A new paradigm for exchange bias in polycrystalline thin films New Paradigm... · 2010. 1. 16. · Title: A new paradigm for exchange bias in polycrystalline thin films Author: K

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ARTICLE IN PRESSMAGMA 56005 XML-IS

Journal of Magnetism and Magnetic Materials ] (]]]]) ]]]–]]]

Contents lists available at ScienceDirect

Journal of Magnetism and Magnetic Materials

0304-88

doi:10.1

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fax: +4

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Glasgow

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journal homepage: www.elsevier.com/locate/jmmm

Topical Review

A new paradigm for exchange bias in polycrystalline thin films

K. O’Grady n, L.E. Fernandez-Outon1, G. Vallejo-Fernandez nn,2

Department of Physics, The University of York, York YO10 5DD, UK

a r t i c l e i n f o

Article history:

Received 17 July 2009

Received in revised form

27 November 2009

PACS:

74.25.Ha

75.30.Gw

75.50.Ee

75.70.� I75.70.Ak

Keywords:

Exchange bias

Polycrystalline films

Grain size

Interface effects

Spin clusters

UNC

53/$ - see front matter & 2009 Published by

016/j.jmmm.2009.12.011

esponding author. Tel.: +44 141 3305580; fa

-publication corresponding author. Tel.: +44

4 1904 432247.

ail addresses: [email protected] (K. O’Grady),

), [email protected] (G. Vallejo-F

esent address: Laboratório de Fisica Aplicada

ologia Nuclear, 30123-970 Belo Horizonte, M

esent address: Department of Physics & Astro

G12 8QQ, UK

e cite this article as: K. O’Grady, et

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a b s t r a c t

In this paper we provide a review and overview of a series of works generated in our laboratory over the

last 5 years. These works have described the development and evolution of a new paradigm for

exchange bias in polycrystalline thin films with grain sizes in the range 5–15 nm. We have shown that

the individual grains in the antiferromagnetic (AF) layer of exchange bias systems reverse over an

energy barrier which is grain volume dependent. We show that the AF grains are not coupled to each

other and behave independently. Understanding this process and using designed measurement

protocols has enabled us to determine unambiguously the blocking temperature distribution of the AF

grains, the anisotropy constant (KAF) of the AF, understand the AF grain-setting process, and predict its

magnetic viscosity. We can explain and predict the grain size and film thickness dependence of the

exchange field Hex. We have also studied interfacial effects and shown that there are processes at the

interface, which can occur independently of the bulk of the AF grains. We have seen these effects via

studies of trilayers and also via the field dependence of the setting process which does not affect the

blocking. From separate experiments we have shown that the disordered interfacial spins exist as spin

clusters analogous to a spin glass. These clusters can order spontaneously at low temperatures or can be

ordered by the setting field. We believe it is the degree of order of the interfacial spins that gives rise to

the coercivity in exchange bias systems. Based on this new understanding of the behaviour of the bulk

of the grains in the antiferromagnet and the interfacial spins we believe that we have now a new

paradigm for the phenomenon of exchange bias in sputtered polycrystalline thin films. We emphasize

that the phenomenological model does not apply to core–shell particles, epitaxial single-crystal films

and large grain polycrystalline films.

& 2009 Published by Elsevier B.V.
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ECTE1. Theories and models of exchange bias

Since its discovery in 1956 [1] the phenomenon of exchangebias has been one of the most fascinating and complex effects thathave ever been studied in the field of magnetism. After more than50 years there is still no definitive theory that can account for theobserved effects which include the well-known hysteresis loopshift (Hex) and the increased coercivity (Hc) defined as half theloop width, when an AF material is placed in intimate contactwith an F material and field cooled through its Néel temperature(TN). One of the reasons why no clear and comprehensive theoryhas been developed lies in the fact that a wide range of samples

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x: +44 141 3304606.

1904 432289;

[email protected] (L.E. Fernande

ernandez).

, Centro de Desenvolvimento

inas Gerais, Brazil.

nomy, University of Glasgow,

al., J. Magn. Magn. Mater. (

has been studied. These include nanoparticles where obviouslythe AF/F interface is not flat [2], epitaxially grown films [3] wherethe interface is expected to be almost flat, and sputteredpolycrystalline films [4] where the interface has significantroughness and can lead to both structural and magnetic disorder.Interestingly the largest exchange bias effects at room tempera-ture are observed in polycrystalline granular films produced bysputtering and it is these materials exclusively that are used, orproposed, for applications in devices such as magnetic recordingread heads and MRAM applications. It is such sputtered metallicpolycrystalline films alone which this study addresses.

In a major review of exchange bias published in 1999 in Vol 200of this journal entitled ‘‘Magnetism Beyond 2000’’ Berkowitz andTakano provided a comprehensive review of the known state of theart in this field [5]. Interestingly they state ‘‘A model of the exchangebias mechanism must resolve the following discrepancies and questions:

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What structural and magnetic parameters are responsible for the

drastic reduction of the interfacial exchange energy density from

the ideal case?

(2)

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What are the origin and role of the interfacial uncompensated AF

spins?

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www.elsevier.com/locate/jmmmdx.doi.org/10.1016/j.jmmm.2009.12.011mailto:[email protected]:[email protected]:[email protected]:[email protected]/10.1016/j.jmmm.2009.12.011


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How is the magnitude of the exchange field dependent upon the

AF grain structure?

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What determines the temperature dependence of the exchange

field?

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What are the roles of interfacial exchange Jexnand AF magneto-

crystalline anisotropy KAFin unidirectional anisotropy?’’

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In this work we now attempt to answer these five questionsbased on a new conceptual paradigm of the exchange bias effectin polycrystalline materials.

1.1. Early theories of exchange bias

The first and simplest model proposed to explain thephenomena of exchange bias is that of Meiklejohn and Bean [1].In their paper they studied single-domain spherical Co particleswith and AF CoO shell. These particles had uniaxial anisotropyand their easy axis aligned parallel to the applied field. Theyassumed a perfectly uncompensated AF spin structure at theinterface, which remains rigidly aligned along its easy axis due toa large anisotropy in the AF and a weaker exchange coupling ofthe AF to the F. This mechanism of exchange bias leads to valuesof the shift in the hysteresis loop, Hex, two orders of magnitudelarger than the observed values in small grain polycrystallinefilms although it predicts near correct values in other systems e.g.[6–8]. The original data of Meiklejohn and Bean is shown in Fig. 1.

Chronologically, the second model proposed to explain theexchange bias phenomenon was suggested by Néel [9]. Néelproposed an uncompensated AF spin structure at the interface.

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1. Hysteresis loop of the Co particles embedded in their natural oxidesured at 77 K after field cooling in a 10 kOe magnetic field (solid line) [1].

ease cite this article as: K. O’Grady, et al., J. Magn. Magn. Mater. (

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However, he pointed out that this spin structure is subject todeformation and experiences irreversible changes during thereversal of the F layer. Consequently, both the exchange field, Hex,and the coercivity, Hc, are affected by changes which occur in theAF during the reversal of the F. From his model, two contributionswould be expected to Hc; an intrinsic F component and a termthat would be proportional to the irreversible magnetisationchanges which occur in the AF. Also, Néel considered that forrealistic rough interfaces both AF sub-lattices would be present atthe interface, leading to partial compensation of the AF moments.In the case of polycrystalline AFs the number of spins at theinterface of each AF grain would be statistically distributed,leading to fluctuations in the moment of each AF grain. This modelagain fails to predict reasonable values for Hex.

