high performance heads for perpendicular recording

IEEE TRANSACTIONS ON MAGNETICS, VOL. 24, NO. 6, NOVEMBER 1988

HIGH PERFORMANCE HEADS FOR PERPENDICULAR RECORDING (invited)

V. Zieren. S.B. Luitjens, M.J. Piena, R.W. de Bie, C.P.G. Schrauwen and J.P.C. Bernards

Philips Res. Labs., P.O. Box 80000, 5600 JA Eindhoven, The Netherlands

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ABSTRACT

In this paper several important features of historical, present-day and future developments in the field of heads, specifically designed for perpendicular DL (double-layer) media, are outlined. The emphasis lies on probe heads (PHs) which are positioned on one side of the medium only. A description is given of the way our experimental, high efficiency PHs, the so-called VSPs, are fabricated and measured. Several important design aspects, such as efficiency and resolution, will be discussed in more detail. The experiments indicate that thin Co-Cr layers, having a high coercivity, are needed for a good short-wavelength response, when using a high-resolution PH. This, in turn, will impose several requirements on the pole material, such as a high saturation magnetization, low Barkhausen noise and a high permeability. A playback model is described which enables us, by comparison with our recording results, to analyze our head, medium and interface parameters. Also, the model has been used to make an estimation of the bit densities that can be obtained with PHs on DL media. Depending on the criteria for signal and noise applied in the recording channel, we expect that an areal density of 1 bit/pm* is feasible.

1. INTRODUCTION

Renewed scientific interest in perpendicular recording started in 1977, when Iwasaki and co-workers [ l ] demonstrated the existence of perpendicular anisotropy in Co-Cr thin films. Si- multaneously, they introduced a new type of head: the Single- Pole head (SP), preferably called the Probe Head (PH). This type of head is able to produce recording fields that are pre- dominantly in a direction perpendicular to the surface of the medium. In this paper several important features of the historical, present-day and future developments in the field of heads, specifically designed for perpendicular media, will be outlined. The emphasis will lie on PHs which are positioned on one side of the medium only. After a brief discussion on the properties and preparation conditions of double-layer media, we describe our way of manu- facturing the experimental one-sided PHs. An overview will be given of the in-contact recording measurements which are used for characterizing our heads and media. The output voltages initially obtained from a PH on a double-layer (DL) medium were not as large as those obtained from a ring head (RH) on a single-layer (SL) medium. An analysis showed that this behaviour could be ascribed ro several causes. The initial geometry implied a low efficiency, which can be increased considerably by changing the shape of the coil chamber. Also, the head-to-medium distance was rather high, which mainly re- duced the short-wavelength output. These items and ways leading to improvement will be discussed by presenting some of our results from a playback model using input parameters of head and medium. It will be shown that a well-designed PH geometry, careful choice of smooth head materials, special thin pole films, a narrow track and optimum medium parameters may lead to very high bit densities (e.g. 1 bit/pm2).

2. BASIC TYPES OF PROBE HEADS

Since the early days of perpendicular recording several interesting proposals have been published for accomplishing a combined recording and playback head for perpendicularly magnetized media. Although the RH at present is still a can- didate for high density systems using perpendicular SL media [2] , we will restrict ourselves to the description of some basic types of PHs. In one of the next sections we will briefly discuss the different behaviour of an RH and a PH on a DL medium.

The mother of all PHs is the double-sided head [I ] , which has two separate parts, one on each side of the medium. Fig. la shows the version in which a driving coil is wrapped around a block of ferrite: the auxiliary pole. Opposite to it there is a very thin soft-magnetic film (main pole) clamped between two non- magnetic supporting blocks of glass or ceramic. When the coil is excited a magnetic flux will emanate from the auxiliary pole and will be concentrated by the main pole, which is very close to the perpendicular registration layer, e.g. a Co-Cr thin film. When a soft-magnetic layer is deposited under the Co-Cr layer, this has a considerable influence on the form of the (perpendicular) head fields, as the flux will be concentrated near the pole tip. Thus, the playback performance [3] will change as well. A version having the coil wrapped around the main pole also exists. Both types have the advantage of the relatively simple fabrication. The main disadvantage is that the head cannot easily be applied in a rigid disk drive or in a (video) helical scan recorder due to its two-sided nature. A more attractive form see Fi . lb) in this respect is the W- shaped SP head (WSP) 147 - f7] and types strongly related to it, such as the MSP [SI or the VSP [SI. They have in common the one-sided construction, meaning that the auxiliary pole is positioned at the same side of the medium next to the main pole. This makes them better applicable in the above- mentioned systems. Fig. IC shows a third basic form: the thin-film PH [ 103 which consists of a main pole, a coil and an auxiliary yoke, all real- ized in thin-film (TF) technology. This T F technology is com- monly used to fabricate RHs, which have a gap length in the order of 0.3 pm. The TF-PH is essentially different at this point: the 'gap' distance, G, between the main- and the auxiliary pole tips is much larger (typically 5 pm . A high efficiency is claimed for comparable structures [ 11],?12] as will be discussed later on. An advantage might be the possibility of batch fabrication of single- or multi-track heads. An early hybrid T F head [I31 did not yet have this advantage, because the main pole had to be constructed separately.

