995.

3) W.Jin and M.Fossorier, “Reliability-Based Soft-Decision Decoding with Multiple Biases,” IEEE Trans. on Info. Theory, pp 105-120, Jan. 2007

4) W.Jin and M.Fossorier, “Probabilistic Sufficient Conditions on Optimality for Reliability Based Decoding of Linear Block Codes,” IEEE Int. Symp. Inform. Theory, July. 2006.

72

F2

PERFORMANCE AND DECODING COMPLEXITY OF NONBINARY LDPC CODES FOR MAGNETIC RECORDING

Wu CHANG and J. R. CRUZ

The University of Oklahoma, Norman, OK 73019, USA wuchang, jcruz@ou.edu

I. INTRODUCTION

Binary low-density parity-check (LDPC) codes are being considered for possible replacement of the widely used Reed-Solomon (RS) codes in the next generation of read-channel architectures for perpendicular magnetic recording channels (PMRCs). These LDPC-only solutions provide substantial coding gains over RS codes, at a considerable cost in complexity. Such architectures would be more attractive for high-end applications, if the coding gains over current RS-only solutions were significantly higher. One possible step in that direction is to consider nonbinary LDPC codes, which have been shown to provide remarkable coding gains on various magnetic recording channels. However, the decoding complexity of q-ary LDPC codes was thought to be prohibitively high for practical applications. We investigate the complexity of decoding q-ary LDPC codes and the coding gains which can be achieved over binary LDPC codes. Once we establish that a fairly significant coding gain can be achieved, we pose the following two questions: 1) What is the increase in decoding complexity of a q-ary vs. binary LDPC coded system? 2) How does the complexity change with the Galois field size? To answer these questions, we consider a set of high performance LDPC coded PMRCs, in which the channel targets are optimized and the LDPC codes are over fields of various sizes. We show that the q-ary LDPC coded channels provide a 1-dB coding gain over a practical binary LDPC coded architecture at user bit density (UBD) of 3.5, and evaluate the decoding complexities of these systems in terms of both the number of floating-point (FLP) operations and computational time.

II. LDPC CODE DESIGN

In order to construct high-performance LDPC coded channels, we need to design “good” LDPC codes. By “good” codes we mean codes with sharp waterfall regions, low error floors, and very large coding gains over hard-decision decoded RS codes, measured at a sector error rate of 10-5. From an implementation viewpoint cyclic or quasi-cyclic LDPC codes are desirable, for they substantially reduce the encoding complexity. We first considered the finite geometry (FG) LDPC codes and a number of algebraic methods for construction of quasi-cyclic q-ary LDPC codes. The Tanner graphs of these LDPC codes have girths of at least six. However, they cannot be used in our investigation, because we need to freely vary the Galois field size while the column weights of the parity-check matrix should be kept small, around three, and the code rate must be high, around 0.9. If we drop the cyclic or quasi-cyclic specification, LDPC codes constructed by the progressive edge-growth (PEG) algorithm [1] are the most appropriate LDPC codes for our experiments. LDPC codes generated by the PEG method have not only maximized global girth but also maximized local girths, and significantly outperform randomly constructed codes. In addition, the PEG construction is very flexible and can be used to construct both binary and q-ary LDPC codes with arbitrary code rates, Galois field sizes and column weights.

III. CONSTRUCTION AND PERFORMANCE OF LDPC CODED CHANNELS

We first generate a regular binary LDPC code with weight four, and three regular q-ary LDPC codes with weight three, using the PEG method. The three q-ary LDPC codes are over GF(24), GF(26) and GF(28), and are denoted as Codes 1, 2, and 3, respectively. We use the binary LDPC code on a PMRC, where the channel detector is a soft-output Viterbi algorithm (SOVA) with a maximum of two turbo iterations and five decoder iterations. The three q-ary LDPC codes are used on PMRCs with a symbol-based Bahl-Coke-Jelinek-Raviv (BCJR) algorithm [2] for channel detection without turbo equalization, and decoded with a maximum of fifty iterations. In Fig. 1, we present the simulation results for these channels at UBD=3.5. They perform well compared to a hard-decision decoded RS code. It is worth noting that the performance does not improve with increasing Galois field size. According to Hu et al. [3], if we want LDPC codes over larger Galois field sizes to perform better than those over smaller field sizes, we should keep the density of their parity-check matrices constant. We constructed another two regular q-ary LDPC codes, over GF(26) and GF(28), with weight two and denote them as Codes 4 and 5, respectively. The parity-check matrices of Codes 1, 4 and 5 have similar densities. In Fig. 2 a new set of simulations on PMRCs clearly shows that the performance of Codes 1, 4 and 5 improves with field size, as expected. Unfortunately, Code 4 has a high error floor and therefore fails to qualify as a “good” code and must be excluded from the complexity comparison.

J. R. CRUZ The University of Oklahoma E-mail: jcruz@ou.edu Fax: +1-405-325-3836 Tel: +1-405-325-4280 202 West Boyd, Room 219, Norman, OK 73019, USA

73

F2

IV. COMPLEXITY COMPARISON

We use the binary LDPC coded PMRC as the reference system in our decoding complexity comparisons. Based on the results presented in Section III, we are interested in quantifying the decoding complexity of q-ary LDPC coded PMRCs vs. the binary LDPC coded reference system, for a 1-dB of coding gain at UBD = 3.5. The q-ary LDPC Code 1, achieves approximately 1-dB gain over the binary reference system. We refer to this example as System 1. For the system using q-ary LDPC Code 5, we reduce the maximum number of belief propagation (BP) iterations to degrade its performance, until we get a 1-dB coding gain over the binary reference system. This was accomplished with a maximum of eleven BP iterations. We refer to this example as System 2.

The decoding complexity of Systems 1, 2 and the reference system are carefully calculated in the following way. First, all FLP operations used in channel detection and LDPC decoding are classified and counted on a per bit basis. Second, the computational times for the different FLP operations are tested in our simulation environments, which include a personal computer and a supercomputer cluster named Topdawg. In addition, we also consider the computational times of FLP operations on a field-programmable gate-array (FPGA), without actually implementing it. Finally, the decoding complexity ratios of Systems 1 and 2 to the reference system are computed, in terms of both the number of FLP operations and computational time. We present some decoding complexity ratios in Table I. After some careful analysis, it is reasonable to conclude that the time complexity ratios are always smaller than the ratios obtained by the number of FLP operations, which do not exceed 7.42. Furthermore, experimental results show that the size of the Galois field does not affect the decoding complexity.

REFERENCES

1) X.-Y. Hu, E. Eleftheriou, and D.-M.Arnold, “Progressive edge-growth Tanner graphs”, in Proc. IEEE Global Telecommun. Conf., 2001, pp. 995-1001.

2) W. Chang and J. R. Cruz, “Optimal symbol-by-symbol channel detection,” submitted to IEEE Trans. Commun. 3) X.-Y. Hu and E. Eleftheriou, “Binary representation of cycle Tanner-graph GF(2b) codes," in Proc. IEEE Intern. Conf.

Commun., 2004, pp. 528-532.

7.5 8 8.5 9 9.5 10 10.510-6

10-5

10-4

10-3

10-2

10-1

100

SNR (dB)

Blo

ck E

R

Code1 GF(16)Code2 GF(64)Code3 GF(256)SOVA2+BLDPC5RS code

Fig. 1. Performance of PMRCs coded by q-ary LDPC Code 1, 2, 3 and the binary LDPC code, UBD = 3.5.

7 7.5 8 8.5 9 9.5 10 10.510-6

10-5

10-4

10-3

10-2

10-1

100

SNR (dB)

Blo

ck E

R

Code1 GF(16)Code4 GF(64)Code5 GF(256)SOVA2+BLDPC5RS code

Fig. 2. Performance of PMRCs coded by q-ary LDPC Code 1, 4, 5 and the binary LDPC code, UBD = 3.5.

Table I: Decoding Complexity Ratios Computational Time Complexity Ratios Number of Operations

Topdawg PC Virtex-5 FPGA

1 /System referenceC C 3.63~7.12 1.66~2.32 2.30~3.68 2.78~4.59

2 /System referenceC C 3.79~7.42 1.82~2.55 2.54~4.06 2.99~4.94

74

F3

ERROR CORRECTING CODES FOR 4K-BYTE SECTORS

Toshio ITO1 and Toshihiko MORITA2 1) Fujitsu Laboratories Ltd., Kanagawa, Japan, ito.toshio@jp.fujitsu.com 2) Fujitsu Laboratories Ltd., Kanagawa, Japan, tmorita@jp.fujitsu.com

I. INTRODUCTION

Hard disk drives (HDDs) in the near future are expected to adopt the 4K-byte sector format to help increase recording density. The most possible error-correcting code (ECC) for this longer sector format would be the Reed-Solomon (RS) code over GF(212). Coding over GF(212), however, is several times more complex than conventional coding over GF(210). On the other hand, the continuous use of the RS code over GF(210) results in interleaved coding, which degrades performance. Integrated interleaving [1] is one way of improving the performance of the interleaved RS code, yet it is difficult to completely compensate the loss caused by interleaving.