One of the most successful models of exchange bias is that ofFulcomer and Charap [10,11]. These workers undertook bothexperimental and theoretical studies of exchange bias in permal-loy films where a treatment with acid vapour progressivelyoxidized the nickel in the alloy producing isolated AF grains onthe surface of the films. They observed progressive changes in theexchange bias of such systems with both the grain size and thenumber of grains of AF material grown. Numerical modellingbased upon a granular reversal model analogous to a Stoner–Wohlfarth system gave good agreement with experimentalobservations. In particular, Fulcomer and Charap predicted thatthe exchange field from the F acting on the AF would result inthermally activated changes in the orientation of the AF sub-lattices leading to variations in the observed value of Hex. Oneimportant characteristic of this model is that a wide range ofparticle sizes and shapes was considered within the AF. This waythe anisotropy and coupling energies were varied widely. Theparticle size distribution was assumed to be such that all areas areequally probable up to some maximum and that there were nolarger particles. They found that it was important to consider adistribution of particle size although the exact form of thatdistribution was not critical. This model was able to predict thetemperature dependence of Hex and Hc over a wide range oftemperatures even above TN as reported by Grimsditch et al. [12].This model has formed the base of other granular models basedon thermal fluctuation effects. For instance, Nishioka et al. studiedthe temperature dependence of exchange bias in NiFe/FeMn [13]and Co/CrMnPt [14] using the temperature dependence of thecoupling proposed by Fulcomer and Charap. More recently, Xi [15]proposed a thermal fluctuation model to study the dependence ofthe blocking temperature (TB) in exchange bias bilayers also basedon the work by Fulcomer and Charap. Xi found a monotonicincrease in Hex with AF layer thickness (tAF) for large grainsystems (D�40 nm). He also found a linear decrease of TB withmeasurement time and a linear increase with the Néel tempera-ture of the AF grains. This model is significant because it extendsthe work of Falcomer and Charap into a more completedescription of thermal effects. However, the calculations are fora single-grain volume and hence do not describe real systems.

In 1987, Mauri et al. [16] proposed the first domain model ofexchange bias. They suggested that the formation of domain wallsparallel to the F/AF interface results in a lower interfacial energythan that predicted by the model of Meiklejohn and Bean. Thisresults in more reasonable values of Hex. However, this modeldoes not explain features such as the enhanced Hc of the F layer,or the reduction of the loop shift upon field cycling. One of themain assumptions of this model is that the AF spin sub-latticesand the F spins lie parallel to a perfectly flat interface. Thismodel also relies on thick AF layers necessary to accommodate adomain wall parallel to the interface, although exchange bias hasbeen reported for systems containing AF layers as thin as a fewatoms.

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Malozemoff [17] introduced a random interface roughnessbetween the F and AF layers and predicted values of Hex of thesame order of magnitude as those obtained by Mauri et al [16].The rough nature of the interface gives rise to compensated anduncompensated areas at the interface that exert fields on the Finterfacial spins. The magnetostatic energy of these fields and theanisotropy of the AF result in the formation of AF domains withdomain walls perpendicular to the interface. The movement ofsuch AF walls would explain the reduction of Hex due to fieldcycling. However, this model is only applicable to single-crystalAFs. In the case of polycrystalline materials it is expected thatmore complex behaviour would result which would depend onthe microstructure of the AF. Also, this model relies on surfaceroughness and does not explain the appearance of exchange biason perfectly compensated interfaces.

Koon proposed a microscopic explanation of exchange bias forcompensated F/AF interfaces [18]. In this model, the F magnetisa-tion tends to orient perpendicular to the AF easy axis. Bothcompensated and uncompensated interfaces were predicted tolead to similar values of Hex. These results do not concur with thetheories of Mauri [16] and Malozemoff [17]. The main result ofKoon’s model was the prediction of spin–flop coupling at theinterface between the F and AF layers. Exchange bias was due tothe formation of a domain wall in the AF parallel to the interfacewhen the F rotates away from the field cooling direction as theapplied field is reversed. Furthermore, Koon also showed that thespins in the AF exhibit canting. This canting angle decays rapidlyas a function of distance from the interface, becoming zero at 5–6monolayers.

Schultness and Butler [19] solved the Landau–Lifshitz–Gilbertequation in order to study the exchange coupling at F/AFinterfaces. They showed that for perfectly flat interfaces, spin–flop coupling does not lead to exchange bias although it leads toan increase in the F layer coercivity typical of exchange biassystems. The introduction of defects at the interface leads tovalues of the exchange field of the correct order of magnitude[20]. However, their model only applies to idealised situations inwhich both the AF and the F layers are single crystals and in asingle-domain state.

After the turn of the millenium when Berkowitz and Takanoposed their five questions [5] the use of large-scale atomisticmodels of magnetic systems became more common. Thisprovided the opportunity for models of realistic spin systems tobe used to predict the complex multifaceted behaviour ofexchange-biased systems. Prior to this time all theories wereeither analytical or micromagnetic.
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RR1.2. Recent theories of exchange biasIn 1999 Stiles and McMichael proposed a model to describe thebehaviour of polycrystalline F–AF bilayers [21]. No intergranularexchange coupling in the AF was assumed. The AF grains werecoupled to the F layer both by direct exchange to the net momentsat the interfaces of the grains and by spin–flop coupling. In orderto account for high field rotational hysteresis and the loop shift,some of the grains were assumed to make irreversible transitions.These transitions were included in the model in the form of acritical angle above which the AF becomes thermally unstable andundergoes a transition to another state. The temperaturedependence of the loop shift was assumed to arise due to thermalinstabilities in the state of the AF grains. At low temperatures, theAF grains remain in a stable configuration as the F layermagnetisation is rotated. At high temperatures, the AF grainsbecome thermally unstable over long timescales due to thermalexcitations over energy barriers. The model is valid for systems

Please cite this article as: K. O’Grady, et al., J. Magn. Magn. Mater. (

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where the Curie temperature of the F layer is much greater thanthe ordering temperature of the AF [22]. Hence, the properties ofthe F layer were assumed to be temperature independent. The AFgrains were classified as stable, partially stable and unstable as afunction of temperature and field direction. The behaviour of eachgrain determines its contribution to the unidirectional anisotropy.The saturation of the unidirectional anisotropy at low tempera-tures is determined by the ratio of the average spin interfacialcoupling energy to the zero temperature domain wall energy.

Based on this model, Stiles and McMichael found two differentcontributions to the enhanced coercivity: one was due toinhomogeneous reversal and the other to irreversible transitionsin the AF layer [23]. Two different dependencies of Hc on thethickness of the F layer were predicted as a function oftemperature based on the contribution from each term.

Stamps suggested the existence of two different mechanismsfor exchange bias [24]. The first mechanism is due to thereversible formation of domain walls in the AF. A secondcontribution arises due to irreversible processes leading toasymmetric hysteresis loops. A key result of this model is theexistence of higher-order coupling terms when more than one AFsublattice is present at the interface. The concept of a naturalangle suggested by Camley et al. [25] was introduced tocharacterise exchange bias at mixed and geometrically roughinterfaces. A mean field theory was used to explain thetemperature dependence of Hex and Hc. A thermal activationtheory was used to describe the rate at which equilibrium wasapproached. These energy barriers were considered to be of twotypes: those involved with in-plane rotation of the magnetisationof the F layer and those related to out-of-plane rotation. There isthen no need for anisotropy in the F layer for the appearance ofthe unidirectional anisotropy in contrast to the rigid models.

In 2002, Nowak et al. [26] proposed the domain state model forexchange bias based on their previous work [27]. The F layer wasassumed to be coupled to a diluted AF. The dilutions wereintroduced in the system in the form of non-magnetic atoms. Inthis model exchange bias arises due to a domain state in the AFwhich develops during field cooling carrying an irreversiblemagnetisation. During the field cooling process, the AF is incontact with a saturated F layer and exposed to an externalmagnetic field. The dilutions introduced in the system favour theformation of this state since domain walls preferentially passthrough the non-magnetic sites and, therefore, reduce the energynecessary to create a domain wall [26]. The domain state is ametastable state which develops and becomes frozen duringcooling and depends upon the concentration of non-magneticsites. This way no further assumptions about the size or structureof these domains are required. Monte Carlo simulations wereperformed on a model consisting of an F monolayer exchangecoupled to a dilute AF film typically consisting of nine mono-layers. Note that in this model KAF is taken to be very large andhence the width of these domain walls is assumed to be zero. Themodel was used to predict several features of exchange bias. Forinstance, strong dependence of the exchange bias field ondilution, positive exchange bias, temperature dependence ofexchange field, etc. The attempt to predict the peak in Hex withtAF was partially successful although the value of tAF at which thepeak occurred was only a few atomic layers. The model did notinclude discretised grains. Hence this model might be valid forsingle-crystal films but it is unlikely that it can be applied topolycrystalline films where the AF grains are exchange decoupled.

