magnetic properties of antiferromagnetic oxide materials · franco ciccacci. dipartimento di fisica...

Edited by Lamberto Duo, Marco Finazzi, and Franco Ciccacci

Magnetic Properties of AntiferromagneticOxide Materials

Surfaces, Interfaces, and Thin Films

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Edited by

Lamberto Duo, Marco Finazzi, and

Franco Ciccacci


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Edited by Lamberto Duo, Marco Finazzi, and Franco Ciccacci


Surfaces, Interfaces, and Thin Films

The Editors

Lamberto DuoMarco FinazziFranco CiccacciDipartimento di FisicaPolitecnico di Milano20133 MilanoPiazza Leonardo DA Vinci 32Italy

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ISBN: 978-3-527-40881-8

V

Contents

Preface XIList of Contributors XV

1 Low-Dimensional Antiferromagnetic Oxides : An Overview 1Marco Finazzi, Lamberto Duo, and Franco Ciccacci

1.1 Introduction 11.2 Finite-Size Effects on the Magnetic Ordering Temperature 21.3 AFM Anisotropy 61.3.1 Magnetocrystal Anisotropy 71.3.2 Dipolar Anisotropy 71.4 Interlayer Coupling in AFMFM Bilayers and Multilayers 91.4.1 AFMFM Interface Coupling 91.4.2 Coupling between FM Layers Separated by an AFM Oxide Spacer 121.5 Micromagnetic Structure at AFMFM Interfaces 141.6 Applications 171.7 Conclusions 18

References 18

2 Growth of Antiferromagnetic Oxide Thin Films 25Sergio Valeri, Salvatore Altieri, and Paola Luches

2.1 Introduction 252.2 Nickel Oxide 292.2.1 Ultrathin NiO Layers 292.2.2 Thick NiO Films 352.3 Cobalt Oxide 402.3.1 Ultrathin CoO Layers 402.3.2 Thick CoO Films 432.4 Other Oxides 472.4.1 MnO(001) 472.4.2 FeO 482.4.3 -Fe2O3 50

Magnetic Properties of Antiferromagnetic Oxide Materials.Edited by Lamberto Duo, Marco Finazzi, and Franco CiccacciCopyright 2010 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 978-3-527-40881-8

VI Contents

2.5 OxideSubstrate Interface 532.6 Polar-Oxide Surfaces 562.7 Conclusions and Perspectives 58

Acknowledgments 60References 61

3 Dichroism in X-ray Absorption for the Study of AntiferromagneticMaterials 69Jan Vogel and Maurizio Sacchi

3.1 X-ray Absorption and X-ray Dichroism 703.1.1 X-ray Magnetic Circular Dichroism in the One-Electron

Approximation 713.1.1.1 Spin-Orbit Coupling in the d-Band 733.1.1.2 Core-Hole and Other Many-Body Effects 733.1.2 XMCD in the Strongly Correlated Limit: Multiplet Effects 753.1.2.1 Ligand Field Atomic Multiplet Calculations 763.1.2.2 Charge-Transfer Effects 773.2 Sum Rules for X-ray Dichroism 783.2.1 Orbital Moment 783.2.2 Spin Moment 793.2.3 Sum Rule for Linear Dichroism 803.3 Experimental Determination of X-ray Absorption 813.4 Linear X-ray Dichroism in Rare-Earth Compounds 833.4.1 FexTb1x Amorphous Thin Films 843.5 Magnetic Dichroism in TM Oxides 863.5.1 Magnetic Linear Dichroism in Thin NiO Films on MgO 863.5.1.1 Calculations 873.5.1.2 Sample Preparation 893.5.1.3 Experiment 893.5.1.4 Results 893.6 Conclusions 93

References 94

4 Antiferromagnetic Oxide Films on Nonmagnetic Substrates 99Tjipke Hibma and Maurits W. Haverkort

4.1 Introduction 994.2 Electronic Structure of TM Oxides 1004.2.1 Mott-Hubbard and Charge Transfer Insulators 1004.2.2 Ligand Field Theory 1014.2.2.1 Independent Electron Ligand Field Theory 1014.2.2.2 Multiplet Ligand Field Theory 1034.2.3 SpinOrbit Coupling in Cubic Symmetry 1034.2.3.1 Single Electron in an Open t2g Shell 1044.2.3.2 d6 and d7 Configurations 1054.3 Magnetic Structure 106

Contents VII

4.3.1 Magnetic Ordering of MnO, FeO, CoO and NiO 1064.3.1.1 MnO and NiO 1074.3.1.2 FeO and CoO 1074.4 X-ray Absorption Spectroscopy 1084.4.1 Magnetic Linear Dichroism 1104.5 Strain 1154.6 Linear Dichroism Results for AF TM Monoxide Layers 1204.6.1 XMLD of Epitaxial NiO(100)/MgO layers 1204.6.2 Ligand-Field-Induced Linear Dichroism in Strained NiO/Ag(100)

Layers 1224.6.3 Isotropic XAS of CoO 1254.6.4 Linear Dichroism of Strained CoO Layers 1274.6.5 Spin Alignment in Strained CoO 1314.6.6 Electronic Stucture of Strained CoO 1324.6.7 Strain-Induced Linear Dichroism in MnO Layers 1334.7 Conclusions 137

Appendix: Polarization and Spin Direction Dependence of the LinearDichroism in Nonspherical Symmetry 137References 140

5 Exchange Bias by Antiferromagnetic Oxides 143Marian Fecioru-Morariu, Ulrich Nowak, and Gernot Guntherodt

5.1 Introduction 1435.2 Theoretical Background 1455.2.1 Diluted Antiferromagnets in a Magnetic Field 1455.2.2 Domain-State Model for Exchange Bias 1485.2.3 Mean-Field Solution of the Domain-State Model 1495.3 Experiments 1565.3.1 Antiferromagnetic Oxides: CoO, Co1y, Co1xMgxO 1565.3.2 Exchange Bias between the Ferromagnet Co and the Diluted