Several variations on the basic types exist. An interesting TF-PH [ 141 has an auxiliary pole extended to the head's surface for obtaining a higher efficiency. As the edge of this part is parallel to the pole, it will give rise to spurious pulses in the

9\ 10 I

yoke (NiFe)

a. b. C.

Fig. 1. Basic PH types: a) double-sided, b) one-sided WSP. c) thin film [lo]. 1 = non-magnetic part; 2 =ferrite; 3 = main pole; 4.5 = adhesive layer; 6 = centre core; 7 = auxiliary pole; 8 = coil; 9 = registration layer; 10 = soft-magnetic underlayer; I I = base film.

- ..--

--I- - I

0018-9464/88/1100-2597$01.0001988 IEEE

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playback signal. This was suppressed by making the edge 'wavy'. i.e. not arallel. The same philosophy lies behind the proposal in [ I S ? . which in fact is a WSP without the non- magnetic parts on top. The ferrite edges next to the pole have been given a V- roove shape to avoid the spurious pulses that may be caused fl6] when the ferrite edge is in contact with the medium. The latter head combines features of a PH and a RH. The use of RHs on SL and DL media has been discussed in several of our previous papers [ 171 - [XI. 3. PERPENDICULAR MEDIA FOR PROBE HEADS

For one-sided PHs it is essential to have a thick, highly per- meable soft-magnetic layer underneath the perpendicular registration layer to close the flux path from the main to the auxiliary pole. In this way the efficiency of the PH is increased. as it depends on the reluctance of the medium as well [7].[9]. We use amorphous Co,,,Zr, ,Nb,, or polycrystalline Ni,,Fe,, as a soft-magnetic layer and Co7,Crz, as the registration layer. which are all deposited by K F sputtering on 14.5 pm thick polyester foils. Depending on preparation conditions, a wide range of properties for both layers can be obtained

The distance, D, between the pole tip and the underlayer. has to be as small as possible for obtaining a small transition width. a,. and a high resolution of the PH [7].[21], although the head's efficiency will drop slightly [SI. Thus, a small head-to- medium distance, a, is needed, as well as a small Co-Cr layer thickness, d.

The Co-Cr layer should have good perpendicular properties and a good microstructure showing a small hexagonal c-axis spread (A05J, which can be accomplished by introducing a thin nucleation layer (such as Ti or Ge) between the Co-Cr and the underlayer [ 201. The requirement of a high permeability of the underlayer usually implies a low underlayer coercivity (Ht). This might be in conflict with the requirement of a high He necessary for avoiding a large contribution of spike noise (as found when an RH is used [ 181). The perpendicular coercivity of the Co-Cr ( H;) should be as high as can be made, as long as the head can generate sufficiently large fields without saturation [ 71. This would also imply the use of thinner Co-Cr layers [20]. A disadvantage of using a D L medium, necessary for a PH, is the desirability of simultaneously optimizing the preparation

[ 201.

a. b

C. d

conditions of two or more layers. The optimization is compli- cated, as the cause of good or bad behaviour in recording experiments cannot always be indicated unambiguously.