The same model was applied to study the temperaturedependence of Hex and Hc using a mean field approach [28].A significant enhancement of the coercivity was found reaching amaximum around the Néel temperature of the AF layer. Thedomains formed after field cooling using the mean field approach

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have the same structure as those obtained with Monte Carlosimulations. However, there are differences in the magnitude ofthe loop shift obtained using both methods. The enhancement ofthe coercivity was attributed to the coupling of the F layer to thepart of the AF interface layer magnetisation that follows theexternal field during a hysteresis loop measurement. Since the AFlayer carries an induced magnetisation above TN, the enhance-ment of Hc persists well above the transition temperature. On theother hand, Hex originates in the frozen part of the magnetisationof the AF interface layer. The main conclusion of the work is thatthe exchange bias and the coercivity are not related.

In 2006, Saha and Victora [29] proposed a large-scale(2.5�105 elements) micromagnetic model for polycrystallineexchange bias systems with uncoupled AF grains. Each F grainwas coupled to a neighbouring AF grain that rotated uniformlyunder the effect of thermal fluctuations. The evolution of the Flayer magnetisation was determined by solving the Landau–Lifshitz–Gilbert equation for each degree of freedom. The couplingbetween the F and AF arises due to the surface roughness of the AFgrains. The dependence of the exchange bias and coercivity as afunction of temperature and AF layer thickness were studied. Oneof the most important conclusions of this model is that systemswith AF symmetry higher than uniaxial exhibit an asymmetricmagnetisation reversal when compared to a sample with uniaxialanisotropy. The model also predicts an increase in Hex atreasonable values of tAF but does not predict the broad peakcommonly observed.

Recently, Choo et al. [30] proposed a granular model of themagnetic properties of exchange biased F–AF bilayers. The F layerconsists of strongly exchange coupled grains. The magnetisationreversal processes involve non-uniform magnetisation states. TheF layer was modelled using a standard micromagnetic approach.On the other hand, the AF layer was formed of highly anisotropicexchange decoupled grains. The F and AF layers are coupled bymagnetostatic and exchange interactions. The magnetic state ofeach AF grain is controlled by thermally activated processes.Hence, a kinetic Monte Carlo approach was used to model theproperties of the AF. As in the model of Fulcomer and Charap[10,11], the energy barrier to reversal for each AF grain is given bythe product of its volume and anisotropy constant, taking intoaccount the orientation of the grain with respect to the localmagnetic field. The probability for each grain to undergomagnetisation reversal is given by the Néel–Arrhenius law. Themagnetic state of the AF layer is represented by an orderparameter (P). This order parameter is indicative of the magnitudeand sign of the exchange field acting on the F layer. For theircalculations, a value of 4�106 ergs/cm3 was assumed for theanisotropy of the AF layer. The distribution of grain sizes withinthe sample was taken to be lognormal. It was shown that thermalinstabilities in the AF layer lead to a peak in the coercivity aroundthe median blocking temperature.

In a more recent work, the same group studied the tempera-ture dependence of exchange bias in bilayer systems [31]. Thisversion of their model takes into account the temperaturedependence of the anisotropy of the AF. It was predicted thatthe measured value of the median blocking temperaturedepended on the strength of the intrinsic interlayer couplingdue to the reduction of energy barriers. This dependence wasfound to be rather weak for normal values of the couplingstrength.

Despite the extensive and often complex attempts to modelexchange bias systems there is still no theory that is able topredict the value of exchange bias in any real system. Criticallythe theories and models provide no guide to those trying todevelop new materials and systems for applications. For example,what is the optimum grain size for a given application? None of


the models predict the film thickness and grain size dependenceof Hex. Similarly what is the role of the anisotropy or interfacestructure? Significantly none of the models come close toanswering the five questions posed by Berkowitz and Takano [5]in a comprehensive way.

One reason for the failure of the models is the wide variety ofsamples that have been studied. The second reason is that mostexperimental data have been taken at arbitrary temperatureswithout regard to possible thermal instabilities in the AF layer.Similarly the degree of order in the AF at the beginning of themeasurement is generally unknown and rarely checked.

We now describe a series of experiments undertaken takinginto account these factors. We have studied sputtered filmsmainly of IrMn/CoFe, which is the system used exclusively inapplications.

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2. Experimental studies of polycrystalline exchange biassystems

There is a plethora of data in the literature relating to exchangebias systems. As indicated in the introduction there are a numberof categories of exchange bias systems including nanoparticles,epitaxial films and polycrystalline films. The work described inthis paper is restricted to metallic polycrystalline films with smallgrains between 5 and 15 nm and hence the brief review ofexisting experimental work applies only to these materials.Furthermore we concentrate on the key issues of grain size, filmthickness and thermal effects.

When comparing previous measurements with our morerecent studies a significant difficulty occurs because until recentlyalmost all authors did not take care to ensure that the AF layerwas fully set. To our knowledge, in no other published work hasan experimental measurement been undertaken to check that theAF layer was fully set before the measurement began. Further-more whilst some authors have clearly been aware of the thermalactivation process affecting the order in the AF, no systematicmethodology has previously been applied to quantify and moreimportantly control, thermal processes in the AF during measure-ments. Nonetheless there are a number of important works whichhave provided signposts to the resolution of these issues.

For example, following on from the initial work of Fulcomerand Charap [10,11], van der Heijden et al [32] discussed in somedetail the time dependence of Hex at different temperatures.Interestingly the published data appears linear in ln t although theauthors did not plot the data in this form. In a separate work thesame authors showed that holding the ferromagnet in a directionopposite to that in which it was originally set can reverse the shiftin the hysteresis loop including a reversal in the sign of Hex[33].Unfortunately the original state of order in the samples was notverified but the concept of reversal of the AF in the presence of areversed exchange field under the influence of thermal energy isclearly defined.

One of the critical variables for applications of exchange bias isthe variation of the value of Hex with the thickness of the AF layer(tAF). It is widely accepted that this variation has Hexp1/tAF

l . Thereare reports that the value of l ranges from 0.3 [34] to 1 [35].However, as noted in these works this inverse relationshipbetween Hex and tAF only occurs for large thicknesses. At lowthicknesses an increase in Hex with tAF is observed. This isassumed to be due to the existence of a critical thickness at whichdomains can form in the AF although there is no experimentalevidence for the presence of such entities. The domain statemodel [26] is able to predict a peak at extremely low tAF but theremainder of the variation is completely different to that which isobserved experimentally.

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The situation regarding the grain size dependence of Hex inpolycrystalline films is even more confusing. For example Takanoet al. [36] reported a decrease in Hex with increasing AF grain size(D) in NiFe/CoO bilayers following Hexp1/D. Uyama et al. [37]observed a decrease in Hex with increasing grain size above 50 nmbut also observed the well-known broad peak in the variation ofHex with tAF. Again for large grain sizes an approximate 1/tAFvariation was observed. The peak in the variation of Hex with tAFwas again attributed to the onset of AF domain formation inagreement with a prediction of the domain state model althoughthe experiment preceded the theory. Thus there is not clearly anestablished description of the effect of grain size and filmthickness on the value of Hex. Also other than speculation as tothe onset of AF domain formation, there is no clear mechanism toaccount for these variations, particularly the Hexp1/tAF formobserved by many groups, but not predicted by the domain statemodel [26].

Whilst there is no agreement from different measurements ofexchange bias there have been a significant number of paperswhich are in broad agreement that the AF grain size increases thethermal stability in exchange bias systems [38]. There is alsoevidence that the AF grain anisotropy also has a direct impact onthe value of the mean blocking temperature. Hence this is perhapsan indication that the phenomena of thermal stability and theactual value of Hex achieved are not directly connected to eachother. It will be shown subsequently that this is the case.

It should be noted that the foregoing brief review ofexperimental data is not intended to be comprehensive and isspecifically intended to be focused on polycrystalline filmsgenerally produced by sputtering and generally consisting ofmetallic materials with small grains. Also the literature which hasbeen surveyed has been selected so as to focus on the topicswhich are discussed in the next section of the review.