Antiferromagnet CoO 1615.3.2.1 Nonmagnetic Dilution of the Antiferromagnet 1625.3.2.2 Hysteresis Curves and Uncompensated Magnetic Moments

(Vertical Shift) 1645.3.2.3 Substitutional versus Structural Defects 1655.3.2.4 Temperature Dependence 1675.3.2.5 Thermoremanent Magnetization and Training

Effect 1705.3.2.6 Cooling-Field Dependence 1735.3.2.7 Antiferromagnetic Thickness Dependence 1745.3.2.8 Blocking Temperature Distribution 1755.4 Model Calculations 1785.4.1 Modeling of Experimental Data 1785.4.2 Anisotropy Dependence 1815.4.3 Structural Dependence 183

VIII Contents

5.5 Conclusions 186References 187

6 Theory of FerromagneticAntiferromagnetic Interface Coupling 191Alexander I. Morosov and Alexander S. Sigov

6.1 Introduction 1916.2 Frustrations on the FerromagnetAntiferromagnet Interface 1926.2.1 Uncompensated Surface of the Antiferromagnet 1926.2.2 Compensated Surface of the Antiferromagnet 1946.3 Mathematical Model 1956.4 The Interface between Thick FerromagnetAntiferromagnet

Layers 1966.4.1 Uncompensated Surface of the Antiferromagnet 1976.4.1.1 R (f , af ) 1976.4.1.2 R (f , af ) 2006.4.2 Compensated Surface of the Antiferromagnet 2016.5 A Thin Ferromagnetic (Antiferromagnetic) Layer on a Thick

Antiferromagnetic (Ferromagnetic) Substrate 2066.5.1 Uncompensated Surface of the Antiferromagnet 2066.5.1.1 The Case of af 1 2066.5.1.2 A Thin Layer with a Much Higher Exchange Rigidity 2136.5.2 Compensated Surface of an Antiferromagnetic Substrate 2186.6 Spin-Valve FerromagnetAntiferromagnetFerromagnet

System 2196.6.1 Domain Walls in a Three-Layer System 2206.6.1.1 f ,af a/af 1 2216.6.1.2 f ,af a/af 1 2226.6.2 Phase Diagram 2266.6.3 Matching Experimental Data? 2336.7 Conclusion 236

References 236

7 AntiferromagneticFerromagnetic Oxide Multilayers: Fe3O4-BasedSystems as a Model 239P. J. van der Zaag and Julie A. Borchers

7.1 Introduction 2397.2 Interface and Structural Effects 2407.2.1 Chemical and Structural Quality Effects 2427.2.2 Interface Effects on Magnetic Properties 2447.2.2.1 Reduced Magnetization and Dead Layers at the Interface 2447.2.2.2 Anisotropy and Interface Anisotropy of Thin Fe3O4 Layers 2467.2.2.3 The Interface Structure: Antiphase Boundaries 2507.3 Magnetic Coupling Studies 2587.3.1 Antiferromagnetic Multilayers 2587.3.1.1 AFNM Multilayers: Finite-Size Scaling 258

Contents IX

7.3.1.2 AFAF Multilayers: Exchange Coupling 2617.3.2 AntiferromagneticFerromagnetic Coupling 2637.3.2.1 Exchange Anisotropy 2637.3.2.2 Dependence on Antiferromagnetic Thickness 2667.3.2.3 Perpendicular Coupling 2697.3.2.4 Reduction of the Blocking Temperature 2747.3.3 Coupling across Intermediary Layers 2777.3.3.1 Coupling across a Nonmagnetic Layer 2777.3.3.2 Coupling across an Antiferromagnetic Layer 2817.3.4 Perpendicular Anisotropy 2837.4 Properties of Coupled Systems 2857.4.1 Magnetoresistance Effects 2857.4.1.1 Tunnel Junctions using Fe3O4 MgO 2867.4.1.2 Tunnel Junctions using Fe3O4 AlOx 2877.4.1.3 Tunnel Junctions using Fe3O4 oxideLSMO 2877.4.1.4 Tunnel Junctions using a CoFe2O4 Spin Filter 2887.4.2 Magnetooptical Effects 2897.5 Conclusions and Outlook 290

Acknowledgments 291References 291

8 Micromagnetic Structure Imaging Antiferromagnetic Domains usingSoft X-Ray Microscopy 301Hendrik Ohldag

8.1 Introduction 3018.1.1 Origin of Antiferromagnetic Domains 3028.1.2 Soft X-Ray Spectroscopy 3068.1.3 Photoemission Electron Microscope 3088.1.4 Soft X-Ray Dichroism 3108.2 Antiferromagnetic Domain Imaging using PEEM 3138.2.1 Imaging Antiferromagnetic Domains and Domain

Walls 3138.2.2 Magnetism and Crystallography 3178.3 Antiferromagnetic Domains in Exchange-Coupled

Systems 3188.3.1 AntiferromagneticFerrmagnetic-Exchange Coupling 3198.3.2 Magnetic Domains at Interfaces of Antiferromagnets with

Ferromagnets 3228.3.3 Origin of Spin Reorientation 3278.4 Temperature Dependence of the Antiferromagnetic Domain

Structure 3298.5 Antiferromagnetic Domains and Exchange Bias 3338.5.1 A Quick Look at a Fluoride 3338.5.2 Magnetic Reversal Mechanism on the Microscopic