4. DESIGN A N D FABRICATION OF VSP-TYPE P H S

In this section we will briefly discuss the design aspects and the processing steps needed in the fabrication of a V-shaped SP head (VSP) 191, named after the V-shape of the ferrite yoke. essentially being one half of the WSP (Fig. Ib). The VSP has some advantages over the WSP, as will be made clear.

a. Resolution. Calculations of the head fields by Finite Element Modelling as well as by an ana!ytisal method [7] were used for determining the shape of the frequency response of a PH on a DL medium. A semi-empirical relation was found between the thickness, T,. of the pole film and the n-th order extinction wavelength, Ion. The most important first pole-null A, , , is about 1.4Tm, if DzT,, . If a density of e.g. 1 bit/jtm' is aimed at. the pole resolution should be sufficiently high and a pole-tip cross-section of T,W,-0.7 pm: is needed, where W is the track width (see one of the following sections). Thus a 5 pm track would need a T, of 0.14 pm.

b. Efficiency. In order to obtain a highly efficient recording and playback head a small reluctance between main and auuiliarq poles is necessary. It was shown by lumped reluctance niodel- ling [7] that the underlayer needs t o ha\e a large \slue of prt. where pr is the relative permeability and t is its thickness. Secondly, the coil chamber 'gap'. G. and the centre core thickness, T,, (see Fig. 1 b). should be small. in the order of several microns. This can be accomplished by using the triangular coil-chamber shape. which has to be made by laser cutting [SI. Other solutions for improving the read efficiency ( r l ) by reducing the reluctance between main and auxiliary poles are:

- the addition of side cores of ferrite [21],[22]; - reduction or omission of the non-magnetic part on top of

a.

7 8 m9

e f

Fig. 2. Fabrication process of the VSP head. 1.3= non-miignetic part ii1.m.). 2 = ferrite: 3.6 = adhesive layer: 5 = pole film. 7.8 = CCM! chamber: 9 = coil.

b. Fig. 3.a. Photomicrograph of the quadrangular cod chamber tndde by laser

cutting i n ferrite. The dashed line marks the narroner tridngulxr forin 191. The bar measures 100 pm. Non-magtietic (&IS.;) pat-ta are !iphter shaded

b. Photoinicrograph of the p i p atid the e n t i e core (\;e\\ through the glasb o i i top). A small laser tnisalignment angle I S \ tsible. Lighter parts are the territe-gla\s interface\ The bar length IS 100 )mi . G 2 17 p i . T, il 20 Jim.

1

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taining a seam. These are two of the advantages of the VSP over the WSP [9]. Again, thermocompression bonding is used to attach the pole substrate to the composite ferrite/n.m. block. The length of the etched poles must be equal to the thickness of block (1). The bar is now polished with a radius of 10 mm and sliced between the poles (Fig. 2d) to obtain 200 pm wide cores. After bonding of the core onto a brass mounting base, a coil chamber can be cut in the ferrite by a laser, such as described in [9]. In some n.m. materials, such as CaTiO,, a second coil chamber may be laser-cut (Fig. 2e), so that a small, low-inductance coil can be wound (Fig. 20. If the n.m. material cannot be laser-cut, the coil is wrapped around the n.m.- core half (see Fig. l a in [SI). Fig. 3 shows some details of the coil chamber in the ferrite of a completed head. The quadiangular form (Fig. 3a) has the same basic dimensions as the regular triangular shape (dashed line) proposed in [9] with 400 pm sides, but offers more room for the coil winding and has an unaltered efficiency. Fig. 3b shows that a gap of about 17 pm has been formed in the ferrite (light shade). The picture was taken through the transparent block on top (in this example, glass). As the central ferrite core has to be very small (TFB I 20 pm), the second coil chamber (when present) is shifted 200 pm aside in order to reinforce this brittle part of the head. Otherwise, it would be impossible to wind the coil. The centre-core width of a symmetric WSP should at least be 200 pm ( = 2TFB) for the same reason. This reduces the WSP efficiency. We calculated the efficiencies of the VSP and the WSP using our reluctance model [9]. Except for the different TFB values for the VSP (20 pm) and the WSP (100 pm), both heads in this comparison have a pole length L = 15, T, = 0.14, 5 5 W I 50, 10 I G 5 100, triangle side Z = 400, D = 0.2 and 250 5 prt 5 500 (all dimensions in pm) and an elevation angle 4 = 10". It appears that the VSP has a factor of 2.2 to 3.3 higher q than the WSP. Maximum q values are 51 YO (VSP) and 18.8 YO (WSP). Finally, the head is lapped by Al,O,-tape on a helical scan recorder until L has the desired value and a suitable profile has been formed.

the auxiliary pole, so that it is in contact with the medium

reduction of the track width to values much smaller than the auxiliary-pole or core width [SI,[ 15],[23].

c141,[ 151;