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2.1. The York Protocol

There are a number of challenges presented in trying to studythe exchange bias phenomenon. The first of these is that formaterials having technological applications it is difficult to heatthe sample to the Néel temperature of the AF layer. For all currentapplications the alloy IrMn3 is the material of choice. Thismaterial has TN equal to 690 K and this temperature would resultin diffusion in multilayer films. However it has been found thatfield cooling from temperatures as low as 475 K can result in thesetting of IrMn layers. This setting process is achieved by thethermal activation of the orientation of the AF lattice within eachgrain as first described by Fulcomer and Charap, albeit for thedisorientation of the AF lattice. A further challenge comes aboutbecause of the thermal instability of AF grains themselves. Asshown by Fulcomer and Charap the state of order in the AF canchange during a measurement, making parameters such as Hexand Hc highly non-reproducible. To overcome these challengescareful management of the thermal and magnetic history of theAF is essential to ensure that a uniform state at the beginning of ameasurement can be reproduced in a subsequent measurement toallow for comparability.

The second challenge when studying exchange bias is that theAF layer itself gives no signal in a conventional magneticmeasurement. All that can be achieved is that careful control ofthe thermal and magnetic history allows one to infer changes inthe state of the AF grains, which then give rise to changes in theproperties of the adjacent F layer. In one sense this is notdissimilar to the study of black holes in astronomy which cannotthemselves be seen but their effects on neighbouring objects canbe discerned.


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We have designed a set of magnetic field and temperatureprotocols that enables reproducibility of measurement to beachieved to high resolution. These protocols allow us todetermine and control the state of order in the AF both prior to,and during each measurement. They also allow for the degree oforder in the AF to be varied in a controlled and systematicmanner.

The basis of the York Protocol for the measurement of blockingtemperatures is shown schematically in Fig. 2a. The precisesequence of the measurement is shown in Fig. 2b. At the time ofstarting a measurement the state of order in the AF is generallyunknown. Often polycrystalline thin films are sputtered in thepresence of a magnetic field. This field induces an easy axis in theF layer but the magnetisation of the F layer during growth and theinevitable heating can lead to the establishment of some degree oforder in the AF layer which is generally deposited first. However,from measurements undertaken in York, but not reported here,we have found that this initial state of order in the AF is highlynon-reproducible.

Thus the first requirement is to set the AF in a reproduciblemanner. This is achieved by heating the sample to increasingtemperatures with a magnetic field sufficient to saturate the Flayer applied in the known direction of the F layer easy axis, to themaximum temperature (Tset) which does not result in interfacialdiffusion. The onset of significant diffusion can be observed byheating for different periods of time and observing generallyadverse changes in the resulting exchange bias. For reasons whichwill become clear, we have found that a setting time (tset) of90 min is adequate for all samples we have examined. A time of90 min has been used because, as shown in Section 2.6, thevariation of Hex with the time of setting (tset) is linear in ln tset.After a time of 90 min the change of Hex with tset is very small(o1%) allowing for reproducibility in the value of Hex. This settingprocess is undertaken with a sample mounted in a conventionalvibrating sample magnetometer, which in our case is a Veeco ADEModel 10 system.

For highly detailed measurements the reproducibility of thesetting process should be checked by repeating the procedureoutlined above. It is now necessary to ensure that no thermalactivation occurs during the time of measurement of the systems.This is achieved by cooling down with the setting field stillapplied, to a temperature at which no thermal activation occurs.We designate this temperature TNA. TNA is determined by havingfirst cooled to a trial TNA and reversing the field so that the F layersaturates in the opposite direction to that used for setting. Thesample is then held in that state of magnetisation for a shortperiod of say 1 min and a hysteresis loop measured. The process isrepeated but this time the sample is kept with the F layer reversedfor half an hour. If the hysteresis loop does not reproduce thenthermal activation will have taken place during the measurementand a lower value for TNA must be sought by trial and error. Itshould be noted here that care must be taken at each stage tomeasure two hysteresis loops so that the well-known first looptraining effect can be removed from the measurement. Thistraining effect occurs on the first hysteresis loop and is believed tobe due to some form of spin–flop coupling which is removed by asingle hysteresis loop cycle [39] The slow training effect thatoccurs on the second and subsequent loops has been shown to bedue to thermal activation of the AF grains and is removed bymeasuring at TNA[40].

Once the sample is correctly set and TNA established,reproducible measurements can be obtained. Interestingly it isnow possible to undertake controlled thermal activation. This isachieved by first setting the sample and establishing TNA. Themagnetisation of the F layer is reversed to negative saturation.The sample is then heated for 30 min in appropriate steps to

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Fig. 2. (colour online) (a) Schematic diagram and (b) measurements steps of the York Protocol.


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activation temperatures Tact, but subsequently cooled back to TNAprior to the measurement of the complete hysteresis loop startingfrom negative saturation. Starting from this point removes thefirst loop training effect and measuring at TNA ensures that slowthermal training does not occur [40].

A thermal activation time (tact) of 30 min was chosen againbecause of the ln(tact) dependence of the resulting order in the AFlayer. It also implies that on resetting the sample between eachmeasurement the setting time of 90 min would completelyreverse any activated grains to their original ‘set’ state. Thesetimes also negate any thermal activation that may occur duringthe temperature rise and fall.

Although the above measurement protocol is somewhattedious and difficult to observe accurately, we have generatedapplication software on our magnetometer, which enablesmeasurements to be made in a relatively automated manner.Using the York Protocol highly reproducible data can be obtainedwhich has elucidated very detailed measurements of effects bothin the bulk of the AF and at the interface.

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T2.2. Measurement of the blocking temperature

The blocking temperature TB is conventionally defined as thetemperature at which the exchange field goes to zero. Theconventional method to determine TconB is based on the measure-ment of hysteresis loops with increasing temperature until theloop shift becomes zero. Above TconB , the exchange bias remainszero. According to Fulcomer and Charap [10], TconB will correspondto the blocking temperature of the AF grain with the largestanisotropy energy. In polycrystalline systems each grain has itsown blocking temperature and therefore the AF is characterisedby a distribution of blocking temperatures. When the conven-tional measurement procedure is used, the AF is subject tothermal activation during the time of measurement at alogarithmic rate [41]. This leads to changes in the state of orderin the AF from measurement to measurement as well as lack ofreproducibility in the data.

Fig. 3 shows a comparison of the measurement of Hex(T) viathe two methods. As expected the standard technique (Hconex ) givesa lower maximum value of TconB and a wider distribution. This is aconsequence of the magnetic viscosity in the AF and values of TconBobtained will depend on the timescale of the measurement. Thiswas predicted by Xi [15] and first reported by van der Heijden


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OFet al [32]. The measurement of Hex(T) via the York Protocol(HYPex ðTÞ) gives highly reproducible data which are not subject totimescale effects since all the data are measured at a temperatureTNA where the system is free of thermal activation. Note that dueto limitations in our new cryostat HYPex can only be measured downto 100 K.

Thermal activation of the AF means that the hysteresis loop ofan exchange biased system can be shifted in the oppositedirection to that in which it was originally set in a controlledmanner [42]. The York Protocol has been used to measure themean blocking temperatures oTYPB 4of all the samples studied inthis work. Examples of the hysteresis loops obtained followingthis measurement procedure are shown in Fig. 4. Heating with theF layer reversed changes the order in the AF from the originalstate to the reverse orientation as shown in the schematicdiagram in Fig. 5. The amount of AF material that undergoesreversal will be a function of the temperature and the exchangefield from the F layer.

The value of Hex is then proportional to the difference in thefractions of the AF grains oriented in opposite directions

HexðTactÞpZ1

Tact

f ðTBÞdTB�Z Tact

0f ðTBÞdTB ð1Þ

Eq. (1) is valid if the coupling between the F and AF grains isindependent of the AF grain size. The quality of the fit betweenour theory and the data, discussed in Section 2.5, shows that thisis the case. However, this may not be valid for very thick AF layerswhere columnar growth is not present.