Scale 335

X Contents

8.6 Summary and Outlook 337References 338

Index 341

XI

Preface

This book is devoted to antiferromagnetic oxides, both in the form of surfaces andthin films, and in the form of interfaces and multilayers with other magnetic ornonmagnetic materials. Films and multilayers with a thickness of a few nanome-ters are important examples of low-dimensionality systems that can exhibit verydifferent physical properties with respect to their bulk counterparts. This field istestifying a great experimental effort in the production of artificial structures withoriginal magnetic properties. An example of relevant scientific and technologicalinterest is the rapid development in the last years of spintronics, a discipline thataims to exploit the intrinsic spin of electrons and its associated magnetic mo-ment, in addition to its fundamental electronic charge, in solid-state devices. Theactual trend toward miniaturized magnetic devices requires new investigations oflow-dimensional magnetic systems from a fundamental point of view. While con-fined systems based on ferromagnetic materials have been the subject of intensivestudy, the investigation of the magnetic properties of antiferromagnetic surfaces,thin films, and interfaces has received much less attention, mostly because of theexperimental difficulties in addressing the local magnetic properties of antifer-romagnetic materials. Nevertheless, the last two decades have witnessed a rapiddevelopment of experimental techniques characterized by a good sensitivity to suchproperties. As a consequence, systems in which a ferromagnet interacts with anantiferromagnetic partner have aroused an increasing interest in the scientific com-munity, which is motivated by the discovery of their unique magnetic properties(e.g., exchange coupling, modification of the magnetic domain structure, and spinorientation) of potential interest for applications. In particular, the phenomenonof exchange bias [1], consisting in the breaking of the time reversal symmetry andin the onset of unidirectional magnetic anisotropy in a field-cooled system wherea ferromagnetic material is coupled to an antiferromagnetic partner, is widelyemployed in the technology of reading heads for modern hard disks.

It is by now widely accepted that the key to understanding such phenomena isthe spin structure at the antiferromagnetferromagnet interface and its dynamicalchanges. In this respect, transition-metal oxides represent an important class ofantiferromagnetic materials because of their high Neel temperature and chemicalstability. They are also large band-gap insulators so that their magnetic propertiescan be accurately described in terms of magnetic moments localized on the


XII Preface

cations, interacting via well-understood short-range interactions. For these reasons,transition-metal oxides occupy a privileged space in the scientific literature and areoften considered as model antiferromagnetic systems. Moreover, the interest inoxide antiferromagnets goes beyond the phenomena that can be observed whenthey interact with a ferromagnetic system. In fact, complex behaviors such as spinreorientation might be induced in antiferromagnetic oxides even in the absenceof bias exchange with a ferromagnetic partner. Antiferromagnetic transition-metaloxides are also important in connection with at least three classes of oxide materialsthat have a great technological relevance (but that will not be discussed in thisvolume), namely, high-Tc superconductor cuprates, colossal magnetoresistancemanganites, and multiferroic materials, where a widely accepted general idea isthat in these materials the interplay of charge and spin fluctuations is a centralissue. In particular, the paradigm model describing this interplay in cuprates is theAndersons superexchange theory, which also governs the magnetic properties ofantiferromagnetic insulators, such as NiO or CoO, often considered as archetypematerials for the antiferromagnetic parent compounds of high-Tc cuprates.

This book gives the first comprehensive account of these topics, bringing togetherexperimental and theoretical methods. It is focused on the study of the magneticbehavior of spatially confined antiferromagnetic transition-metal-oxide systemswhen their dimensions are scaled down to nanometric level, with particularemphasis on the growth and the magnetic characterization through differentexperimental methods and theoretical modeling approaches.

This volume is designed along the following guidelines. The tutorial Chapter 1outlines the magnetic properties of low-dimensional antiferromagnetic transition-metal-oxide systems and contains an overview of the significant physical phenom-ena that intervene in determining their origin. Chapter 2 extensively discussesthe techniques employed to fabricate multilayer and thin film structures. Thischapter highlights the close relationship existing between the structure and mag-netism in low-dimensional antiferromagnetic oxides. Chapter 3 discusses one ofthe most widespread experimental techniques giving access to the properties ofantiferromagnetic materials, namely, X-ray absorption and dichroism. This chapterrepresents a general introduction to X-ray absorption and how it is measured. Itdiscusses the selection rules that give rise to the polarization dependence of X-rayabsorption and how information about the magnetic properties of matter can beobtained from them. Chapter 4 deals with the low-dimensional antiferromagnetictransition-metal oxides as such, describing samples consisting of thin epitaxiallayers on nonmagnetic substrates, which are therefore not influenced by magneticunderlayers. The effects of symmetry-lowering and crystal field in noncubic en-vironments are addressed both experimentally, discussing X-ray absorption anddichroism data, and theoretically, within an atomic multiplet approach. Chapter 5 isdevoted to the phenomenon of exchange bias. The central topic of this chapter is theso-called domain state model in which exchange bias emerges as a consequenceof a net magnetization in the volume and also at the interface of the antiferromagnetstabilized by nonmagnetic defects. Chapter 6 provides a theoretical discussion ofthe phenomena (exchange coupling, exchange bias, spin reorientation, magnetic

Preface XIII

domain structure, etc.) occurring at the interface between a ferromagnetic and anantiferromagnetic material. Phase diagrams describing the behavior of bilayers andtrilayers are obtained as a function of the relevant parameters. Chapter 7 focuseson the experimental investigation of Fe3O4-based ferrimagnetantiferromagnetmultilayers comprising NiO or CoO as model systems for addressing interfacemorphology and chemical structure, anisotropy, interlayer exchange coupling, andhow these mechanisms affect the overall magnetic properties of the multilayers.Finally, Chapter 8 presents an extensive X-ray microscopy study of the micromag-netic structure in exchange-coupled interfaces constituted by a ferromagnetic metaland an antiferromagnetic oxide.