Several apers report a high efficiency obtainable with TF-PHs. In [24f25 to 50 YO of the flux through the pole is linked with the coil. In [ 111 the very high q values seem the result of a very doubtful definition of q , being the ratio of flux in the yoke with realistic permeabilities and of the flux in the yoke with permeabilities of IO6 (except for the underlayer). This is different from the q definition usually applied for RHs [2S] or PHs [9], where the potential difference across the gap or across the pole-to-underlayer distance, respectively, is divided by the coil excitation NI (AT, amp-turns).

c. Fabrication process. Fig. 2 shows schematically the fabrication steps used for the VSP. In a) and b) the bonding of a non-magnetic (n.m.) tile (1) on a ferrite block (2) is depicted. The bonding is carried out by a thermocompression (diffusion) technique using a Mo/Au/Au/Mo sandwich (3) [26]. Mo acts as the adhesion layer between the Au-diffusion layers and blocks (1) and (2). The thermal expansion coefficients of the n.m. part and the MnZn-ferrite should be well matched. The block should also be wear-resistant and have a smooth surface after lapping. These requirements can be satisfied by using glass, glass-ceramics [6] , or a ceramic such as CaTiO,. The composite block is sliced and polished along the dashed lines in Fig. 2b.

A soft-magnetic pole film ( 5 ) is RF-sputtered on a block (4) of the same n.m. material as (1). For PHs having W 2 50 pm and T, 2 0.1 pm we use sputtering targets of Ni,,,Fe,,, (at. YO) or Fe,, sSizooAl,,, (at. YO). High-resolution poles are sputtered from a target of Co,, ,Nb, 6Zrs , (at. %). In order to re- duce, or even avoid, the appearance of closure domains in narrow-track poles [27] two laminae of 70 nm thickness are deposited, which are separated by 5 nm SiO, [28],[29] . Prior to etching, an anisotropy is induced in an in-plane direction perpendicular to the eventual flux flow [30] by annealing in a magnetic field. This bilayer film has a pr 2 700 , poM,xl T , Hc = 230 Aim and H,x870 A/m. This HK value is about the optimum value for a track width of 10 pm using a sin le-layer film [27], but is rather high for a multilayer film ~ 2 9 3 . Nev- ertheless, it was applied in the PH used for the measurement shown in Fig. 11.

Next, the poles are patterned (Fig. 2c) by photolithography and etching (wet-chemical, or ion-milling). The bars remaining after etching have a stripe width equal to the track width W. In this stage, the magnetic pole properties can still be determined easily. Also, the pole film ( 5 ) is deposited on a flat substrate and is not interrupted by a seam (3), such as is present in the counter block (1 + 2) shown in Fig. 2c. In a WSP construction the pole will always have to be deposited on a substrate con-

I I t -301 medium: A

5. EXPERIMENTS

a. Experimental conditions. For the recording experiments we built a system that consists of a turntable on which a flexible medium is stretched like a drumhead. This enables us to do contact recording on small pieces of flexible media. A head is fixed on an adjustable arm and positioned on a track to carry out the recording experiments. The medium velocity (v) varies between 0.7 and 1 mis. Usually, the erasing, writing and reading are performed by the same head. However, one example will be shown in which a so-called cross-measurement is done by using two separate heads.

I O 1

V831B -90 I I I

0 5 10 15 20

v831B I 1

1 2 Exp. model

I

3.0 6.0

Fig. 5. Normalized (sine-)wavelength response of PH (V83 I B) on two media (A and B). Dots: measured. Solid lines: calculated. For PH and media parameters: see Table I. Write currents: 8 mA,,, (A) and 25

I(mArms) - Fig. 4. Normalized sine response at two wavelengths as a function of the rms

write current. Probe head: V831B. Medium: A. Parameters: see Table I. mArmr (B).

2600

I A 1W 16

E 500 I 42

Table I. Head and media properties.

(turns) k m ) Um) k m )

V831E VSP-A m0 28 CaTiO, NiFe

W3438 WSP-0 0.38 2W 37 CaTiO, NiFe

o.m IW 35 - 1

480 0.08 Ge 35 CoZrNb 58 450 400

450 0.15 Ti 20 NiFe 110 8W 8W

C 250 30 450 0.08 Ti 20 NiFe 120 740 4w

medium:A medium8

E O

V83 1 B Y I -8

V83 1 -4

0 17 33 29 0 14

(prn) - (pm) - a. b.