The York Protocol leads to a different meaning of oTYPB 4 . Inour measurement oTYPB 4 occurs at the point where equalfractions of the volume of the AF grains are oriented in oppositesenses and hence is a measurement of the median blockingtemperature in the system which we denote as oTB4 . Theconventional measurement actually determines the maximumvalue of TB and depends critically on the form of the distributionat high values. All measurements described in the work wereobtained via the York Protocol.

2.3. Measurement of KAF

Polycrystalline metallic AFs consist of an assembly of grainsdistributed in size, typically 10 nm in diameter. Each grain is

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Fig. 3. (colour online) Measurement of the blocking temperature for a CoFe/IrMn bilayer following the conventional measurement procedure and the York Protocols.

Fig. 4. Examples of hysteresis loops obtained following the York Protocols for aCoFe/IrMn exchange bias system.

Fig. 5. Schematic of the energy barriers to reversal, showing the fractions of theenergy barriers oriented parallel or antiparallel to the original set direction.


believed to contain a single AF domain due to their size. Single-domain F or AF particles are subject to thermal activation leadingto a magnetic transition over an energy barrier DE=KV[10,11],


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where V is the volume of the AF grain and K its anisotropyconstant. The critical volume below which this behaviour isobserved depends on the measurement time and the temperature.The relaxation time is given by the Néel–Arrhenius law as used byFulcomer and Charap [10].

t�1 ¼ f0exp �KAFVð1�H�=H�KÞ

2

kBT

" #ð2Þ

where f0 is taken to be 109 s�1, V is the grain volume, kB is

Boltzmann’s constant, KAF is the anisotropy of the AF grain and T isthe temperature. Hn is the exchange field from the F layer whichlowers the energy barrier to reversal (DE) of the AF grainspromoting thermally activated transitions. H�K is a pseudo-anisotropy field similar to the anisotropy field (HK) in ferro-magnets. The energy barrier is taken to be KAFV as the limiting case.The value of the pseudo-anisotropy field ðH�KÞ and the exchangefield (Hn) are unknown. However we assume that H�=H�K is small.We have shown that this assumption is correct for most F/AFsystems used in applications [43]. It is important to note that KAF istemperature dependent since its origin is magnetocrystalline. Itstemperature dependence is of the form KAF(T)=KAF(0)(1�T/TN)n.We have used a value for n of unity based on KAFp[mAF(T)/mAF(0)]

3

and the approximation mAF(T)p(T�TN)1/3 where mAF is themoment of one of the AF sub-lattices [22].

There is no experimental evidence of intergranular exchangecoupling between AF grains in metallic polycrystalline AF layers.In ferromagnetic polycrystalline films, such as Co alloy recordingmedia, intergranular exchange coupling occurs via an RKKY typemechanism. This requires a significant moment on each grain topolarise the conduction electrons and the coupling can be reducedor even eliminated by a few atomic layers of antiferromagneticCoCr alloy at the grain boundary [44]. Hence, AF/AF coupling viaan RKKY mechanism is known not to occur. Also, from thecontrast observed in bright and dark field TEM images it is clearthat our samples are not crystallographically ordered and there-fore direct exchange coupling between the AF grains would notoccur. Hence, we believe that an independent single-domain AFgrain model similar to that of Fulcomer and Charap applies. Also,the size of the AF grains used in all sputtered films havingtechnological applications lies in the range 5–20 nm. At thesesizes it is hard to conceive that an AF domain wall could existwithin a grain. Indeed, there are no reports of AF domain effects inpolycrystalline films.

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Fig. 6. (colour online) Variation of the median blocking temperature oTB4 withthe thickness of the AF layer. The line is a guide to the eye.

Fig. 7. (colour online) Variation of KAF with tAF at room temperature. The line is aguide to the eye.


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There have been a number of attempts to measure the value ofKAF in polycrystalline AF films. Most notably Mauri et al. [45]determined KAF for FeMn from the value of Hex at roomtemperature via

Hex ¼tcrtF

KAFM

ð3Þ

where tcr is the thickness of the AF layer above which there is asharp onset of Hex, tF is the thickness of the F layer and M itssaturation magnetisation. This gave KFeMn(295)=1.35�105 ergs/cm3. There are clearly a number of problems with thismethodology. Firstly, unless the measurements are made underthermal activation-free conditions it is unclear what fraction ofthe AF is stable and contributing to KAF. Similarly, as shown inSection 2.2, there can be an uncertainty as to the fraction of the AFthat is ‘set’ giving a similar discrepancy. This is particularly so forIrMn due to its high value of TN.

The more serious problem with this technique is the effect ofthe interface coupling. In all cases this factor is unknown and canonly be controlled to a limited degree. However, the York Protocolremoves the issue of thermally disordered grains and allow for theset fraction to be assessed. In the Hex versus temperature curves,such as that shown in Fig. 3, the point at which Hex=0, is uniquesince the fraction of the AF oriented in opposite senses is equal.Including the interfacial coupling parameter Cn, at oTB4 , Hex isof the form

HexðoTB4 ÞpC�Z oTB 4

0f ðTBÞdTB�

Z1oTB 4

f ðTBÞdTB

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375¼ 0 ð4Þ

At Hex=0 the effect of Cn is negated allowing KAF to be

determined at that temperature. This effect may not completelycancel if there is a grain size dependence of the interfacial spinorder.

We have undertaken a detailed study of a series of sampleswith structure Si/Cu(10 nm)/CoFe(5 nm)/IrMn(tAF)/Ta(10 nm)(tAF=3, 4, 6, 8, 10 and 12 nm) prepared using a HiTUS sputteringsystem [46]. The distribution of grain sizes within the AF has beenmeasured from bright field TEM images measuring over 600grains. The lateral grain sizes and hence the grain volumesfollowed a lognormal distribution [47]. The median grain volumeis given by Vm ¼ pD2mtAF=4 where tAF is the thickness of the AFlayer. From Eq. (2)

KAFðoTB4Þ ¼lnðtf0Þ

VmkBoTB4 ð5Þ

The value of the relaxation time used to calculate KAF wast=1800 s since this was the time for the thermal activationprocess. Fig. 6 shows the variation of the median blockingtemperature oTB4 with the thickness of the AF layer. oTB4increases with tAF due to an increase in the volume of the AFgrains and, therefore, their thermal stability increases aspredicted by Xi [15]. We used Tset=225 1C but TNA changed fromsample to sample depending on the grain volume (i.e. filmthickness). Hence TNA was varied for different samples although asingle low temperature could have been used as long as it did nocause ordering of interfacial spins as discussed in Section 3.3.

In order to calculate the value of KAF at room temperature, thebulk value of TN has been used for the temperature dependence ofKAF, i.e. TN=690 K [48], although the value for thin films may belower. Fig. 7 shows the variation of KAF with the thickness of theAF layer. For samples with tAFZ4 nm KIrMn(295 K)=(5.570.5)�106 ergs/cm3. For tAF=3 nm, KIrMn decreases slightly to(4.770.5)�106 erg/cm3. This is most likely due to a lack ofcrystallisation of the grains.


The value of KAF we obtain for IrMn is significantly higher thanthose reported by others [49]. This is to be expected since thesample is completely set before measurement, the effects ofdisordered grains are removed and the effect of interface couplingnegated. The error tolerances are remarkably small due to the largenumber of grains measured (4600) to obtain Dm and hence Vm.

The sources of systematic inaccuracy lie in the fact that Eq. (2)strictly applies to a system with aligned easy axes. Also the valueof f0 for an AF is unknown. In subsequent work we have shownthat improved texture of the IrMn can increase the measuredvalue of K to (2.070.5)�107 ergs/cm3[50]. Hence all measure-ments of KAF determined in such systems must be regarded aseffective values.

2.4. Setting limitations

IrMn is widely used in most technological applications due itshigh corrosion resistance, high magnetocrystalline anisotropy and

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Fig. 8. Schematic of the grain size distribution in the AF layer after setting at atemperature Tset in a magnetic field and cooling to a temperature where a fraction

of the AF is thermally unstable.

Fig. 9. (colour online) Grain volume distributions for the samples with differentAF thickness.