To conclude, we would like to dedicate the last part of this preface to thank theauthors of the various chapters of this book for their cooperation. We appreciatetheir patience in accepting our reminders for keeping to time and their willingnessin following the editors suggestions. We would also like to thank EdmundImmergut, Wiley-VCH in New York, for his friendly help in first proposing to usto start on this book, in enabling us to overcome our initial hesitations, and inguiding us in the first steps of the project up to the acceptance of the same byWiley-VCH, and Anja Tschortner, Wiley-VCH Ed. Physics Department in Berlin,for her continuous and extraordinary assistance during the preparation of thisbook.

Finally, we would like to express our gratitude towards our friends and colleagues,who are too numerous to list here, to whom we are much indebted for inspiringdiscussions and help.Milano, October 2009 Lamberto Duo

Marco FinazziFranco Ciccacci

Reference

1. Meiklejohn, W.H. and Bean, C.P. (1957)New magnetic anisotropy. Phys. Rev., 105,904.

XV

List of Contributors

Salvatore AltieriUniversita di Modena eReggio EmiliaDipartimento di FisicaVia G. Campi 213/aI-41100 ModenaItaly

Julie A. BorchersNational Institute ofStandards and TechnologyGaithersburgMD 20899USA

Franco CiccacciPolitecnico di MilanoLNESS Dipartimento di FisicaPiazza Leonardo da Vinci 3220133 MilanoItaly

Lamberto DuoPolitecnico di MilanoLNESS Dipartimento di FisicaPiazza Leonardo da Vinci 3220133 MilanoItaly

Marian Fecioru-MorariuRWTH Aachen UniversityPhysikalisches Institut (IIA)Templergraben 5552056 AachenGermany

and

Oerlikon Solar AGHauptstrasse la9477 TrubbachSwitzerland

Marco FinazziPolitecnico di MilanoLNESS Dipartimento di FisicaPiazza Leonardo da Vinci 3220133 MilanoItaly

Gernot GuntherodtRWTH Aachen UniversityPhysikalisches Institut (IIA)Templergraben 5552056 AachenGermany


XVI List of Contributors

Tjipke HibmaUniversity of GroningenZernike Institute forAdvanced MaterialsNijenborgh 4NL-9747 AG GroningenThe Netherlands

Maurits W. HaverkortMax Planck Institute for SolidState ResearchHeisenbergstrasse 1D-70569StuttgartGermany

Paola LuchesNational Research Centre onNanostructures and Biosystems atSurfacesCNR-INFMS3, Via G. Campi 213/aI-41100 ModenaItaly

Alexander I. MorosovElectronics and Automation(Technical University)Moscow State Institute ofRadioengineeringpr. Vernadskogo 78Moscow 19454Russia

Ulrich NowakUniversitat KonstanzFachbereich PhysikUniversitatsstrasse 1078457 KonstanzGermany

Hendrik OhldagStanford SynchrotronRadiation LightsourceSLAC National Accelerator Center2575 Sand Hill RoadMailstop 69Menlo Park 94025CAUSA

Maurizio SacchiSynchrotron SoleilBote Postale 48F-91142 Gif-sur-YvetteParisFrance

Alexander S. SigovElectronics and Automation(Technical University)Moscow State Institute ofRadioengineeringpr. Vernadskogo 78Moscow 19454Russia

Sergio ValeriUniversita di Modena eReggio EmiliaDipartimento di FisicaVia G. Campi 213/aI-41100 ModenaItaly

and

National Research Centre onNanostructures and Biosystems atSurfacesCNR-INFMS3, Via G. Campi 213/aI-41100 ModenaItaly

List of Contributors XVII

Pieter Jan van der ZaagPhilips Research LaboratoriesHigh Tech Campus 12a5656 AE EindhovenThe Netherlands

Jan VogelCNRS and UJFInstitut NeelB.P. 16638042 GrenobleFrance

1

1Low-Dimensional Antiferromagnetic Oxides : An OverviewMarco Finazzi, Lamberto Duo, and Franco Ciccacci

1.1Introduction

In the last two decades, the availability of experimental techniques endowed withhigh sensitivity with respect to the magnetic properties of antiferromagnetic (AFM)materials has motivated a large amount of studies dedicated to the investigation oflow-dimensional AFM systems consisting of small particles or films deposited ontoeither nonmagnetic or ferromagnetic (FM) substrates. Similar to the well-knownFM materials, such confined AFM systems are in fact characterized by magneticproperties that, because of interface or size effects, can be considerably differentfrom the ones observed in the bulk [1]. Examples range from the stabilization of ex-otic AFM ordering to the onset of uniaxial anisotropy in low-dimensional AFM sam-ples. Moreover, systems comprising AFMFM interfaces represent a world of theirown, thanks to their rich phenomenology related to interface exchange coupling.

Finite-size effects in both FM and AFM materials reflect deviations from bulkproperties associated with the reduction of the sample dimensions. So-calledintrinsic effects occur in material systems for which one or more sampledimensions, for example, the thickness of a layer or diameter of a particle, iscomparable with the intrinsic correlation length scale of the property beingconsidered. Strongly correlated systems such as AFM oxides are characterizedby very short correlation lengths, so intrinsic finite-size effects can be observedonly in ultrathin films or nanoparticles. In addition, surface-related finite-sizeeffects might be caused by the competition between the properties of atoms in thecore of a particle or layer and those at the surface, possibly originating from thereduced coordination number. As an example, surface spins often possess highermagnetocrystal anisotropy than the ones in the sample volume because of thereduced symmetry. Chemical or structural effects may also arise due to phe-nomena such as surface segregation, relaxation, or reconstruction. Of course, theenvironment (the material surrounding the particle or the film substrate) can alsodramatically alter the properties of interface atoms through hybridization, strain, orchemical interdiffusion, not to mention the crucial role of exchange in determiningthe magnetism of systems where an AFM material interacts with an FM partner.