Fig. 6. Normalized pulse output voltage as a function of the displacement. Head and media as in Fig. 5. a. medium A; PW,, = 0.84 im . b. medium B; PW, = 1.05 pm.

and reading with two heads. Fig. 7 gives an example of such a series of measurements using an RH and a PH. The upper two curves have been made by using the RH as the playback head, the lower two by using the PH for playback. As the PH in this example is a conventional, low-efficiency WSP ( q < 8 O h ) having wide rectangular coil chambers, its output level is small compared to the RH output. The write capabilities of the PH and the RH are more comparable on this medium (C), than the read capabilities are. The first-order extinction wavelengths, At, and ,It, can directly be associated with their respec- tive T, or g values. However, an additional 'dip' on a wavelength A; appears in both cases in which the RH was used for writing. This additional writing dip is also observed using RHs on SL media [2] and must probably be ascribed to the bipolar character of the perpendicular component of the RH write field. Probably, the 'overwrite' capability is insufficient, owing to which each transition written by the leading field peak is only partly overwritten by the trailing peak. This phenome- non has not been reported for a PH on a DL medium and might be a serious disadvantage of using an RH on a perpendicular medium.

d. Impedance measurement. Fig. 8 shows the frequency de- pendence of the head's impedance (L, R and Q) for the VSP in contact with medium B. In air the L and R would be somewhat smaller and Q larger. The main contribution to the head's noise is from the resistive part of the impedance. The L and R values given in [22] for a WSP with side cores, scaled to N = 20 turns, are : L = 1.33 pH and R = 200 R (at 50 MHz) and 1.11 pH and 9.8 R (at 10 MHz). Especially the R of the head in Fig. 8 is considerably smaller. For comparison, the 10 MHz data of the well-known Tilted-Sendust-Sputtered (TSS) ring head [36] (having W = 27 pm and N = 17 turns), are: L = 1 pH, R = 16 R and Q = 3.9.

I I I t -7 Iwrite: Iread:

........... I p -3Or % PH

.& -50

v - m

-70

\ t

I 4 , \.-.. -90 I 0.0 2.5 5.0

l / h ( l /Urn) - Fig 7. Normalized (sine-)wavelength output of a cross-measurement of an

RH (K21) and a PH (W343B) on DL medium C (Table I). The upper two curves result when the RH is the playback head, the lower two when the PH reads.

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1000 I I I I

V83 1 B

0.1 0 0 10 20 30 40 50

frequency (MHz) - Fig. 8. L-Q-R impedance measurement as a function of the frequency (PH:

V831B, medium: B).

6. PLAYBACK MODEL OF A P H ON A DL MEDIUM

a. Model description. In this section the fundamental back- ground of a model will be briefly described, which may be used to calculate the frequency response of a PH on a DL medium. Also, the noise output of this head-medium combination can be estimated. Combined, these data can be used for:

a) analysis of head and medium parameters by comparison

b) investigation of the possibility for high bit densities. with measured data;

This model has a few things in common with the one presented in [37] . The freauencv resvonse is calculated using the Fourier Transform $(k,y = a) (from the x to the k-domain) of the perpendicular head field H, and after applying a Hanning window. This field is calculated at a distance y = a from the pole tip (at the surface of the Co-Cr) for -8OT, < x < SOT, , using the analytical expression given in [38]. The field has been normalized such that the potential difference across the pole-to-underlayer distance, D, equals 1 AT. The x direction is wrallel to the medium velocity. The wave number k is 2 4 1 . H,(k,a) is integrated over the medium thickness, d. Also, the non-magnetic nucleation layer (thickness d, ) between the (ideal) soft-magnetic underlayer and the Co-Cr is taken into account. The transition width is denoted by a,. Eventually, the following expression is obtained for the output voltage V:

The fact that the PH’s lon -wavelength sensitivity is propor- tional to T, is included in k,,(k,a). For the calculation of the demagnetizing field I&, we choose a criterion which takes into account that Hd, averaged over the medium thickness, is less than H& in the absence of the head. For a square-wave pattern M,(k) is calculated by (4/n)H&/Nd ( I M,) where the demagnetizing factor N, is given by:

Nd = e-k‘dcd’”( sinh[k(d + dn)] - [2 - ekd sinh(kd,)]}/(kd) (2)

The noise-vower sDectra1 density is obtained by replacing M: in the expression for Vz/vW (using Eq. (1)) by the appropriate factors already discussed in [34] for an RH on SL media. This noise model assumes a correlation of the sign of My between neighbouring columns (the magnetic entities).