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the large loop shifts achievable. Since TN for this system is muchgreater than room temperature, it is not possible to field-cool thesystem from above TN since this would damage the structure ofthe sample. Hence, the AF has to be set below TN, where thesetting process is via thermal activation. Fig. 8 shows a schematicof the energy barrier distribution to reversal within an AF layer atT4TNA and after resetting at a temperature Tset for a period oftime tset. In this figure the conditions applied during the settingstage were not sufficient to set the whole AF distribution. As aconsequence, a fraction of the AF grains with V4Vset remainunaligned with the F layer. At temperatures above TNA anotherfraction of the AF grains with VoVc are not thermally stable at thetemperature of measurement Tms. This is analogous to the conceptof superparamagnetic particles in the model of Fulcomer andCharap [10]. Hence, only the grains in the window given by Vc andVset will contribute to Hex. Assuming a uniform value of KAF at thetemperature of measurement and based on this concept of thetwo critical volumes we can write

HexðTmsÞpZ VsetðTmsÞ

VcðTmsÞf ðVÞdV ð6Þ

This simple calculation, whose basis is shown in Fig. 8, can beused to predict the AF grain size and thickness dependence of Hexto high accuracy. Of course, certain aspects of the fabricationprocess may result in partial setting of grains with V4Vset.However, again the quality of the fit to the data in Fig. 8 indicatedthat this is a minor effect.

2.5. Grain volume dependence

We have studied the dependence of Hex on the AF grainvolume [51]. This has been done via two separate experiments inwhich we changed the AF thickness and the lateral grain size.Samples with composition Si/Cu(10 nm)/CoFe(2.5 nm)/IrMn(-tAF=3, 4, 6, 8, 10 and 12 nm)/Ta(10 nm) were used. Samples withfour different lateral grain sizes were prepared for each AFthickness. This control of grain size is easily achieved with ourHiTUS sputtering system in which the growth rate, which iscontrolled via the DC bias, controls the grain size to highresolution. The columnar growth, which has been observed viacross-sectional TEM, ensures that samples of different thicknesshave almost identical lateral size distributions. Varying the biasvoltage allows us to prepare samples of constant thickness anddifferent lateral size. The configuration of the system ensures thatthe grain size on TEM grids is the same as that in the films [46].The grain size distribution for each sample was measured frombright field TEM images using a JEOL 2011 electron microscope.Over 600 grains were measured for each sample. All the


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distributions followed a lognormal function. Fig. 9 shows thevolume distributions for samples with different AF thickness.Even though the distributions are represented by solid lines theywere calculated from the actual experimental data some of whichis shown. Note the significant asymmetry of the distribution ofgrain volumes which is greater than that in D due to the D3 factor.

Having calculated the value of KAF for our samples, we can nowproceed to determine the value of the two critical volumes Vc andVset. Since Vc determines the volume below which an AF grain isthermally unstable and the hysteresis loops were measured atroom temperature, we can write

VcðTÞ ¼lnð100f0ÞkB293

KAFð293Þð7Þ

where the factor 100 arises from the relaxation time t beingequal to the measurement time. Similarly, the second criticalvolume relating to the limit of the set grains will be given by

VsetðTÞ ¼lnð5400f0ÞkB � 498

KAFð498Þð8Þ

where the factor 5400 s is due to t being equal to the time usedto reset the AF, i.e. 90 min. Using the value obtained in theprevious section for KAF, Vc=200 nm

3 and Vset=757 nm3. These

values correspond to lateral grain sizes of 4.9 and 9.8 nm for a filmthickness of 10 nm. The two vertical lines in Fig. 9 represent thetwo critical limits.

Fig. 10 shows the variation of Hex with the AF lateral grain sizefor three different AF thicknesses measured at room temperature(�293 K). Again, prior to measurement the samples were reset at498 K in a positive field sufficient to saturate the F layer, for90 min. For low AF thickness (4–6 nm), the exchange fieldincreases with increasing AF grain size. However, for thickersamples, a decrease of Hex with tAF is also observed. For low valuesof tAF, a large fraction of the AF grains are thermally unstable and,therefore, do not contribute to the loop displacement. Byincreasing the AF thickness, the number of unstable grains isreduced leading to an increase in Hex. For thicker AF layers,�12 nm, the AF is mostly thermally stable. However, themeasured value of Hex is now limited by the fraction of AFgrains that cannot be set. Hence, a decrease of Hex with the AFgrain size is observed. These data and the quality of the fits meanthat we can now explain the apparently irreconcilable data ofTakano et al. [36] and Uyama et al. [37].

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Fig. 10. (colour online) Variation of Hex with the AF grain size for three differentAF thicknesses. The solid lines are calculated from Eq. (6) (using Eqs. (7) and (8))

using the measured value of f(V) with KAF determined from Eq. (5).

Fig. 11. (colour online) Variation of the exchange field with the thickness of the AFlayer. This samples had Dm=7.6 nm and sln D=0.33. The solid line was calculatedfrom Eq. (6) (using Eqs. (7) and (8)) with KAF measured from Eq. (5) and using the

measured values of f(V).


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RRFig. 11 shows the variation of Hex with the thickness of the AFlayer. For this experiment the lateral grain size was Dm=7.6 nmand slnD=0.33. The measurement procedure was the same as thatfor the samples with different lateral grain size. HexHex increasessharply with increasing AF thickness reaching a maximum at�8 nm. For thicker samples, a decrease in Hex is observedfollowing approximately a 1/tAF variation [34,35]. The slowdecrease in Hex for the thicker samples is due to the grainvolume distribution being highly skewed for the larger grains. Thephysical origin of the 1/tAF variation can be seen in Fig. 9 wherethe AF grain volume distribution approximates to 1/V at highvalues. This is equivalent to 1/tAF for constant grain sizes. If thedistribution were symmetric, the sharp increase in Hex would befollowed by an equally sharp decrease in the exchange bias, whichis not observed experimentally as can be seen from Fig. 11. Notethat all the lines in Fig. 10 and Fig. 11 correspond to calculationsusing Eq. (6), i.e. the integral between the two critical volumes Vc


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and Vset of the grain volume distribution. The agreement betweenthis simple theory and the experimental data is remarkable. Thissuggests that a simple granular model including an accuratemeasurement of the volume distribution, can account for thegrain volume dependence of the exchange bias.

The fit between the experimental values and the linescalculated from Eq. (6) is excellent. Of course the values of Hexhave been scaled along the ordinate using Cn as a fittingparameter. However, to fit to the form of the data, within error,to the grain volume measurement confirms the validity of oursimple theory. Further confirmation of our theory is provided bythe calculated lines in Fig. 10. No other theory has ever provided afit to data for the grain size distribution, particularly consideringthat the calculated values are based on actual measured grainsizes. Note that the error bars on the theoretical line are derivedfrom the error in the measurement of the grain sizes and the valueof KAF. None of the theories based on AF domains can predict theform of the data. This is particularly so when the thickness of theAF layer is 12 nm.

2.6. Magnetic viscosity in the AF

Due to the two critical volumes introduced in Section 2.5, anarrow AF grain size distribution is needed to ensure the settingand thermal stability of the entire distribution. However, samplesproduced by sputtering present a wide distribution of grain sizes.This distribution of grain volumes leads to a wide distribution ofenergy barriers f(DE). In ferromagnetic systems, this widedistribution of energy barriers leads to a ln(t) law in the timedependence of the magnetisation [52]. In the case of AF films, thewide distribution of DE gives rise to an ln(tset) law for the degreeof order in the AF. The order parameter (P) then controls Hexwhich follows an ln(t) law. Therefore, the setting process will havean associated time dependence coefficient S=(dP/d ln tset) that canbe written as [53]

SðTÞp2PSkBTf ½VPðTÞ� ð9aÞ

VPðTÞ ¼lnðtsetf0ÞkBT

Kð0Þð1�T=TNÞð9bÞ

where Ps is the saturation value of the AF order and f(VP) is thecritical value of the energy barrier distribution at the settingtemperature that determines Vp. This critical value of the energybarrier will be determined by the grain volume distribution, thetemperature dependence of KAF and the setting time.