In this paper, we propose a new error correcting method for the 4K-byte sector format. The method, which we call the interleaved RS code with error estimation (IRSE), is based on the four-way interleaved RS code over GF(210) combined with additional error-detecting parity. It utilizes soft information from the channel decoder and performs several iterations over the RS decoder. Using the soft information as well as the parity information, the method efficiently estimates the location of errors, and thus attains superior performance even compared with the non-interleaved RS code over GF(212).

II. ENCODER

The block diagram of the proposed IRSE system is shown in Fig. 1. The user data is first encoded into run-length-limited (RLL) codes and is supplied to the RS encoder, which interleaves the data into four blocks and generates an RS codeword for each block. The RS encoder is followed by the parity encoder that divides the interleaved block into sub-blocks of p bits. Four sub-blocks in the same column of the interleaved blocks are connected to make a sequence of 4p bits, for which the parity encoder computes 2-bit parities as shown in Fig. 2. Note that all of the parity bits are placed together at the end of the data and are sent to the channel.

III. DECODER

In decoding, the equalized channel output is first processed by the noise-predictive soft-output Viterbi algorithm (NP-SOVA). The NP-SOVA sends its hard-decision output to the RS decoder, which performs error correction for each RS codeword. The NP-SOVA also produces soft information for each bit and sends them to the error location estimator that determines the location of errors by the following steps:

1. The erroneous bits are contained only in the interleaved block for which the error correction by the RS decoder failed.

2. The erroneous bits are contained only in the sequence of 4p bits for which the parity violation occurred. The possible locations of erroneous bits in the sequence can be determined more accurately by comparing the recalculated parity and received parity. Since 2-bit parities are used, most of the error events in the perpendicular recording channel can be located.

3. Using the soft information, the bits with the highest error probability are selected among the candidates derived by the preceding steps.

Toshio Ito Fujitsu Laboratories Ltd. E-mail: ito.toshio@jp.fujitsu.com phone: +81-46-250-8840 fax: +81-46-250-8841 10-1 Morinosato-Wakamiya, Atsugi 243-0197, Japan

75

F3

As a result of these steps, the error location estimator determines the possible location of erroneous bits and flips them. The result is sent back to the RS decoder, which performs error correction again. By iterating this process, the number of errors gradually decreases and all errors in the interleaved blocks are corrected by the RS decoder.

IV. SIMULATION RESULTS

We evaluated the performance of the proposed IRSE method by simulation using perpendicular magnetic recording channels. The channel was equalized to a PR(5,6,0,-1) target [2]. The ratio of media noise to total noise is 90%. To take into account the code rate of the ECC, the extended user density [3], defined as EUD = Kp Re, is fixed at 1.114, where Kp is the user density and Re is the code rate of the ECC. The proposed method is based on the four-way interleaved RS code. The number of correctable symbol errors t of the RS code is 40. The sub-block length p for the additional parity is 20 bits and therefore the code rate of the parity is 80/82. The sector length is 4K bytes and the number of iterations is three.

Figure 3 shows the performance of the proposed method in terms of a sector error rate after ECC. Comparison was made against the non-interleaved RS code over GF(212) with t = 160, and the four-way interleaved RS code over GF(210) with t = 55, both having a 4K-byte sector length. As a reference, the performance of the RS code over GF(210) with t = 30 having a 512-byte sector length is also shown. Note that the value of t for each RS code is optimized by our simulation.

In the figure, the proposed method shows a 0.5dB gain over the conventional method using the same four-way interleaved RS code over GF(210). It is also revealed that the method is 0.4dB better than the non-interleaved RS code over GF(212). These results show that the method provides significant SNR improvement in perpendicular magnetic recording channels.

Moreover, the comparison above may not be fair in the sense that the proposed method utilizes soft information while the other methods do not; it might be possible to obtain similar performance by incorporating some soft-decision decoding algorithm for the RS code. Yet it is important to point out that the proposed method has low complexity and is suitable for use in practical hard disk drives.

REFERENCES

1) M. Hassner, et al., IEEE Trans. Magn., vol. 37, no.2, pp. 773-775, Mar. 2001. 2) M. Madden, et al., IEEE Trans. Magn., vol. 40, no. 1, pp. 241-246, Jan. 2004. 3) K. Saeki, et al., IEEE Trans. Magn., vol. 37, no.2, pp. 708-713, Mar. 2001. Fig. 1 Block diagram. Fig. 2 RS codewords with 2-bit

parities. Fig. 3 SER performance.

200/201 RLL

RSEncoder

ParityEncoder

PMRchannel

EQ NPSOVA

RSDecoder

200/201RLL

Error Location Estimator

Encoding

Decoding

ECC

ECC

Interleaved Block

Interleaved Block

Interleaved Block

Interleaved Block

P

RS parity

RS parity

RS parity

RS parity

P ・ ・ ・

P P P

P

p p

-5

-4

-3

-2

-1

0

16.5 17 17.5 18 18.5SNR [dB]

Sect

or e

rror

rate

(log

)

PR(560-1)EUD = 1.114Rm:Re = 90:10NPSOVA

4Kbyte

512byte

non-interleave

4-wayinterleave

IRSEmethod

0.4dB 0.5dB

76

F4

READ CHANNEL WITH INNER LDPC CODES

Weijun TAN LSI Corp., Longmont, CO, Weijun.Tan@lsi.com

I. INTRODUCTION

Low density parity check (LDPC) codes have been intensively studied since their rediscovery in 1990's. The outstanding performance of the LDPC codes has stimulated investigations on how to implement LDPC codes in the magnetic recording read channel. Toward this goal, two problems must be overcome. First, the performance of LDPC codes must be guaranteed to be superior to the traditionally used Reed Solomon (RS) codes. Second, the prohibitive high complexity in both encoding and decoding of the LDPC codes must be reduced. While it is still up to debate, whether the LDPC codes should totally replace the RS codes, or just be used as an inner codes, we designed LDPC codes as inner codes in this work. Simulation results show that the code we designed performs better than a RS plus single-parity codes (SPC). This overcomes the first problem of finding gain over the traditional RS codes. On the other hand, the codes feature simplicity in terms of fast encoding, easy decoding, and programmability. This solves the second difficulty of implementing LDPC codes: overcoming the high implementation cost. This work is another stepping stone in introducing LDPC codes to magnetic recording.

II. LDPC CODE DESIGN METHODOLOGY

In this work, outer RS codes of error correction capability T=20 and 70 for 512 and 4k byte sectors are used. Unlike as outer codes, LDPC codes as inner codes must have symbol error distribution matching RS T-level. Therefore, all codes designed in this work have column weight Wc≤3, although it is well known that high rate LDPC codes of Wc=3 are generally weak. This section describes the methodology to design three types of SPC-based LDPC codes. Due to the simplicity of SPC code, these codes have the following features: low and linear encoding complexity, low decoding complexity, and good programmability. The Type-I code has a structure similar to 3-D turbo product code (TPC) codes. However, instead of putting data bits in a 3-D array, we put them in a 2-D array with one row and two columns of parity bits. Let the numbers of user data rows/columns be K1 and K2. Let the numbers of user data rows/columns be K1 and K2, then this is a ((K1+1)(K2+2), K1K2) code, whose rate R=K1K2/(K1+1)(K2+2). Each SPC parity bit in the last row is associated with K1 randomly selected user bits, one from each row. Similarly, each SPC parity bit in the two parity columns is associated with randomly selected K2 user bits, one from each column. How these user and parity bits are selected defines the code. Equivalently, this code is defined by three sets of interleavers, one for each set of SPCs. The parity-check matrix H of this code has column weights Wc=3 for the user bits, and Wc=2 for the parity bits. In order to make the H matrix be regular in row-wise, we usually use K1= K2. This way, the code becomes a ((K1+1)( K1+2), K1K1) code. Obviously the length and rate of this type of codes is not very flexible. For example, we want to design of R~0.93, then K1=39 is a good solution, which gives a (1640,1521) code of rate R=0.9274. This method can be extended to design longer codes. For example, the data bits can be arranged in a ((K1+1)( 3K2+6) 2-D array with the last row and the last six columns being parity bits. The difference is that every SPC parity bit in the six parity columns is associated with K2 randomly selected user bits, one from every three columns. A LDPC code (4920,4563) of R=0.9274 is designed using method, whose performance will be shown in Section III. The Type-II codes have three parity columns and no parity row. Let the numbers of user data rows/columns be K1 and K2, then this is a ((K1( K2+3), K1K2) code, whose rate is K2/( K2+3). Each parity bit is associated with K2 randomly selected user bits, one from each column. In addition, each parity bit in the second parity column is also associated with one parity bit in the first parity column, and each parity bit in the last parity column is associated with one parity bit in the first parity column and one parity bit in the first parity column. Therefore, the H matrix has column weight Wc=3 for the user bits, and Wc=1, 2, and 3, respectively, for parity bits in the first, second and last parity column. Apparently, this type of codes has very flexible code length and rate, therefore does not need code length extension.