2 1 Low-Dimensional Antiferromagnetic Oxides : An Overview

The high degree of correlation between the magnetic, chemical, structural, andmorphologic features obviously makes the preparation and the characterizationof high-quality samples a crucial point in any study involving low-dimensionalsystems (see 2). In this respect, AFM transition-metal (TM) monoxides are oftenregarded as a privileged reference. The reasons for this choice are manifold. First,these oxides can be grown as high-quality thin films on appropriate substrates andare characterized by a high chemical and mechanical stability. Second, their AFMordering temperature (Neel temperature TN ) is relatively high: to cite two relevantcases, TN = 523 K for bulk NiO and TN = 291 K for bulk CoO. In the latter case, theproximity of TN to room temperature represents an additional advantage in realizingexchange-biased systems, where field cooling from above to below TN is required.Another important feature of TM oxides is their insulating nature resulting fromstrong inter- and intra-atomic electronic correlations. Their magnetic propertiesarise as a consequence of the short-range superexchange interaction mediated bythe oxygen bonds [2]. Because of the absence of itinerant magnetism associatedwith conduction electrons, the only long-range magnetic interaction is representedby the dipoledipole interaction, which can be neglected in many cases. Therefore,from the magnetic point of view, TM oxides can be described in the frame ofthe Heisenberg or Ising formalism as ensembles of well-localized spins withnear-neighbor interactions. Finally, we would like to mention that AFM TM oxidesare also considered as model systems for the AFM parent compounds of high Tccuprates since, in the latter, the interplay between charge and magnetic orderingis described by the Andersons superexchange theory, which also governs themagnetic properties of AFM insulators such as NiO or CoO.

In this introductory chapter, we present a survey of the peculiar magnetic phe-nomena observed in low-dimensional systems based on AFM TM oxides, suchas surfaces, thin films, interfaces with magnetic or nonmagnetic materials, andmultilayers. We also give an overview of the significant physical phenomena thatintervene in determining their origin. The chapter is organized as follows: inSection 1.2 we address finite-size effects on the value of the Neel temperaturefor AFM oxide particles and thin films. Section 1.3 is dedicated to AFM thin-filmmagnetic anisotropy and how it is influenced by interaction with a nonmag-netic substrate, while interlayer magnetic coupling and micromagnetic structureat AFMFM interfaces and multilayers are examined in Sections 1.4 and 1.5,respectively. Finally, Section 1.6 concludes the chapter by discussing applications.

1.2Finite-Size Effects on the Magnetic Ordering Temperature

The reduction of the critical magnetic ordering temperature Torder is a typicalfinite-size effect in both FM (Torder = TC = Curie temperature) and AFM (Torder =TN ) low-dimensional systems. It can be seen as a consequence of the sampleasymptotically approaching the conditions at which the MerminWagner theoremapplies as its size is progressively reduced. This theorem states that, becauseof fluctuations, continuous symmetry cannot be spontaneously broken (i.e., the

1.2 Finite-Size Effects on the Magnetic Ordering Temperature 3

sample cannot develop long-range FM or AFM order) at finite temperature insystems with short-range interactions in dimensions d 2 [3]. Experiments haveevidenced drastic reductions in the magnetic transition temperature TN for avariety of AFM oxides in low-dimensional geometries such as CuO nanoparticles[47], NiO thin films [8, 9], CoO nanoparticles [10] and films [11, 12], and Co3O4nanoparticles [1315], nanotubes [16], and nanowires [17].

In a simple mean-field approach, which assumes Torder to be proportional to theexchange energy density of the particle or thin film, the reduction of the magnetictransition temperature is due to the decrease in the total exchange energy associatedwith the reduced number of neighboring atoms. In this picture, the systemenvironment is not passive and might contribute to defining the total exchangeenergy, for instance, by inducing surface magnetic anisotropy via a strain field or bymodifying the magnitude of the interface moments and the strength of their mutualcoupling through hybridization or other interactions (see below). According to themean-field model, the variation of Torder with respect to the bulk value Torder()is expected to be proportional to the inverse of the particle size or of the filmthickness D. However, this prediction is not consistent with the experimentalresults, and the reduction in the ordering temperature Torder with size is betterdescribed in terms of scaling theories [18], according to which the correlationlength of the fluctuations of the AFM order parameter diverges logarithmicallywith the reduced temperature (T Torder)/Torder as the temperature T approachesthe magnetic ordering transition Torder. For a system with size D much larger thana characteristic length describing the spatial extent of the spinspin coupling,this yields a fractional decrease of Torder that follows a power-law curve [19]:

Torder() Torder(D)Torder() =

( + a

2D

)(1.1)

where is the (constant) shift exponent and a is the lattice spacing. ForD , Torder is expected to vary linearly with respect to D [19]:

Torder(D) = Torder() D a2 (1.2)

The details of the measured dependence of Torder upon D show large differencesover the experimentally investigated systems, suggesting that environment effectsplay a significant role. Moreover, the value of is model-dependent: as anticipatedabove, one obtains = 1 in mean-field theory [18], while = 1.4 or 1.6 for a systemdescribed by either the three-dimensional Heisenberg [20] or Ising [21] Hamilto-nian, respectively. In practice, and are considered as adjustable parameters thathave to be fitted to the experimental data: has been found to be close to 1.1 forCo3O4 nanoparticles [15], while 1.5 for CuO thin films [11], being of the orderof a few nanometers in both cases. A more recent model explicitly considers the dis-ordering effect of the lattice thermal vibrations on the spinspin coherence lengthat the transition temperature. It predicts a Torder dependence on D of the form [22]

Torder(D)

Torder() = e(

1D/D01

)(1.3)


In the previous expression, D0 = 2(3 d)a (with d = 0 for particles, d = 1 fornanorods, and d = 2 for thin films), while = 2s (D)/ 2v (D), s and v correspond-ing to the root-mean square average amplitude of the oscillations of atoms at thesurface (or interface) and in the volume at the transition temperature, respectively.In this model, TN is again expected to depend on the total systemenvironmentinterface exchange energy.