In order to validate this idea, a sample with composition Si/Ru(5 nm)/IrMn(10 nm)/CoFe(3 nm)/Ta(10 nm) was prepared [54].The grain size distribution within the AF layer was measured frombright field TEM images. Over 600 grains were measured and thegrain size distribution was found to be lognormal withDm=(6.070.4) nm and s=(0.3370.03), where Dm is the mediangrain size and s is the standard deviation of ln(D).

Prior to measuring the time dependence of Hex, the originalstate of the AF has to be known. This is done by heating the F/AFsystem to a temperature Tset in the presence of a negative fieldHset(=�1 kOe) large enough to saturate the F layer. The bilayerwas held in this configuration for 5400 s. If Tset is large enough, allthe AF grains will reverse. In our case, Tset=498 K was sufficient toreverse the whole AF distribution. This was confirmed from thefull reversal in the value of Hex. This particular system was chosenfor this experiment so that the whole AF could be set at moderatetemperatures. Further increases in Tset or waiting times resultedin very small changes (o1%) in Hex over a period of 6 h.

Once the state of order in the AF was set, the system washeated to the aligning temperatures TAl, at which the AF is reset inthe opposite sense to that in which it was originally set. This was

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Fig. 13. (colour online) Experimental and calculated time dependence coefficientsfor a IrMn(10 nm)/CoFe(3 nm) exchange couple.

Fig. 14. (colour online) Structure of the trilayer sample studied.


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done for different periods of time tAl. This was done in thepresence of a positive field large enough to saturate the F layer. Byincreasing the aligning temperature we increase the fraction of theAF that undergoes reversal. This procedure was repeated for awide range of temperatures (293 KrTAlr498 K). After thealigning process, the system was cooled to room temperaturewhere the AF is free of thermal activation and hysteresis loopswere measured starting with the F layer in negative saturation.This way, training effects were removed.

Fig. 12 shows the time dependence of Hex over the range oftemperatures studied as a function of ln tAl. Hex varies linearlywith tAl for all values of TAl as indicated by the quality of the linearfits. The gradient dHex/d(ln tAl) exhibits a peak with TAl at �413 K.Above 413 K, the gradient decreases. It is important to note thatthe values of Hex obtained after resetting at 293 and 498 K are thesame but of opposite sign. This is a further confirmation that theentire AF energy barrier distribution was fully reversed.

The time dependence coefficient S(T) can now be measuredfrom the slope of the lines in Fig. 12. Fig. 13 shows the variation ofS(T) with TAl. Note that the error bars in Fig. 13 are based only onthe linearity of the lines in Fig. 12 and do not take into accounterrors in the grain size distribution nor KAF(T). The coefficient S(T)increases with increasing values of TAl reaching a peak at themeasured value of oTB4to75 K. Fig. 13 also shows thecalculated values of S(T) based on Eqs. (9a) and (9b) (solid line).For the calculation a time constant tAl=120 s was used since thatwas the shortest period of time spent at TAl for each set of datapoints. The absolute values of the term f(VP) have been scaled by aconstant factor to account for the proportionality sign in Eq. (9a).The fit between the theoretical prediction and the experimentaldata is again remarkable. Note that the calculated curve deviatesslightly from the experimental data points at the edges of thedistribution. That is due to the fact that when measuring the grainsize distribution most of the grains have a grain size �Dm.Therefore, fewer grains with diameters at either end of thedistribution can be measured leading to a higher uncertainty.The fact that the distribution is symmetric comes from thetemperature dependence of KAF.

Again our simple model has been found to describe theobserved behaviour accurately. This is the third independentmeasurement where our theory has been found to fit the data.Again no other model can fit this result.

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Fig. 12. (colour online) Time dependence of the exchange field with ln(tset).


3. Interfacial effects

For many years there has been significant controversy over therole of interfaces in exchange bias [e.g. 55,56]. This controversyconcerns whether the interface itself gives rise to the shift in thehysteresis loop. This is obviously the case in core–shell nanopar-ticles where the thickness of the antiferromagnet is comparable tothe typical thickness of an interface itself. There also exists thedifficulty of understanding the role of the interface in the couplingbetween the F and AF layers. Obviously there will be a differencein the coupling between a compensated and uncompensatedinterface. Also the degree of spin order at the interface is difficultto ascertain. However, we have been able to obtain someinformation about the behaviour of spins at the interface andtheir influence on exchange bias via a series of unusualexperiments. These experiments relate to studies of trilayersystems, field setting effects and an observation of spontaneousordering of interface spins at low temperatures.

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3.1. Trilayer studies

We have reported on studies of trilayer stysems where a singleAF layer is coupled above and below to F layers of differentthickness [57]. A schematic of the system studied is shown inFig. 14. Due to the F layer thickness dependence of exchange bias,such a system gives rise to two hysteresis loops shifted bydiffering amounts [58]. The initial hysteresis loop for the system is

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Fig. 17. Thermal activation measurements for the trilayer system at �150 Oe(i.e.only one F layer reversed) for a variety of temperatures.


shown in Fig. 15. Fortuitously because of the thicknesses of the Flayers chosen, this system gives rise to a plateau region betweenthe two loops. Note also from Fig. 14 that the thickness of the AFlayer is only 5 nm. From the data shown in Fig. 15 it is clear that itis now possible to undertake the thermal activationmeasurements described in Section 2.1 with either both F layersoriented in the opposite direction to that in which the AF wasoriginally set, or to have one F layer oriented in the oppositedirection and the other remaining in the set direction. This issimply achieved by undertaking thermal activation in a reversefield with a value coinciding with the plateau between the twoloops.

Fig. 16 shows measurements of thermal activation with bothloops oriented in the reverse direction. As expected the thermalactivation process re-orients the AF system progressively as thetemperature of activation is increased. This results in bothhysteresis loops translating from negative field into positivefield in a similar manner to that which occurs for a single-layersystem when the thermal activation is undertaken with just thesingle F layer reversed. Fig. 17 shows the effect of thermallyactivating the antiferromagnet using just the exchange field fromthe thicker ferromagnetic layer. Thermal activation at moderatetemperatures (o155 1C) shifts only the loop for the thicker

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Fig. 15. Initial hysteresis loop for a CoFe(2 nm)/IrMn(5 nm)/CoFe(12 nm) trilayer.

Fig. 16. Thermal activation for a trilayer system with both F layers at negativesaturation for a variery of temperatures.


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ferromagnetic layer. In fact detailed studies have shown that theloop for the thinner layer with the larger exchange bias remainsunaltered for activation temperatures of 130 1C or lower, to theresolution of our measurement capability, which is about 1 Oe.

Given the thickness of the AF layer (5 nm) there is only onepossible explanation for this observation in that the materialwhose structure was changed is that found at the interfacebetween the thicker F layer and the AF layer. Obviously both theinterface with the thinner layer and the bulk of the material mustbe entirely unaffected by the thermal activation process whenonly the thicker F layer is reversed.

These results imply that there is some degree of order in theinterface spins that is established when the AF is originally set.The degree of order in the interface spins then determines thestrength of the coupling between the AF and F layers. Surprisinglythe data in Fig. 17 shows that an exchange field from an adjacent Flayer together with sufficient thermal energy can reorder theinterface spins without affecting the bulk of the AF.

Interestingly the fact that the loop for the thicker layer shiftsfurther with increasing temperatures indicates that the order inthe interface spins does not have a single-order parameter. Thisimplies that there is a distribution of activation energies for thereordering of these spins. This distribution is clearly different tothat of the distribution of energy barriers to reversal in the bulk ofthe AF grains. Further evidence for this view is presented inSection 3.2 below. Given that we believe the degree of order in theinterface determines the coupling between the AF and F layers, itwill give rise to a distribution of coupling energies.