77

F4 The Type-III codes are simple extension of Type-II codes. The differences are two-folded. First, the interleavers are specifically designed to guarantee that the girth of such codes g≥8. Note that these exactly same girth control technique can be used on Type-II codes as well. In this sense, Type-III codes are a special subset of Type-II codes. From the discussions in [1], slopes sets without triangles among them result in code of g≥8. This technique used a small integer lattice to obtain a set of small submatrices, then to construct a code matrix by cyclic shifting these sub-matrices. One drawback of [1] is that it is very hard to design very high rate codes, e.g., R>0.9. We modify the technique in [1], and design a matrix based on the data block lattice itself and then use the transpose of this matrix as H-matrix for an LDPC code. Doing so makes the design of high rate codes easier. However, the code length is relatively large. The smallest size of a rate R=10/11 and g =8 code we designed using this technique is a (5379, 4890) code. The second difference in Type-III codes is that parity bits in any one parity column are associated with parity bits in other two columns as well. This change makes the Type-III codes regular with Wc=3 and they are not SPC-based codes any more. However, they can be easily reduced to SPC-based codes to take advantage of the simplicity while keeping the girth control property.

III. SIMULATION RESULTS

This sections shows simulation results for the three types of codes designed in Section II. The codes evaluated are Type-I code (4920,4563), Type-II code (4914,4563), Type-II code (5379,4890). As references, SPC (64,63), and interleaved TPC code (1225,1156) are also evaluated. The channel we use is a perpendicular recording channel of user bit density UBD=2.0, and 90% jitter noise. The channel detector and LDPC decoder run 3 inner iterations and 4 global iterations. Shown in Figs. 1 and 2 are the sector failure rate performance for 512 and 4k byte sectors, respectively. From both figures, we have the following observations. First, the designed LDPC codes have around 0.4 dB and 0.7 dB gains over SPC for 512 byte sector at SFR=10-6, and for 4k byte sector at SFR=10-10, respectively. Second, type-II codes are a little bit worse than type-I codes while having the flexibility in code length and rate. Third, g=8 codes performance slightly better than g=6 code, which implies LDPC codes as inner codes are not very sensitive to the girth.

REFERENCES

1) B. Vasic, "High-rate girth-eight LDPC codes on rectangular integer lattices," IEEE Trans. Commun., 52, 1248-1252, (2004).

15.8 16 16.2 16.4 16.6 16.8 17 17.210

-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

SNR

SFR

SPC,R=63/64TPC,R=1156/1225LDPC-I,R=4563/4920LDPC-II,R=4563/4914LDPC-III,g=6,R=4890/5379LDPC-III,g=8,R=4890/5379

15.6 15.8 16 16.2 16.4 16.6 16.8 17

10-16

10-14

10-12

10-10

10-8

10-6

10-4

10-2

100

SNR

SFR

SPC,R=63/64TPC,R=1156/1225LDPC-I,R=4563/4920LDPC-II,R=4563/4914LDPC-III,g=6,R=4890/5379LDPC-III,g=8,R=4890/5379

Fig. 1 SFR for 512 byte sector. Fig. 2 SFR for 4k byte sector.

Weijun Tan LSI Corp. (former Agere Systems) Weijun.Tan@lsi.com fax: +1-720-864-4011 tel: +1-720-864-4081 1811 Pike Road, Suite 2C, Longmont, CO 80501,

78

F5

SYNDROME ECC DECODING USING BIT RELIABILITIES

Victor Y. KRACHKOVSKY1, Jonathan J. ASHLEY2, Clifton J. WILLIAMSON3 and German FEYH4 LSI Corporation, Milpitas, CA, USA

1) victor.krachkovsky@lsi.com, 2) jon.ashley@lsi.com 3) clifton.williamson@lsi.com, 4) german.feyh@lsi.com

I. INTRODUCTION

Reed-Solomon codes play important role in magnetic channels for their error and burst correction properties. With recent advances of iterative coding, RS ECC could still be used, especially with sector sizes larger than 512B. Achieving 1e-10 sector failure rates requires significant ECC correction power, but at the same time we want to limit the ensuing rate loss. For this purpose, one may use soft information that is often available in state-of-the art recording channels. At present, several approaches to soft ECC decoding are known. GMD algorithm [1] is the easiest one and has on-the-fly implementations [2]. Another direction is to use soft versions of Sudan-type algorithms. Although their complexity growth is polynomial with ECC length, they are too complex on large sectors. Even more gains can be achieved from Chase decoding, but its complexity grows exponentially with correction power. Here, we consider RS decoding in traditional syndrome-based scheme. Several soft ECC decoding algorithms based on bit flagging are further considered. Performance analysis and simulation results are provided.

II. SOFT INPUTS AT ECC DECODER In soft-output detection schemes, soft information is often available in form of bit reliabilities. Via threshold comparison, we can flag the most unreliable bits. In addition, we can flag some bits based on side information such as modulation or parity constraint violations. Let us introduce 2 probabilities: α (probability of hit, i.e. that the error is flagged) and β (probability of valid flag, so that 1-β is probability of false flag). Having high β is important to achieve SNR gains under limited decoder complexity. On the other side, we need high α to supply enough flags to the decoder. These requirements often contradict each other, so optimization of parameters is required. For example, if the flags are set based on bit reliabilities only, we cannot get probability of false detection only about ½, so we need to use side information for further its reduction. This could be especially important for iterative schemes, where density evolution distorts the original LLR distribution. From available bit information we can estimate reliabilities of ECC symbols and flag some of them. Five possible types of output symbols are: type 0 (correct, non-flagged), type 1 (all errors flagged, no false flags), type 2 (some flags, no errors), type 3 (both errors and flags, either some flags are false or some errors are not flagged), type 4 (some errors, no flags).

III. DECODING STRATEGIES For soft ECC decoding we may treat flagged symbols differently, depending on flag types. By assigning erasures to flagged symbols, we can run GMD or Chase decoding as first option. For type-1 flags, more efficient strategy however could be “guessing” the correct symbol by flipping the flagged bits. If the guess is correct, we can increase the decodable distance for type-1 symbol by 2, compared to 1 if the symbol is just erased. If most flagged symbols are of type-1, this strategy could be more efficient than erasure decoding. Another justification for using this approach with iterative decoding and bit interleaving is that the error events are split into isolated bit errors and, most likely, a flagged symbol would have exactly one bit flagged. Further on, we consider a variant of GMD algorithm in case when error values could be guessed along with error locations. The proposed algorithm uses BM decoder to compute the error locator polynomial Α(x) of degree l and helper polynomial B(x), and further constructs the candidate error locator solution as: 0)0(,1)0(,))(deg(,))(deg(),()()()()( ==+−≤+−≤⋅+⋅Λ= qpmtlxqmltxpxqxBxpxxλ (1)

Victor Krachkovsky LSI Corporation E-mail: victor.krachkovsky@lsi.com Fax: +1-610-712-4217 Tel: +1-610-712-6583 1110 American Pkwy NE, Allentown, PA 18103, USA

79

F5 where t is the designed error correction capability, and m is the target error correction capability. We propose an iterative computation of solution (1) by adding entries from a list of flagged symbols. Depending on the flag type (1,2, or 3) our guess on error/location pair will be “valid”, “false”, or “half-valid”. If we just erase the symbol, the outcome will be “valid”, “false”, or “valid” for these types, respectively. As it is further shown, simple rules exist to distinguish between valid, half-valid and false pairs once a candidate solution (1) is computed. A decoding distance bound taking different flag types into account is studied. Apart from single-run GMD, other decoding strategies based on this idea can be considered, including Chase decoding and multiple GMD attempts with permutations of flagged symbols. Further on, we also consider a simplified Chien search that can be used to test the solution candidates without calculating the complete root set. In case of multiple decoding attempts, such strategy could ease the computation bottleneck caused by the full-scale Chien search. Finally, an algorithm to compute error values for different types of error/location pairs is proposed.