The models discussed above can be generalized to low-dimensional systems ininteraction with magnetic environments. In this case, the total exchange energydensity of the low-dimensional sample might be even higher than in the bulkbecause of interface exchange coupling. In this case TN might increase as thesample size is reduced, as observed in NiO/CoO and Fe3O4/CoO multilayers[8, 23]. Similarly, it has been demonstrated that the magnetic coupling of Conanoparticles embedded in a CoO matrix leads to a marked improvement in thethermal stability of the moments of the FM nanoparticles, with an increase of almost2 orders of magnitude in the temperature at which superparamagnetism sets incompared to similar particles in a nonmagnetic medium [24]. An intriguing andnot yet understood size-related effect is the dependence of the blocking temperatureTB upon the AFM layer thickness in exchange-biased AFMFM multilayers. TBis defined as the temperature above which the system does not display any bias,and in Fe3O4/CoO multilayers it is observed to decrease by reducing the CoO layerthickness while TN , as mentioned above, increases [23].

To further highlight the active role even a nonmagnetic substrate might havein determining the value of TN in a thin film, we conclude this section bydiscussing the case of NiO ultrathin films epitaxially deposited on MgO(001)and Ag(001) single-crystal substrates [25]. Stoichiometric and high-quality NiOfilms were grown by atomic-oxygen-assisted reactive deposition and capped in situwith a protecting MgO film consisting in 25 monolayers (MLs) that avoided NiOfilm contamination by the residual gas inside the ultrahigh-vacuum chamber andprevented possible oxygen loss during thermal cycling. NiO and MgO have thesame rock-salt crystal structure with a lattice constant of 4.2 and 4.1 A, respectively,corresponding to a tiny lattice misfit of 0.2%. Ag has a face-centered cubic (fcc)structure with a lattice constant equal 4.09 A and compared to NiO has a latticemisfit of about 3%. Nevertheless, misfit dislocations are avoided by keeping the filmthickness below the critical thickness for strain relaxation (about 30 ML for NiO/Ag)[26]. The magnetic properties of the NiO layer have been investigated with X-raymagnetic linear dichroism (see Chapter 3) performed at the Ni L2 edge. By plottingthe dichroic signal (L2 ratio) as a function of temperature, as done in Figure 1.1,one obtains a direct measure of the long-range order parameter and of the Neeltemperature of the material. Figure 1.1 reports results measured for 3-ML- and30-ML-thick NiO films on Ag(001) and for a 3-ML-thick NiO film on MgO(001). Forthe 30-ML NiO/Ag film, an ordering temperature TN = 535 K in thus measured,which is close to the bulk value of 523 K [27]. Apparently, the 30-ML NiO/Ag filmis already thick enough to act as the bulk oxide and is not affected any longer by theunderlying Ag substrate [28, 29]. Figure 1.1 also suggests that there is no magneticorder in the 3-ML NiO/MgO sample in the measured temperature range, denoting

1.2 Finite-Size Effects on the Magnetic Ordering Temperature 5

1.20

1.15

1.10

1.05

1.30

1.25

1.20

1.15

1.05

1.000 100 200 300 400 500 600

30 ML NiO/Ag(100)

30 ML NiO/Ag(100)

3 ML NiO/MgO(100)

TN = 535 K

TN = 390 K

TN < 40 K

Temperature (K)

L 2 r

atio

L 2 r

atio

(a)

(b)

Figure 1.1 Temperature-dependent Ni linear dichroismsignal (L2 ratio) of (a) 30-ML NiO/Ag(100) and (b) 3-MLNiO/Ag(100) and 3-ML NiO/MgO(100). Reprinted figurewith permission from [25]. 2009, by the American PhysicalSociety.

a strong finite-size-induced reduction of TN that can be interpreted as discussedearlier in this section. Conversely, the Neel temperature of the 3-ML NiO/Ag filmis TN = 390 K, at least a factor of 10 higher than in the 3-ML NiO/MgO sample. Itis important to notice that the NiO/Ag and NiO/MgO films are essentially identicalas far as the NiO part is concerned (same thickness, crystal quality, interfaceroughness), except for the different value of the lattice mismatch with respect tothe substrate. The origin of such a strongly different TN value in NiO/MgO andNiO/Ag must thus be external to the NiO film itself and should be looked for inthe different types of interactions at the NiO/MgO and NiO/Ag interfaces. To thispurpose, we have to consider how the superexchange interactions in the NiO filmscan be modified by the presence of the substrate. The value of the superexchangecoupling constant J in a system subjected to charge fluctuations described by theHubbard energy U and the cationanion charge-transfer energy [30] is given bythe following expression [3133]:

J = 2t2

2

(1U

+ 1

)(1.4)


with t being the anion 2p-cation 3d transfer integral. The value of J can be alteredin three ways by the interaction with the substrate, resulting in a consequentmodification of TN .

The first mechanism refers to the prediction that a medium with a high dielectricpolarizability should provide an effective screening for various charge excitations ina nearby located material [34]. Such a screening effect on the band gap, the Hubbardenergy U, and the charge-transfer energy has indeed been experimentallyconfirmed in C60/Ag [35] and MgO/Ag [28, 29, 36]. According to this expectation, theobserved higher TN value for NiO/Ag compared to NiO/MgO would be associatedto the conducting nature of the Ag substrate with respect to the insulating characterof MgO, leading, in agreement with Eq. (1.4), to a higher superexchange couplingconstant J as a result of the reduction of U and by image-charge screening.