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3.2. Field dependence of interfacial order

It has been known in the magnetic recording industry formany years that a large field is required to set the AF layer in aspin valve or a spin tunnel junction head. This leads to somethingof a conundrum since the F layers are typically a CoFe alloy whichsaturates readily in a few hundred Oe and is certainly fully alignedin a field of 1 kOe. The usual understanding is that it is theexchange field from the F layer that aligns the AF grains. Hencethe application of a field greater than that required to saturate theF layer would be of no benefit. In recent years almost allcompanies manufacturing spin valve or spin tunnel junction readheads have begun to use superconducting magnets, offering fieldsof 2 T or greater, for the setting process. The exact motivation for

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Fig. 18. (colour online) Variation of Hex with Hset for the two CoFe layers in thetrilayer system. Note the different axes for the two layers.

Fig. 19. (colour online) Thermal activation at negative bias with different settingfields for both CoFe layers.


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doing this has never been published but it is known to lead to asignificant improvement in Hex[59].

In order to try and establish the origin of this improvement wehave undertaken studies of the value of the exchange biasachieved as a function of the setting field (Hset). The fieldlimitation in our vibrating sample magnetometer meant thatmeasurements could only be made from low fields up to 2 T.Fig. 18 shows the variation of the exchange bias in the sametrilayer system used for the experiments described in Section 3.1.Hence we have two separate CoFe layers that can be considered.Note the two separate axes for the two layers. For this system anincrease in the exchange bias of approximately 20% is observedfor both layers when the setting field (Hset) is increased from 1 to20 kOe. Interestingly the exact form of the variation for the twolayers is not identical. This is a further indication that the appliedfield is changing the interfaces and that the bulk is unaffected.Also when considering Fig. 16 in conjunction with Fig. 18 it isclear that both F layers are fully saturated by 350 Oe and hencethe exchange field from the F layer is maximised. Subsequentchanges in the exchange bias beyond this point are therefore notdue to changes in the bulk AF and have to be due to changes in theinterface spin order.

This suggestion has been confirmed by undertaking measure-ments of the distribution of blocking temperatures in the samemanner as that described in Section 2.2 having set the AF layers indifferent fields. Fig. 19 shows the variation of blockingtemperatures for the trilayer sample after setting in fields of 1,10 and 20 kOe. The distribution of blocking temperature isidentical in each case to within the resolution of themeasurement which is 72 K. Hence there has been noalteration in the order of the bulk of the AF and this confirmsthat the setting field effect is entirely due to interfacial spins andthe effect of their order on the coupling across the F/AF interface.

This result appears to contradict the findings of Fitzsimmonset al. [60], who found a variation in the net AF moment in an FeF2single crystal with cooling field. We cannot account for thisdiscrepancy other than to remark that the exact superposition ofthe Hex(T) curves for different cooling fields indicates that anychange in the bulk of the AF grains is tiny and is unlikely toaccount for the increase in Hex which is of the order of 25%.

In addition to the data presented here we have shown thatfield alignment of the interfacial spin order and the consequentcoupling across the interface occurs in many different systems[61]. However, whilst the magnitude of the effect changes the


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value of Hex by typically 20–30%, there is significant variation inthe scale of the effect. There appears to be some correlation withthe texture of the AF and some influence of the composition of theF layer at the interface. At this time insufficient data are availablefor us to be able to define exactly the origin of the effect. Onefactor that is now clear is that we are able to write down aformula which links the exchange bias not only as beingproportional to the degree of order and stability in the AF layer,but also to the behaviour of the interfacial coupling.

Under ideal conditions there would be an intrinsic value of Hexdenoted Hiex, but this value of the exchange bias is moderated bythe fraction of the bulk of the AF that contributes to Hex and alsoby the strength of the interfacial coupling Cn. We have now shownthat Cn is a thermally activated factor which also depends uponthe setting field used and hence should be written as Cn(Hset, Tset).Hence the value of Hex is

HexðHset; TsetÞ ¼HiexC�ðHset; TsetÞ

Z VsetðTsetÞVcðTmeasÞ

f ðVÞdV ð10Þ

Note that in Eq. (10) we replace the proportionality factor inEq. 4. A further consequence of the data shown in Fig. 19 is thatthis data again confirms that the interface spins behave largelyindependently of the AF grains and can be viewed almost as aseparate layer in the system.

3.3. Temperature dependence of interfacial spin order

The nature of the spin structure at the interface remains tosome extent an open question. Clearly from the field dependenceof the exchange bias it is obvious that the spins at the interfaceare not independent. If they were then fields of the order 2 Twould have little influence. These spins experience the exchangefield from the F and the AF layers and hence some degree of orderis to be expected. Spin–spin interactions will also occur. Hence itmight be expected that these spins would exist in clusters orbehave cooperatively in a manner similar to, but not necessarilyidentical to, a spin glass.

In an attempt to compare the blocking temperatures derivedfrom the York Protocol and those from a standard measurement ofthe blocking temperature distribution at elevated temperatures,we have undertaken a study of both IrMn/CoFe and FeMn/NiFe[62]. These data are shown in Figs. 20 and 21, respectively. As canbe seen, both measurements of the blocking temperature

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Fig. 20. (colour online) Exchange bias field measured following the York Protocoland measured via standard procedure for IrMn(3 nm)/CoFe. Solid lines are a guide

to the eye.

Fig. 21. (colour online) Exchange bias field measured following the York Protocoland measured via standard procedure for FeMn(10 nm)/NiFe. Solid lines were

calculated from Eq. (6) using Eqs. (7) and (8).


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min. For the York Protocol measurements we establish thetemperature TNA so that the AF is completely stable and hencethe only origin of this further increase in Hex must lie in theinterfaces. We have interpreted this effect as being due to anincrease in the ordering of the spins at the interface which thenincreases the degree of coupling across the interface between theF and AF layers. Fig. 21 shows that this effect is more pronouncedin FeMn almost doubling the value of Hex. Hence the parameter C

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discussed above will also have a marked temperature dependencedue to spontaneous ordering of the disordered spins at theinterface. Similar effects were observed by Takano et al. [36].


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From the form of the low-temperature data in Figs. 20 and 21the spontaneous spin freezing at low temperatures does not occurat a single temperature. Hence it is not a phase transition similarto a Curie temperature in a ferromagnet but is more similar to ablocking temperature distribution in a spin glass. This is notsurprising since due to interface roughness, the exchange fieldexperienced by each cluster will vary. Due to the distribution ofgrain size it might be expected that the cluster size will also vary.This in turn will lead to a variation in cluster–cluster exchangeand dipole–dipole interactions.

3.4. Field dependence of interfacial spin ordering

Given the experimental data described above it is now possiblefor us to speculate on the nature of the interfacial spin ordering. Ina separate study of films with structure Ta(5 nm)/Seed/IrMn(tAF)/CoFe(2 nm)/Ru(5 nm) we have again examined the variation ofHex with Hset the setting field, where the seed is NiFe, Cr or Ru.Since the value of Hex increases with Hset this implies that theorder of the interface spins is ferromagnetic in character. Thissuggestion is supported by the spontaneous ordering that occursat low temperatures. We postulate that this ordering shouldfollow some type of Langevin function (L(x)), assuming that thecoupling between the F and AF layers depends linearly on thedegree or order of the interfacial spins. Hence we would expect avariation of the form

HexðHset; TsetÞpHiexLðxÞ with x¼NmBðHsetþH�Þ

kBTsetð11Þ

where Hn is now the exchange field which the spins experiencedue to both the F and AF layers and spin–spin interactions, mB isthe Bohr magneton and N is the number of spins in each cluster.Unfortunately this form of Langevin function contains twounknowns, Hn and N. It is now impossible to obtain a unique fitto the data. However it is possible to put boundaries on thenumber of spins that must be ordering to give rise to the increasein Hex. For example if the extreme value N=1 is taken, i.e.assuming that the spins act singly, then the resulting value for theexchange field would have to be of the order of 2�105 kOe whichis physically unrealistic. Typical exchange fields for ferromagneticmaterials derived from molecular field theory are of the order of104 kOe. Given that this is an interface between an F and an AFlayer the value for bulk iron quoted above would also seem to beinappropriate. However, if a value of half of the exchange field foriron is used then we are able to fit our experimental data allowingthe parameter N to float. Us

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A new paradigm for exchange bias in polycrystalline thin films New Paradigm... · 2010. 1. 16. · Title: A new paradigm for exchange bias in polycrystalline thin films Author: K