IV. MODELING AND PERFORMANCE COMPARISON. To evaluate different decoding strategies, the analytical block-multinomial approach [3] may be too complex, so we consider the probabilistic Monte-Carlo evaluator based on 4-dimensional probability function that describes the joint weight distribution of type 1-4 symbols within a code block. For simplicity, we did not involve the sorting of LLR values in the SFR evaluation but just apply the optimal threshold. Results of the study are shown in Figs 1 and 2, where L and K denote the numbers of flags and valid flags (whatever applicable).

REFERENCES 1) G. D. Forney, Jr., "Generalized minimum distance decoding," IEEE Trans. Inform. Theory, Vol. 12, pp. 125-

131, Apr. 1966. 2) N. Kamiya, "On acceptance criterion for efficient successive errors-and-erasures decoding of Reed-Solomon

and BCH codes," IEEE Trans. Inform. Theory, Vol. 43, pp. 1477-1488, Sept. 1997. 3) Z.A. Keirn, V.Y. Krachkovsky, E.F. Haratsch, and H. Burger, "Use of redundant bits for magnetic recording:

single-parity codes and Reed-Solomon error-correcting code," IEEE Trans. Magn, Vol. 40, No 1, pp. 225-230, Jan. 2004.

16 16.05 16.1 16.15 16.2 16.25 16.3 16.35 16.4 16.45 16.510-6

10-5

10-4

10-3

10-2

10-1

100

SNR (dB)

Sect

or F

ailu

re R

ate

BMAGMD/erasures (M=1)GMD/errors (M=1)Chase (L=10)GMD (M=50)

1 2 3 4 5 6 7 8 9 1010-6

10-5

10-4

10-3

10-2

10-1

100

∆

P f (∆)

M=1M=5M=10M=20M=50M=100

Fig.1. Probability of failure for M GMD error decoding attempts, L=20, K=13, as function of error correction overhead ∆ .

Fig. 2 Comparison of different decoding strategies on the modeled distribution, T=20, 512B sectors.

80

F6

Maximum a Posteriori Estimation with Vector Autoregressive Models for q-ary LDGM Coding Systems in Digital Magnetic Recording Channels

Hidetoshi SAITO1, Masayuki HAYASHI2 and Ryuji KOHNO2

1) Kogakuin Univ., Tokyo, Japan, h-saito@cc.kogakuin.ac.jp 2) Yokohama National Univ., Yokohama, Japan, masayuki@kohnolab.dnj.ynu.ac.jp, kohno@ynu.ac.jp

I. INTRODUCTION

In recent signal detection of various high density digital magnetic recording systems, it needs to mitigate the effect of mixture signal-dependent transition noise (media noise) and colored Gaussian thermal noise [1]. Data sequences with such mixture noise are assumed to be non-linear time-series. The univariate (scalar) autoregressive (UAR) model has been introduced in [2] to estimate media noise and a mixture of UAR models has been used in channel modeling. But, it is difficult to estimate a specific distributional approximation for total noise in comparison with each noise component. In this digest, total noise is estimated to use a mixture of multivariate (vector) autoregressive (MAR) components for superior inference in maximum a posteriori probability (MAP) sequence detection. From severe demand for signal detection and the latest trend for recording in units of long sectors instead of a single sector which consists of 512 information 8-bits bytes, q-ary (non-binary) low-density parity-check (LDPC) codes will be one of candidates and important error correcting codes for future recording systems. A q-ary code is a given set of sequences which each symbol is chosen from the alphabet of q elements over the Galois field Fq. In this digest, we present the bit error rate (BER) performance of signal processing systems combined with non-binary LDPC codes based on linear codes with low-density generator matrix (it defined as LDGM codes [3] in this digest) and the MAP sequence detection scheme using MAR models.

II. MAGNETIC RECORDING SYSTEMS WITH VECTOR AUTOREGRESSIVE MODELS

Fig.1 shows the block diagram of the LDGM coded PR system with the proposed system. In this read/write system, a raw data sequence ak with bit rate fb is inputted into the runlength limited (RLL) encoder with (0,k) constraints and a RLL sequence is generated. The RLL sequence is transformed into a codeword sequence bk' in the LDGM encoder and additional symbols have been inserted into inserted into the sequence bk' to be satisfied with (0,k) constraints. The sequence bk' is transformed into a sequence ck' at the precoder. The sequence ck is NRZ-recorded on the perpendicular double-layered medium. Here, an isolated reproducing waveform at the reading point is assumed to be a hyperbolic tangent function-like waveform given by h(t,w) = Ap tanh (ln3t/2w) where Ap is a half of the amplitude and T50 = 2w is the time interval which h(t) needs to rise from -Ap/2 to Ap/2. The normalized linear density (user density) is defined as Kp = T50/Tb where Tb is a user bit interval. A reproducing waveform corresponding to the recording sequence read back by the reading head is written as h(t+∆tk’, w+∆wk’) ≅ h(t,w) + ∆tk’ ∂h(t,w)/∂t + ∆wk’ ∂h(t,w)/∂w [1] and inputted into the equalizer which consists of a low-pass filter with the cut-off frequency xh normalized by bit rate fb and the transversal filter with Nt taps.∆tk’ and ∆wk’ is subject to independent Gaussian random variables which represent the effect of position jitter and width variation noise, respectively. In this read/write system, the noise at the reading point consists of additive white Gaussian noise w

kn ' and transition noise mkn ' . The equalization is

performed so that the overall characteristic between the input of recording head and the output of the equalizer is equal to the aimed PR characteristic. It assumes that total noise at the reading point is zero-mean, white Gaussian noise with two-sided power spectral density equal to N0/2 and transition noise whose powers in the bandwidth of 0.6fb are 2

wσ and 2mσ , respectively.

The signal-to-noise ratio (SNR) at the reading point is defined as a = Ap / 2m

2w σσ + . The equalizer output sequence dk' is

decoded by the proposed MAP detector based on MAR channel models. A log-likelihood ratio sequence L(bk') corresponds to the soft output sequence of bk' is obtained from the MAP detector output. This sequence L(bk') is a codeword sequence generated by the LDGM encoder and the codeword sequence is decoded by a revised sum-product algorithm based on a decomposed minimal trellis of each parity check codeword in the LDGM decoder. An output data sequence ak' is obtained from the RLL decoder output after the recursive decoding process between the proposed MAP detector and LDGM decoder. The BER of this read/write system is evaluated by computer simulation.

Hidetoshi SAITO Department of Information and Communications Engineering, Faculty of Engineering, Kogakuin University E-mail: h-saito@cc.kogakuin.ac.jp fax: +81-3-3348-3486 tel: +81-3-3342-1211 (ext.2635) 24-2 Nishi-Shinjuku 1 chome, Shinjuku-ku, Tokyo, 163-8677 Japan

81

F6

III. VECTOR AUTOREGRESSIVE MODELS AND LDGM CODES

In the MAP detector, a mixture of p MAR components is defined as follows:

( ) ( ))()('

)(

1'' ',,,| ii

ki

n

p

iipkppk UANUAnf

kψδψδ ∑

=

= .

The notation p is used to represent a set of p elements of the same kind; e.g. Ap = A(1), … , A(p). Total noise nk’ is r-dimensional vector of observations. In our MAR model, r = 3, nk’ = (∆tk’,∆wk’ , w

kn ' ) and mkn ' = (∆tk’,∆wk’ ). )(i

tψ is an mi-dimensional regressor and mi equals to order of AR models (AR(mi)). imri RA ×∈)( is the regression coefficient matrix of the i-th AR component and rri RU ×∈)( is the covariance matrix of the innovations process associated with each component where the notation R is the set of real numbers (i = 1, … , p).δi is defined as the time-invariant weight of the i-th AR component and 0 ≦δi ≦1. Nx is the multivariate Normal distribution of x [4]. The (0,k) q-ary LDGM code is given as ((m-1)(m+2)+M,(m-1)2-s) code and it is possible to correct up to any continuous erasures of length 2m-3 symbols in a codeword sequence where m is a prime number. M and s are dummy symbols which are needed to satisfy (0,k) constraints.