A second explanation considers the different strain state induced in the NiO over-layer by the Ag or MgO substrate. By modifying the in-plane interatomic distance,strain influences the overlap between adjacent orbitals and the value of the transferintegral t, affecting the value of J and hence TN . We recall that the application ofhydrostatic pressure is known to enhance TN in TM oxides [3740]. However, thetheoretical [38] and experimental [39, 40] dependence of J and TN on the lattice pa-rameter variation is too weak to justify the 10-fold increase of TN in NiO/Ag with re-spect to NiO/MgO as due to the different strain state. Moreover, the strain in an epi-taxial layer is nonisotropic and one could expect that the lattice-spacing effect on TNwill be smaller than the one in an isotropically compressed system, since, in the firstcase, the change in the interatomic spacing along the surface normal is generallyopposite to that in the film plane. Indeed, it has been experimentally shown that forNiO and CoO films on MgO uniaxial strain up to 2% has a negligible effect on TN [8].

Finally, interface hybridization might represent a third mechanism accordingto which the substrate might be capable of influencing TN . In this respect, wenote that density-functional band-structure calculations on both free-standing andAg(001)-supported ultrathin NiO films find that the superexchange constant Jof a 3-ML-thick film should hardly be affected by a nearby substrate [41, 42].These arguments leave screening effects as the only possible phenomenon thatis able to account for the large value of the Neel temperature in 3-ML NiO/Agthin films, suggesting at the same time an effective method to counterbalancefinite-size-related reduction of critical temperatures in oxide systems.

1.3AFM Anisotropy

As mentioned in the previous section, even a nonmagnetic substrate might playan active role in determining the value of TN in a thin film. In this section, wediscuss how the substrate can also influence the magnetic anisotropy of an AFMoverlayer. We limit the discussion to nonmagnetic substrates, leaving AFMFMcoupled layers to the next section.

Well known and long-studied in FM systems, magnetic anisotropy is a phe-nomenon that has been unveiled only quite recently in AFM thin films. For

1.3 AFM Anisotropy 7

instance, while the surface magnetic structure of cleaved NiO(001) single crystalsis said to be bulk terminated [43], NiO(001) thin layers (less than 20 ML) epitaxiallygrown on MgO(001) exhibit an out-of plane uniaxial anisotropy [9]. On the otherhand, the AFM anisotropy of epitaxial NiO/Ag(001) is found to depend on the NiOthickness: for 30-ML-thick NiO/Ag films, AFM domains with easy axis closer tothe surface normal are favored, while 3-ML NiO/Ag are characterized by in-planeAFM anisotropy [44]. CoO films display local moments with magnitude and ori-entation strongly dependent on the strain induced by the substrate: the magneticmoments in CoO/MnO(001) are oriented out of plane while those in CoO/Ag(001)are in-plane [45]. Hereafter, we discuss the possible sources of AFM magneticanisotropy.

1.3.1Magnetocrystal Anisotropy

While a 3d isolated ion is described by a Hamiltonian that has spherical symmetry,the same ion embedded in a crystal is subjected to the crystal field resulting fromthe interactions of the electrons belonging to each ion with the surrounding atoms.If this crystal field is strong enough, the orbital degeneracy is completely removedand the ground state is an orbital singlet (the orbital momentum is quenched)[46]. In these conditions, spin represents the only contribution to the total magneticmoment of the ion, and is, to first approximation, completely decoupled fromthe lattice. In other words, the system does not develop any magnetic anisotropy.However, if the crystal field is not too large, the spinorbit interaction, which isproportional to L S (L = total orbital momentum operator; S = total spin operator),prevents the quenching of the orbital momentum and couples the spin to the lattice,establishing magnetic anisotropy [46]. In a cubic ionic 3d compound, the crystalfield can be considered as a small perturbation (of the order of 104 K) with respectto the Coulomb interactions between the electrons occupying the d-shell, but isconsiderably larger than the spinorbit interaction (about 100 K). Sizable anisotropycan thus emerge only when the symmetry of the lattice and the degeneracy of theground state are further reduced by a small perturbation. The above-mentionedanisotropy observed in CoO strained films can be explained in this frame (see alsoChapter 4): the tetragonal distortion imposed by the substrate further splits thepartially occupied t2g orbitals that constitute the ground state resulting from theapplication of a cubic crystal-field to the 3d shell. The sign of the splitting dependson the type of tetragonal strain (compressive or extensive) and determines whetherthe CoO spins will preferentially align in-plane or out of plane [45].

1.3.2Dipolar Anisotropy

Long-range magnetic dipoledipole interactions have been suggested to play animportant role in determining the bulk AFM structure of TM monoxides such asMnO and NiO, where the magnetocrystal anisotropy is expected to vanish [47].


In MnO, this happens because the d-shell electronic configuration of the Mn2+

ion is 3d5, corresponding to an orbital singlet ground state even in the isolatedion. The case of NiO is different: the Ni2+ 3d fundamental state is characterizedby completely filled t2g orbitals and partially occupied eg orbitals. Now, L S doesnot have matrix elements coupling different eg states, implying that the spinorbitinteraction is also negligible for NiO.

The fcc lattice formed by the cations in TM monoxides can be viewed asa combination of four simple cubic lattices. In each sublattice, the momentsare forced by the superexchange interaction to align ferromagnetically within{111} planes, while adjacent {111} planes are coupled antiferromagnetically. Thesuperexchange interaction does not couple the magnetic moments of cations indifferent simple cubic sublattices since these are connected by 90 oxygen bonds.The relative orientations of the four lattices with respect to each other and to thecrystallographic axes are instead imposed by anisotropic interactions. In MnO andNiO, the larger source of anisotropy is provided by the magnetic dipole interaction,which favors a collinear alignment between the sublattices, resulting in the so-calledtype-II AFM order. These are characterized by AFM domains (T-domains) in whichthe moments form FM foils parallel to one of the four equivalent {111} planes ofthe fcc lattice [47], with the spin aligned in the plane of the foil [47]. This type ofAFM ordering is further stabilized by a rhombohedral distortion in the directionperpendicular to the foils caused by magnetostriction. Inside each (111) foil, thespin is driven to align along one of the three equivalent [112] directions (giving threeequivalent so-called S-domains) by sources of smaller anisotropy (see Figure 1.2).