b. Results and discussion. One application of the model is illus- trated in Fig. 5, where the solid lines represent the calculated signal response, using the physical parameters of Table I and

t -70 1 s: -100

- -130 a

-160 ’ I I I I 0 25 50

frequency (MHz) - Fig. 9. Calculated signal and noise bf a PH as a function of the frequency

at v=10 mjs. Head: W = 5 pm, N = 20 turns, Tm=0 .14pm , r~ = 0.5; Medium: d = 100 nm, a = 50 nm, a, = 50 nm, M, = 400 kA/m, Mf/M, = 0.25, H$ = 90 kA/m . Noise slot-bandwidth: 10 kHz.

a spacing, a, of 90 nm (A) and 190 nm (B). These values include the effects of the transition width, a,. Probably, the thicker medium B yields a larger a, in addition to a larger a value due to a rougher substrate surface, as was observed using an SEM and a mechanical surface-roughness scanner. The 9 value used for fitting the long-wavelength output is 0.12 for curve A, which is equal to the value calculated by the reluctance model [9]. For medium B an 9 of 0.25 was calculated. The smaller value necessary for the fit (0.13) might be due to problems with the head-medium contact, owing to which the written track is smaller than the pole or core width. This was observed on a Bitter fluid pattern of a track written by the same head on a similar medium. Noise characteristics are not displayed, because the electronics noise level exceeded the medium noise.

The second application is shown in Figs. 9-10, in which the feasibility of high areal bit densities is indicated. Fig. 9 shows the result of a calculation at v = 10 m/s for a high-resolution pole on a thin, highly coercive DL medium. For the calculation of the head noise (V/m) we used the resistive part of the impedance of an RH (180 t2 at 50 MHz, larger than that of our PHs). The spike noise possibly due to the pole and the underlayer was neglected. The electronics noise voltage was obtained from an equivalent resistance of 20 a. The most important characteristics for the domain/column statistics are: a domain period of 60 nm, a domain width of 50 nm and a mean column width of 30 nm [34]. Fig. 10 depicts S/N at the detector, S/Nde,, as a function of the bit length when the pulses are detected by the so-called integrated detection method [2]. The dotted line represents the minimum S/Ndn of 12 dB, needed for detection with a 10-5 error probability. This criterion would indicate a minimum bit length of about 0.18 pm, yielding a minimum bit area of 0.92

7 O0.0 5.0 10.0

itbitlength ( l fum) - Fig. 10. S/NdL versus the inverse of the bit length for the response of

Fig. 9, using the integrated detection method. Dotted line: see text. Minimum bit length: 0.18 pm , yielding 0.92 pm2/bit.

T-

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medium: A

I 01 1-80

? t m v911 I I

I

L- E - I Fig. 11. Measured wavelength response of VSP 911 on medium A. W =

5.6 pm, T, = 2 x 70 nm, (laminated CoZrNb pole), L = 9 pm. N = 20 turns.

pm2. A track width as small as 3 pm would even yield a bit area of 0.76 pm2, provided that all other parameters remain unchanged.

Fig. 11 shows a measurement of one of our first narrow-track VSPs (V911). Its normalized long-wavelength output on medium A is even better than that of V831B in Fig. 5. As W is a factor of 36 smaller, the signal is seriously disturbed by the electronics noise. This is visible by the levelling-off of the output for wavelengths < 0.5 pm. The lower curve is the averaged medium noise. The S/N might be improved by using a higher velocity than the actual 0.8 mjs.

In conclusion, we have demonstrated that the playback model yields reasonable results when compared with experiments. As the model is not capable of analyzing recording effects, only a rough estimate of the real head-to-medium spacing can be made. The noise modelling does not include the influence of Barkhausen (spike) noise caused by domain-wall motions in the underlayer and/or pole. We indicated that a further refinement of the PH and enlarging of the Co-Cr H,I may lead to bit areas as small as 1 pm2, if a small head-medium spacing can be real- ized and if the spike noise can be suppressed sufficiently.

ACKNOWLEDGEMENTS

The authors are much indebted to J.J.M. Ruigrok for many helpful discussions on the theory of the playback and the efficiency models. We also wish to thank J.P.M. Verbunt. F.C.J. Hendriks and C.W.M.P. Sillen for their efforts in realizing the probe heads.

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