IV. SIMULATION RESULTS

Fig.2 shows the BER performances of the 8-ary LDGM coded PR2 systems in iterative decoding. This read/write system uses a 64/65 RLL code with (0,8) constraints [5] and an irregular type (4629,4355) LDGM code over F8 which has column weight 3 and row weights 67, 134, m= 67, M = 75 and s = 1. It is assumed that he ratio of the transition noise power to the total noise power accounts for 90% and transition noise consists of 50% position jitter and 50% width variation. This code corrects continuous long erasure symbols which maximum burst of length is 131. The real line shows the BER performance of the system with the proposed MAR channel models where Kp=1.5, xh = 0.4, p=32 and Nt = Ntopt. The symbol Ntopt is the optimum value of Nt which gives the near minimum BER. The dotted line indicates the BER performance of the same system with the UAR channel model. As can be seen the Fig.2, the performance of the proposed system with MAR models improves the SNR by about 1.5 dB over the system with UAR models at a BER of 10-4, where the PR2 channel with 1 symbol delayed precoder is used.

V. CONCLUSION

In this digest, it is shown that the maximum a posteriori probability decoding using multivariate autoregressive models is useful in magnetic recording channel with media noise and additive white Gaussian noise. Our result shows that the proposed iterative decoding system with multivariate autoregressive models outperforms the system with univariate autoregressive models in the bit error rate performance using the PR2 channel.

REFERENCES

1) R. Pighi, R. Raheli and U. Amadei, IEEE. Trans. Magn., vol.42, no. 7, pp.1905-1916, Jul. 2006. 2) J. Moon and J. Park, IEEE J. Sel. Areas Commun., vol. 19, no. 1, pp.730-743, Apr. 2001. 3) H. Saito, M. Hayashi and R. Kohno, IEEE. Trans. Magn., vol.43, no. 2, pp.733-739, Feb. 2007. 4) G. R. Reinsel, Elements of Multivariate Time Series Analysis, Springer-Verlag New York, 2003. 5) H. Saito, et al., IEICE Trans. on Electronics (Japanese Edition), vol.J86-C, no.8, pp.952-961, Aug. 2003 (in Japanese).

Fig. 1 System diagram. Fig. 2 BER performances.

82

P1 Optimal Characteristic Impedance of Suspension Interconnect Considering Output

Impedance of Write Driver and Signal Loss

Eunkyu JANG 1 1) Samsung Information Systems America, San Jose, CA 95134, USA, ekjang@sisa.samsung.com

With the increasing demand of area density on hard disk drives, data rate requirements of some drives are exceeding a 2 Gb/s. To achieve reading and writing at a data rate of 2 Gb/s, required -3 dB bandwidths are about 1.3 GHz for read traces and 2.33 GHz for write traces. If the write head is not impedance-matched to the write trace, the output impedance of write driver must be matched to the line impedance to avoid reflections [1]. Both characteristic impedance of interconnect and output impedance of write drivers should be kept low to obtain high current at load for a given source voltage, according to the lossless transmission line theory [2]. But low characteristic impedance (e.g., 30 Ω) can cause high signal losses because of the stainless steel backing of suspension interconnects [3]. One of practical approaches to reduce the signal loss is removing some portion of the stainless steel (so-called windowing). But the “windowing” will result in high characteristic impedance if there is no change in the write trace width. Because of physical space constraints, therefore, it is not easy to design the write trace matching the output impedance of write driver or having low characteristic impedance while keeping signal losses low. A system approach for designing the channel path of disk drives is required for achieving high data rates [4]. In this work, a simple method is suggested for determining an optimal write trace impedance for a given output impedance of write driver. A 2-D field solver is used to calculate differential characteristic impedance (Zdiff) and signal loss (α) of write traces. A two conductor transmission line driven at one end and terminated at the other end is depicted in Fig. 1. The current at the load, expressed in an exponential form or in a hyperbolic form, is [2].

)(sinh)/()(cosh)()1(

1)1()( 2 sZZZZsZZV

ee

ZZV

sIcslcsl

ss

sl

sl

sc

s

γγρρρ γ

γ

+++=

−−

+=

−− (1)

where ρl = (Zl - Zc) / (Zl + Zc) and ρs = (Zs - Zc) / (Zs + Zc) are the reflection coefficients of source and load, s is the length of interconnect, )()( CjGLjRj ωωβαγ +⋅+=+= is the complex propagation constant, and

)/()( CjGLjRZ c ωω ++= is the characteristic impedance. At high frequencies (ωL >> R and ωC >> G), the propagation constant and the characteristic impedance are well approximated by CLjGZZR cc ωγ ++= 2/)/( and

CLZc /= . The signal attenuation consists of conductor loss (αc) and dielectric loss (αd) as Eq. (2).

2

tan2

)( c

cdc

ZCZ

R ωδωααα +=+= (2)

Typical two-conductor microstrip lines with trace width of 100 µm, trace-to-trace spacing of 25 µm, and length of 50 mm, is used for this study. The laminate thicknesses are 20, 10, 15, and 5 µm for the backing stainless steel, the base polyimide (PI), the copper layer, and the cover-coat dielectric layer, respectively. Conductor loss (σ (Cu) = 5.8 × 107 S/m and σ (SST) = 1.45 × 106 S/m) and dielectric loss (tan δ = 0.03) are taken into account. The characteristic impedance ranges from 35 to 75 Ω as the “windowing” percent varies. Fig. 2 shows characteristic impedance and signal loss as a function of frequency for the interconnects. Interconnect of high characteristic impedance (e.g., 75 Ω) shows lower signal loss than that of low impedance (e.g., 35 Ω). However, the optimal Zdiff, which gives a maximum current value, is not the highest Zdiff if output impedance of write driver (Zs) is considered. The current at the load is calculated using Eq. (1) with Vs = 5 V, Zl = 10 Ω, and f = 2 GHz condition. Fig.3 shows the currents of the initial and the steady-state signals under different write driver’s output impedance (Rs=30-100 Ω) and interconnect impedance (Zdiff =35-73 Ω) conditions. The optimal Zdiff for the initial and the steady-state signals are 50 Ω and 46.3 Ω, respectively, for Rs = 40 Ω. They are 69 Ω and 60.2 Ω for Rs = 80 Ω. Fig. 4 shows optimal characteristic impedance and its peak current as a function of the write driver output impedance.

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[1] K. Klaassen, J. Contreras, and J. van Peppen, IEEE Trans. Magn., vol. 40, no. 1, pp. 263–267, Jan. 2004 [2] A. Smith, Radio Frequency Principles and Applications: The Generation, Propagation, and Reception of Signals and Noise, IEEE Press, 1998, pp. 162-176. [3] J. Pro and M. Roen, IEEE Trans. Magn.,vol. 42, no. 2, pp. 261–265, Feb. 2006. [4] J. Contreras, IEEE Trans. Magn.,vol. 42, no. 10, pp. 2600–2602, Oct. 2006.

Figure 1. Schematic of two conductor transmission line with source and load

Figure 2. Electrical parameters of suspension interconnect - characteristic impedance (a) and signal loss (b)

Figure 3. Peak currents for initial signal (a) and steady-state signal (b)

Figure 4. Optimal characteristic impedance as a function of the write driver output impedance (a) and

Eunkyu Jang, Samsung Information Systems America, 75 W. Plumeria Drive, San Jose, CA 95134, USA E-mail: ekjang@sisa.samsung.com Tel: +1-408-544-5754 Fax: +1-408-544-5723

84

P2 MEASUREMENT AND INTERPRETATION OF THE TRANSVERSE FIELD

DEPENDENCE OF MAGNETIC FLUCTUATION NOISE IN TUNNELING MAGNETORESISTIVE HEADS

Peter GEORGE1 and Guchang HAN2

1) St. Cloud State University, St. Cloud, USA, george@stcloudstate.edu 2) Data Storage Institute, Singapore, Han_Guchang@dsi.a-star.edu.sg

I. INTRODUCTION

As magnetic head sensors continue to decrease in size, magnetic noise increases inversely proportional to volume. This high-frequency noise can become a limiting signal-to-noise factor in head design and can also be used as a diagnostic tool to understand head operation. Prior transverse field measurements [1] of the peak noise value have been extended to the point where reference layer (RL) reversal takes place and the effect on the peak power spectral density (PSD) is observed. The interpretation of the data is aided by single domain calculations for the field stiffness [2] of the free and reference layers. Micromagnetic calculations trace the magnetization of these layers correlating well with measured PSD peaks. Two PSD peak regions are identified with the noise from the free and reference layers.