The removal of translation symmetry and the possible presence of substrate-induced strain reduce the symmetry of the bulk and cause AFM anisotropy.Since in an AFM material there is no net magnetization, one can apply first-order

(001)

(010)

(100)

Figure 1.2 Collinear arrangement of magnetic cations inMnO and NiO. A domain with (111) ferromagnetic foilsand moments parallel or antiparallel to the [112] directionis shown.

1.4 Interlayer Coupling in AFMFM Bilayers and Multilayers 9

perturbation theory [48] to evaluate the effects of the AFM film finite thickness and of the tetragonal strain = (c/a) 1 (c and a being the out-of-planeand in-plane lattice parameters, respectively). Inclusion of tetragonal strain intoa bulk AFM MnO or NiO lattice energetically favors S-domains with mainspin component perpendicular (S) to the strain axis for < 0 (compression)and S-domains with main spin component parallel (S||) to the strain axisfor > 0 (expansion). In uniformly strained films, this effect coexists with athickness-dependent perturbation to the total dipolar anisotropy, which stabilizesS|| domains and in-plane anisotropy [48]. At variance with the well-known shapeanisotropy of FM thin films, which is proportional to the film volume, thisAFM shape anisotropy is proportional to 1 [48]. In the original work [25], thethickness-dependent AFM anisotropy experimentally observed in NiO/Ag(001)films was indeed interpreted as being a consequence of AFM dipolar anisotropy.

1.4Interlayer Coupling in AFMFM Bilayers and Multilayers

AFM surfaces are said to be compensated when the surface magnetization of theAFM material is null. In TM monoxides, which are characterized by an AFMorder similar to that shown in Figure 1.2, {001} and {011} planes are nominallycompensated, while the {111} surfaces are totally uncompensated. The latter,however, exposes the same chemical species and a net electric charge (TM oxidesare highly ionic compounds). For this reason, the {111} surfaces are unstable andtend to reconstruct. At compensated AFMFM interfaces, the exchange interactionis strongly frustrated. Frustration can be partially released by the presence of defects(chemical interdiffusion, atomic steps, missing atoms, dislocations), which makethe interface partially uncompensated, at least on a local scale. Defects are instead asource of frustration at nominal totally uncompensated interfaces. There is a generalconsensus in the scientific community about the importance of considering thisinterplay between frustration and defects to understand magnetic properties suchas exchange bias, interlayer coupling, and micromagnetic structure of AFMFMbilayers and multilayers. We omit to discuss exchange bias in this introductorychapter, since this argument is extensively treated in this book (see Chapters57). We concentrate instead, in Section 1.4.1, on interlayer coupling, while themicromagnetic structure at AFMFM interfaces is the subject of Section 1.4.2.

1.4.1AFMFM Interface Coupling

Micromagnetic calculations based on energy minimization show that theground-state configuration of an ideal magnetically compensated AFMFMinterface corresponds to a perpendicular orientation of the bulk FM momentsrelative to the AFM magnetic easy axis direction, an arrangement known asspin-flop state [49]. This configuration is stable since the magnetic moments both


0.14

0.12

0.10

0.08

0.06

0.04

0.02

0

u

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Hex / m JAFM

Collinear coupling

In-planeorthogonal coupling

Figure 1.3 Diagram describing the regionsin the parameter space for which the AFManisotropy axis is either collinear or orthogo-nal to the FM magnetization, obtained for anAFMFM bilayer with the characteristics ofNiO/Fe(001). Hex represents the magnitudeof the effective exchange field of magneti-cally active defects at the AFMFM interface,while u is the fraction of interface atomic

sites occupied by such defects: u = 0 foran ideal compensated interface; u = 1 for atotally uncompensated interface. JAFM and mare the values of the superexchange couplingconstant and of the local magnetic momentsin the AFM material, respectively. Reprintedfigure with permission from [51]. 2004, bythe American Physical Society.

in the FM and in the AFM layer exhibit a small canting from the 90 couplingthat vanishes away from the interface but induces a small magnetization in theAFM layer. The spin-flop ground state was also suggested to lead to exchange bias[49], a result that was later confuted by a more accurate model describing the spindynamics in terms of moment precession rather than energy minimization [50].The presence of defects can, however, destroy the spin-flop ground state, inducinga collinear coupling between the AFM and FM moments across the interface.The reason why this happens can be captured by a mean-field calculation wherethe perturbation associated with the defects is simulated by an effective exchangefield of magnitude Hex acting on the atoms belonging to a compensated AFMFMinterface reproducing the characteristics of the NiO/Fe(001) bilayer [51, 52]. Theresult is summarized in Figure 1.3, which shows the type of average AFMFMcoupling (collinear rather than perpendicular) between the two layers as a functionof Hex and of the fraction u of magnetically active defects at the interface. MonteCarlo simulations find AFM spins aligning collinearly with the FM momentsabove TN , with a transition from collinear to perpendicular alignment of theFM and AFM spins at a lower temperature in the case of rough interfaces [53].Besides interface defects, also volume defects such as dislocations inside theAFM material can influence the coupling between the FM magnetization andthe AFM anisotropy axis by disrupting the collinear alignment of the spins insidethe AFM layer [54].

magnetic properties of antiferromagnetic oxide materials · franco ciccacci. dipartimento di fisica...

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