II. EXPERIMENTAL DETAILS AND RESULTS The original noise measurements made on 100 nm track-width tunneling magnetoresistive (TMR) heads were limited to a transverse field magnitude of about 1000 Oe due to the pole spacing of the electromagnet. This field was inadequate to observe complete RL reversal, so permanent magnets placed close to the sample heads were used to extend the data to –3000 Oe where complete RL reversal is shown to take place. The high frequency noise measurement system was the same as described by Han et al [1]. The combined results for previous measurements of the peak PSD and the extended results are shown in Figure 1. The new contribution is a plateau region extending from about –1000 Oe to –2500 Oe which falls to the saturation value outside this region. It is believed that the new region is a result of the RL reversal. The plateau region in the PSD at zero transverse field arises from the free layer. These results are confirmed by single domain modeling of the angular and field dependence of the field stiffness of each layer and micromagnetic simulation of the magnetization of each layer reversal.

III. SINGLE-DOMAIN-APPROXIMATION FIELD STIFFNESS CALCULATIONS Analytical modeling of the free and reference layers was performed using the formalism of J.V. Peppen and K.B. Klaassen [2] while assuming the layers could be treated using a single domain approximation. The results show that when the layers are saturated in either direction (perpendicular to the air-bearing surface (ABS)), the stiffness is high and when the magnetization lies along the direction of the longitudinal bias (parallel to the ABS), the stiffness is low. Since the peak PSD can be shown to be related to the reciprocal of the field stiffness of the layers, the results provide a basis for interpreting the PSD results. The negative offset for the field location of the PSD peak for the RL is shown to be related to the exchange coupling and demagnetizing fields of the saturated free and pinned layers. Calculations of the field dependence of the peak PSD for free and reference layers are in good qualitative agreement with the experimental results of Figure 1.

Corresponding AUTHOR SCSU, St. Cloud State University E-mail: george@stcloudstate.edu fax: 320-308-5127 tel: 320-308-4921 720 Fourth Avenue South, St. Cloud, MN 56301, USA

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IV. MICROMAGNETIC SIMULATION RESULTS FOR GMR AND LAYER MAGNETIZATIONS Additional confirmation of the anticipated reversal behavior of the free and reference layers was obtained by making micromagnetic calculations of the magnetization in each layer as a function of applied field for a 100 nm track- width TMR head. The results confirm the anticipated single domain reversal behavior which, together with the angular dependence of the field stiffness, further confirm the peak PSD results. Results are presented for the field dependence of the GMR along with the layer magnetizations at various fields. The onset of RL reversal is illustrated at the point where the GMR begins to drop at negative fields. The micromagnetic results, taken together with the angular dependence of the field stiffness (derived on the basis of single domain behavior), further provide confirmation for the interpretation of the experimental data and provide a complete picture of the transverse field dependence of the peak PSD for the free and reference layers.

REFERENCES

1) G. C. Han, Y. K. Zheng, Z. Y. Liu, B. Liu, and S. N. Mao, “Field dependence of high-frequency magnetic noise in tunneling magnetoresistive heads,” J. Appl. Phys. 100, 063912 (2006).

2) J. V. Peppen and K. B. Klaassen, “A new approach to micromagnetic simulation of thermal magnetic fluctuation noise in magnetoresistive read sensors,” IEEE Trans. Magn. 42, 56-69 (2006).

Fig. 1 Transverse field dependence of the measured peak value for the two PSD noise peaks observed between 1 and 10 GHz. The open curve marker data was originally

reported in [1] using an electromagnet limited to 1000 Oe and the solid curve marker data is an extension to negative field values made using a permanent magnet

instead of the electromagnet.

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P3

EXCHANGE COUPLING IN SYNTHETIC ANTIFERROMAGNETIC MULTILAYERS FOR WRITE HEAD

Yun-Hao XU1, Hai JIANG2, Kyusik SIN3, Yingjian CHEN4 and Jian-Ping WANG5

1) University of Minnesota, Minneapolis, MN, USA, xuxx0181@umn.edu 2) Western Digital Corporation, Fremont, CA, USA, Hai.Jiang@wdc.com

3) Western Digital Corporation, Fremont, CA, USA, Kyusik.Sin@wdc.com 4) Western Digital Corporation, Fremont, CA, USA, Yingjian.Chen@wdc.com

5) University of Minnesota, Minneapolis, MN, USA, jpwang@umn.edu

I. INTRODUCTION

Since the discovery of long range oscillatory indirect magnetic exchanging coupling in ferromagnetic/non-magnetic/ferromagnetic (FM) sandwich structures [1], many important aspects have been understood and applications have been realized. The examples include early giant magnetoresistance (GMR) sensors [2] and synthetic antiferromagnetic (SAF) multilayers [3] as soft underlayer (SUL) in perpendicular recording. The exchange coupling between the FM layers depends on the thickness of the non-magnetic layer and is very sensitive to the structure defects and interface quality. This effect offers us an extra path to control the effective anisotropy of the layers as well as the magnetic configuration and switching sequence of the whole structure.

Soft magnetic films in write head are required to have well-defined in-plane anisotropy with proper magnitude to enable the usage of them in in-plane hard axis direction, in addition to the requirements of high saturation magnetization (Ms), low remanent magnetization (Mr) and low coercivity field (Hc). In this report, we demonstrate that the SAF multilayers with three layers of FM layers and two non-magnetic layers provides the control of effective anisotropy and switching sequence of each layer through the exchange coupling, which shows discrete steps of magnetization in the easy axis (E.A.) hysteresis loop. It is now possible to use the SAF multilayers in their E.A. direction and have a step function-like operation in write head. Bilinear and biquadratic exchange coupling constants [4, 5] were extracted from the measurements and compared.

II. EXPERIMENT

The SAF multilayers were deposited by sputtering. The film structure is shown in Fig. 1, which consist three ferromagnetic layers (M1, M2, and M3) separated by two Ru layers. The ferromagnetic material is FeCoN. M2 is twice as thick as M1 and M3. Two different underlayers (UL1 and UL2) were used to induce different interface roughness in the structure. Magnetic properties were measured by vibrating sample magnetometer (VSM).

III. RESULTS AND DISCUSSION

The hysteresis loops of SAF multilayers are shown in Fig. 2, A, B and E. Calculation of hysteresis loops assumed coherent rotation in three coupled single magnetic single domain thin films and were obtained by minimizing the energy per unit area

2 2 21 1 2 2 3 3 1 1 2 2 3 3

2 212 1 2 23 2 3 12 1 2 23 2 3

( sin sin sin ) ( cos( ) cos( ) cos( ))

cos( ) cos( ) cos ( ) cos ( )

E K d d d MH d d d

J J Jq Jq

θ θ θ θ φ θ φ θ φ

θ θ θ θ θ θ θ θ

= + + − − + − + −

+ − + − + − + −

where d1, d2 and d3 are thickness of each FeCoN layer, θ1, θ2, and θ3 are angles between magnetization of FeCoN and its E.A., φ is the angle between the applied field and E.A. (Fig. 1B), J12 and J23 are the bilinear exchange coupling constants between M1 and M2, and M2 and M3, respectively. Jq12 and Jq23 are the biquadratic exchange coupling constants of these layers. The E.A. of the three FM layers were assumed to be aligned. By fitting the measured hysteresis, J and Jq were extracted and listed in Table 1. The different interface roughness induced by different ULs affects the both bilinear and biquadratic exchange coupling, though the bilinear exchange couplings are impacted more severely. Larger roughness at the interface corresponds to decreased exchange coupling.

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REFERENCES

1) S. S. P. Parkin et al., Phys. Rev. Lett. 64, 2304 (1990). 2) M. N. Baibich et al., Phys. Rev. Lett. 61, 2472 (1988). 3) P. Grünberg et al., Phys. Rev. Lett. 57, 2442 (1986). 4) M. Desai et al., IEEE Trans. Magn. 41, 3151 (2005). 5) C. Chesman et al., Phys. Rev. B 58, 101 (1998). Table 1 J12 (erg/cm2) J23 (erg/cm2) Jq12 (erg/cm2) Jq23 (erg/cm2) UL1 1.18 0.55 0.43 0.19 UL2 0.55 0.05 0.35 0.35

Fig. 1 (A) The layer structures the synthetic antiferromagnetic multilayers. M1, M2, and M3 stand for ferromagnetic layer 1, 2, and 3, respectively. (B) The schematic diagram of the angles between applied field, moment of each ferromagnetic layers and the easy axis.

Fig. 2 (A) and (B) Measured and calculated easy axis and hard axis hysteresis loops of sample with UL1. (C) and (D) Calculated angles between each ferromagnetic layer and easy axis of the films vs. applied field. H is along EA in (C) and HA in (D). (E) Measured and calculated EA hysteresis loops of sample with UL2.

Jian-Ping WANG MINT Center & Department of Electrical and Computer Engineering, University of Minnesota E-mail: jpwang@umn.edu fax: +01-612-625-4583 tel: +01-612-625-9509 200 Union Street SE, Minneapolis, MN, USA 55455

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P4

Correlation of noise spectrum in GMR and TMR head with bias field Shengxian SHE1 and Dan WEI2

1) DMSE, Tsinghua University, Beijing, China, ssx06@mails.tsinghua.edu.cn 2) DMSE, Tsinghua University, Beijing, China, weidan@tsinghua.edu.cn

I. INTRODUCTION

The thermal noise spectrum in GMR and TMR read heads are important topics [1]. In GMR heads, the magnetic field caused by the sense current is considered. In TMR heads, the sense current is set to be less than 0.5mA thus the magnetic field of the sense current is quite small, and the spin transfer effect [2] is neglected.

Table.1 Main parameters in our micromagnetic model Fig 1. Magnetization distribution in TMR Heads

II. RESULTS AND DISCUSSION

The magnetic model of the TMR head consists of one free layer and two SAF layers. In the simulation, the integration time step t is smaller than 5ps and the time interval t1 used for calculation of the magnitude of thermal noise is set to be 20 ps, so that the results of simulation would be independent from those time scales [3].

Fig2.Thermal noise spectrum in GMR heads Fig3.Thermal noise spectrum in TMR heads

In Figure 2 and 3, it can be seen that higher bias field from permanent magnets (PM) would shift the noise peak towards higher frequencies, in both GMR head and TMR heads [4]. It is interesting to find which physical quantity determines the noise peak with respect to the thermal activation. As listed in Table 2, the noise peak frequency is in the same order of the estimation f=γHbias, but not f=γHeff, where γ is the gyromagnetic constant, Hbias and Heff are the averaged bias field and the effective field respectively among all clusters in the free layer.

89

P4 Table 2 : Noise peak and effective field in GMR and TMR heads

In Fig.4, it is found that, in TMR heads, the pattern of magnetization pattern in the free layer is similar to that of the bias field distribution in free layer, while the pattern of the effective field is somehow in a state of chaos. One possible explanation of the phenomenon is that the thermal activated force sways the effective field, while the magnetization pattern is less dependent on thermal activation due to the small thermal noise field. Fig.5 shows the distribution of effective field, bias field and magnetization pattern without thermal activation for comparison.

Fig.4 Distribution of effective field, bias field and Fig.5 Distribution of effective field, bias field and magnetization in free layer of TMR head, when the magnetization in free layer of TMR head, when the bias field is 6000Oe, with thermal activated noise bias field is 6000Oe, without thermal activated noise

References [1] J. C. Jury, K. B. Klaassen, J. C. L. van Peppen, S. X. Wang, Measurement and Analysis of Noise Sources in Giant

Magnetoresistivesensors up to 6 GHz, IEEE Trans. Magn, 38, 3545-3555(2002) [2] Jian-Gang Zhu, and Xiaochun Zhu, Spin Transfer Induced Noise in CPP Read Heads, IEEE Trans. Magn. 40, 182-188

(2004) [3] Shengxian SHE and Dan WEI, Algorithm of Micromagnetic Simulation for Thermally Activated Noise in Magnetoresistive

Head, IEICE Technical Report, MR2006-26, 106,7-9,(2006) [4] Jian-Gang Zhu, Yuchen Zhou, and Sining Mao, Spin Torque Enhancement of Thermally Excited Ferromagnetic Resonance

in Tunneling MR Heads, 42, 2441-2443(2006)

Dan WEI Dept. of Materials Science and Engineering, Tsinghua University Beijing, 100084, China fax: +81-10-627-71160 tel: +86-10-627-73449 Preferred category: #P9 E-mail: weidan@ tsinghua.edu.cn

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P5

EFFECTS OF LAMINATED LAYERS ON RISE TIME OF WRITE HEAD

Liang QUAN1 and Dan WEI2 1) Tsinghua University, Beijing, China, quanl@mails.tsinghua.edu.cn

2) Tsinghua University, Beijing, China, weidan@tsinghua.edu.cn

I. INTRODUCTION The pole tip driven perpendicular write head [1] is a promising design for perpendicular magnetic recording hard disk drives, while the issues concerning its unstable switching characteristics remain unsettled [2]. The laminated SPT head is adopted to avoid the eddy current, regulate the rise time and improve the writing performance [3].

II. RESULTS AND DISCUSSION A micromagnetic model based on LLG equations is applied to simulate pole tip driven heads with nano-scale main pole tip. The lamination layer is inserted in the y-z plane and its number can be altered to identify its effects upon the rise time of head field. The main pole tip volume is 160×80×80nm3. The total number of clusters is in the order of 104. The soft magnetic material is chosen as FeCo, while the insertions are supposed as antiferromagnetic transition metal, as thick as 5nm each. In the static magnetization pattern in Fig.1(a), there are several domains when one lamination layer is inserted; therefore the domain size is around 50nm.

Fig. 1 (a)(b) Magnetization pattern in the pole tip driven heads, the drive field is applied by surface magnetic pole Bs=2T at a plane y=160nm (3D view, x-down track, z-cross track), one lamination layer without or with the drive field applied (c)(d) Switching characteristics of two heads with no lamination and one lamination layer, respectively When the main pole tip volume is decreased to 100×40×40nm3, the magnetization patterns with 0-3 lamination layers are given in Fig. 2(a) to (d) respectively, still with driven field of surface pole Bs=2T at a plane y=160nm. The corresponding switching characteristics curves are plotted in Fig. 3(e) to (h) respectively.

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P5

Fig. 2 (a)-(d) Magnetization pattern in pole tip driven heads, the drive field is applied by surface pole Bs=2T at a plane y=160nm, 0-3 lamination layers (e)-(h) Switching characteristics, 0-3 lamination layers respectively

III. CONCLUSION It is found that the SPT head with one lamination layer, each layer is 50nm thick and close to the scale of the throat height, displays the best switching property, which has shorter and more stable rise time compared to the non-laminated design. When the number of inserting layers is increased further, the rise time fluctuates largely.

REFERENCES 1) H. Muraoka, K. Sato, Y. Sugita and Y. Nakamura, "Low inductance and high efficiency single-pole writing head for perpendicular double layer recording media, " IEEE Trans. Magn., 35, 643, (1999) 2) K. Ouchi, et al., Overview of Latest Work on Perpendicular Recording Media, IEEE Trans. Magn. 36(1), 16 (2000). 3) M. Mochizuki, C. Ishikawa, et al., Reduction in Remanent Magnetization Using a Multi-layered Single-Pole Writer, JMMM. 287(2005) 372-375.

Dan WEI Dept. of Materials Science and Engineering, Tsinghua University E-mail: weidan@tsinghua.edu.cn fax: +86-10-62771160 tel: +86-10-62773449 Tsinghua University, 100084, Beijing, China

92

P6

EFFECT OF HEAD SCALING ON INITIAL PERMEABILITY OF POLE-TIP DRIVEN HEAD

Sumei WANG1, Liang QUAN2 and Dan WEI3

1) Tsinghua Univ., Beijing, China, pandajj03@gmail.com 2) Tsinghua Univ., Beijing, China, quanl@mails.tsinghua.edu.cn

3) Tsinghua Univ., Beijing, China, weidan@tsinghua.edu.cn

I. INTRODUCTION

The soft magnetic materials with high permeability and high saturation should be used for SPT head [1] to conduct magnetic flux and create large head field in writing process. In this work the effects of scaling and frequency are studied on initial permeability of FeCo pole-tip driven head [2] based on micromagnetic simulation.

II. RESULTS AND DISCUSSIONS

Initial permeability of FeCo elements at different scales has been calculated, as seen in Fig.1. The Ladder-type domain pattern is chosen as static state [3]. The real initial permeability at low frequencies, with 0.05 damping constant, are approximately 3.3, 6.5, 8.5 and 13.5 for the element with 40×40, 80×80, 160×160 and 320×320 nm2 cross-section, respectively. It can be seen that the permeability rises with larger element size at nano-scales.

Fig. 1 Simulated real (solid) and imaginary (dotted) initial permeability for FeCo elements. The micromagnetic cluster is 10×10×10nm3. The total number of clusters is (a) 4×4×4 (b) 4×8×8 (c) 4×16×16 (d) 4×32×32

The initial permeability of the main pole in pole-tip driven perpendicular write head [3] is also studied. The cluster size is 5×5×5 nm3. The static state of two heads, with 40nm×40nm main pole tip in the y-z plane and a down-track thickness 20 and 40nm in the x-direction, are plotted in Fig.2(a) and (b), respectively; in Fig.2(a), the domain structure is the ladder-type in the trapezoid region but there is still a vortex in the pole tip, while in Fig.2(b) there are two vortices in the trapezoid region and pole tip respectively.

The frequency responses of initial permeability in the two pole tips are also calculated, as seen in Fig2(c) and (d). At low frequencies the real initial permeability is approximately 19 and 10, and the imaginary initial permeability is 5.8 and 0.6, for the tip with 20nm and 40nm down-track thickness, respectively.

III. CONCLUSION

Therefore the initial permeability (both the real parts and imaginary parts) is highly dependent on the static domain structure. The real initial permeability might decrease with higher y-component (perpendicular to ABS) of averaged magnetization in the pole tip driven heads. It is also interesting that the imaginary initial permeability is quite large even at low frequencies for some static domain patterns.

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REFERENCES

1) S. Khizroeva,Y. Liu and K. Mountfield et al. "Physics of perpendicular magnetic recording: writing process," JMMM 246, 335-344, (2002).

2) H. Muraoka, K. Sato, Y. Sugita and Y. Nakamura, "Low inductance and high efficiency single-pole writing head for perpendicular double layer recording media," IEEE Trans. Magn. 35, 643-648, (1999).

3) Dan Wei and Xuan Zhang. "Correlation of domain pattern and high-frequency response in pole-tip of inductive thin film head," J. Appl. Phys. 97, 024501, (2005).

Dan WEI Dept. of Materials Science and Engineering, Tsinghua University E-mail: weidan@ tsinghua.edu.cn fax: +81-10-627-71160 tel: +86-10-627-73449

Fig. 2 (a)(b) Simulated static domain pattern in cross-track y-z plane in pole tip driven heads, the down-track thickness is 20nm and 40nm in (a) and (b) respectively. (c)(d) simulated real (solid) and imaginary (dotted) initial permeability corresponding to (a) and (b) respectively. The damping constant is 0.02.

94

Index

Name Paper Page Name Paper Page Albrecht, T.R. D1 48 Gratrix, S. E4 66 Alex, M. A1,D4 12,54 Guan, L. B1 24 Alhussien, H. E1 60 Gupta, V. C2 38 Ashley, J.J. F5 78 Han, G. P2 84 Balasubramaniyam, S. C3 40 Hashiomoto, S. A2 14 Bance, S. B2 26 Hatatani, M. A3 16 Bandic, Z.Z. D1 48 Hayashi, M. F6 80 Batra, S. E5 68 Heinonen, O. B3 28 Benakli, M. B3 28 Hentges, R. D5 56 Berger, A. D4 54 Hernandez, S. D3 52 Bertram, H.N. D4, E3 54, 64 Hoshino, K. A3 16 Bogy, D.B. C2 38 Hoshiya, H. A3 16 Buchan, N. C1 36 Hrkac, G. B2 26 Buttar, J. C3 40 Hsu, Y. D4 54 Carey, M.J. A1 12 Hua, W. C4 42 Carey, K. A1 12 Huang, Q. A4 18 Challener, W.A. B5 32 Huber, W.D. D6 58 Chang, W. F2 72 Hwang, L.C. D6 58 Chaw, M. C1 36 Ikeda, Y. D4 54 Che, X. D2 50 Inturi, V. B3 28 Chen, Y. A4 18 Ito, T. F3 74 Chen, Y. P3 86 Iwasaki, H. A2 14 Chiah, V.M.F. A5 20 Jackson, R. E4 66 Childress, J.R. A1 12 Jang, E. P1 82 Choi, D.H. C5 44 Jiang, C. A4 18 Chou, S. A4 18 Jiang, H. P3 86 Cruz, J.R. F2 72 Jin, W. F1 70 Do, H. D4 54 Ju, G. B5 32 Dobisz, E. D1 48 Kagami, T. A6 22 Dovek, M. A6, B1 22, 24 Karakulak, S. E3 64 Druist, D. A1 12 Katada, H. A3 16 Ertl, O. B2 26 Katine, J.A. A1 12 Feyh, G. F5 78 Kawasaki, S. A2 14 Fong, W. C1 36 Kercher, D. D1 48 Fontana, R.E. A1 12 Kief, M. B3 28 Fossorier, M. F1 70 Kim, N. D2 50 Fuke, H.N. A2 14 Kimball, G. D5 56 Gage, E. B5 32 Knigge, B. C1, D1 36, 48 George, P. P2 84 Kohno, R. F6 80 Goncharov, A. B2 26 Krachkovsky, V.Y. F5 78

95

Index

Name Paper Page Name Paper Page Kuroki, K. C1 36 Roscamp, T. E5 68 Kuznetsov, A. E2 62 Rosen, H. D4 54 Lai, A.W.Y. A6 22 Rottmayer, R.E. B5 32 Lee, E. C1 36 Rubin, K. D4 54 Lee, S.C. C6 46 Rudman, V. C3 40 Lee, H.J. D2 50 Sahashi, M. A2 14 Lengsfield, B. D4 54 Saito, H. F6 80 Leung, E.C.W. A6 22 Salo, M. D4 54 Li, H. A4 18 Schabez, M. B2, D4 26, 54 Li, W. A4 18 Scholz, W. E5 68 Lille, J. C1 36 Schrefl, T. B2 26 Liu, Y. B1 24 Seigler, M.A. B5 32 Liu, Z.J. B4 30 She, S. P4 88 Liu, F. C3 40 Shen, X. D3 52 Liu, B. C4 42 Shiimoto, M. A3 16 Lu, B. B5 32 Shimizu, T. A5, A6, B1 20, 22, 24 Maat, S. A1 12 Siegel, P.H. E3 64 Miyake, K. A2 14 Sin, K. P3 86 Moneck, M. D2 50 Sladek, E. C3 40 Moon, K. D2 50 Smith, N. A1 12 Moon, J. E1 60 Smith, D. C1 36 Moore, J. A1 12 Smyth, J. B1 24 Morita, T. F3 74 Son, S.H. C5 44 Moser, A. D4 54 Song, S. C3 40 Nakamoto, K. A3 16 Stoev, K. C3 40 Olson, T. D4 54 Strand, T. C1 36 Pan. T. C3 40 Suess, D. B2 26 Park, J. E1 60 Suk, M. C1 36 Parnell, T. E4 66 Sullivan, M. C6 46 Pelhos, K. B5 32 Sun, M. B3 28 Peng, C. B5 32 Sun, B. C3 40 Polycarpou, A.A. C6 46 Tabakovic, I. B3 28 Prabhakaran, V. C3 40 Takagishi, M. A2 14 Pro, J. D5 56 Takahashi, N. D2 50 Quan, L. P5, P6 90, 92 Takano, K. B1 24 Rausch, T. B5 32 Takano, K. D4 54 Reiley, T. C1 36 Takei, H. A3 16 Riemer, S. B3 28 Tam, Y.M. A5 20 Robertson, N. A1 12 Tan, W. F4 76 Roen, M. D5 56 Tang, Y. D2 50

96

Index

Name Paper Page Teng, Z. A4 18 Thomson, T. D4 54 Tipton, W.C. D6 58 Tsang, C. A1, D4 12, 54 van der Heijden, P. D1, D4 48, 54 Vanhecke, G.J. D5 56 Vas'ko, V. B3 28 Venkataramani, R. E2 62 Victora, R.H. D3 52 Wang, G. A4 18 Wang, J.P. P3 86 Wang, S. P6 92 Watanabe, K. A3 16 Wei, D. P4, P5, P6 88, 90, 92 Weresin, W. D4 54 Williamson, C.J. F5 78 Wilson, B. D4 54 Wolf, J.K. E3 64 Wong, P.K. A5, A6 20, 22 Wong, C.H. C4 42 Wu, T.W. D1 48 Xu, Y.H. P3 86 Yan, G. A4 18 Yang, X. B5 32 Yang, H. D1 48 Yeo, C.D. C6 46 Yin, L. A4 18 Yoon, S.J. C5 44 Yoshida, N. A3 16 Yu, S. C4 42 Zaboronski, O. E4 66 Zhang, K. A4 18 Zheng, L. C3 40 Zhou, H. B5 32 Zhou, W. C4 42 Zhu, J.G. B6, D2 34, 50 Zhu, X. B6 34

97

Notes