Exchnage Anisotropy a Review Article JMMM 200 552 1999 H_EB_ref

*Corresponding author. Tel.: #1-858-534-5627; fax: #1-858-534-2720.

E-mail address: [email protected] (A.E. Berkowitz)

Journal of Magnetism and Magnetic Materials 200 (1999) 552}570

Exchange anisotropy * a review

A.E. Berkowitz!,*, Kentaro Takano"

!Department of Physics and Center for Magnetic Recording Research, University of California at San Diego, La Jolla, CA 92093-0401, USA"IBM Almaden Research Center, 650 Harry Rd., San Jose, CA 95120, USA

Received 12 March 1999

Abstract

Exchange anisotropy refers to the magnetic manifestations of an exchange coupling at the interface between twodi!erent magnetically ordered systems. Of particular current technological interest is the unidirectional anisotropy, or&exchange-bias' "eld produced in a ferromagnetic "lm that is coupled to an appropriate antiferromagnetic "lm.Experimental characterization and theoretical models are discussed for these types of bilayers for a variety of metallic andoxide "lm couples. ( 1999 Elsevier Science B.V. All rights reserved.

Keywords: Exchange anisotropy; Interfaces; Thin "lms

1. Introduction and background

In 1956, Meiklejohn and Bean (M}B) reported[1,2] &A new type of magnetic anisotropy has beendiscovered which is best described as an exchangeanisotropy. This anisotropy is the result of an interac-tion between an antiferromagnetic material and a fer-romagnetic material'. In the more than 40 yearssince its discovery, the phenomenon of exchangeanisotropy has become the basis for an importantapplication in information storage technology, witha high current level of world-wide research anddevelopment activities. However, it has only beenwithin the last decade or so that a basic, quantita-tively predictive, understanding of exchange anisot-ropy has begun to be developed signi"cantly

beyond the initial seminal model presented byM}B. The relatively slow pace of rigorousmodeling is due primarily to the fact that exchangeanisotropy is the result of an interfacial exchangeinteraction between ferromagnetic (FM) and anti-ferromagnetic (AFM) materials, and only recentlyhave the required experimental and analytical toolsfor dealing with interfacial behavior at the atomiclevel become available. This review will discussprimarily those research results which, at present,seem to o!er the most insight into a reliable model.Previous reviews in which exchange anisotropy isconsidered in signi"cant detail are found in Refs.[3}5].

1.1. Meiklejohn and Bean's research

M}B's discovery was initiated by the observationthat the hysteresis loop below room temperature ofa sample of nominal Co nanoparticles was shiftedalong the "eld axis after cooling in an applied "eld.

0304-8853/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved.PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 4 5 3 - 9

Fig. 1. (a) Hysteresis loops at 77 K of partially oxidized Coparticles. Curve (1) shows the resulting loop after cooling thecompact in a 10 kOe "eld. Curve (2) shows the loop whencooled in zero "eld. (b) Torque curves on partially oxidized Coparticles cooled in a "eld to 77 K, where h is the angle betweenthe cooling "eld axis and the direction of the measuring "eld.Curves a and b in (b) are for counterclockwise and clockwiserotations, respectively. From Refs. [1,2].

It was subsequently established that the particleshad been partially oxidized to CoO which is anAFM. Thus, the particles could be considered toconsist of a core of single-domain Co with a shell ofAFM CoO. M}B described how the exchange in-teraction across the interface between the FM Coand the AFM CoO could produce the shifted hys-teresis loop and the other unique manifestations ofexchange anisotropy. The initial papers of M}B[1,2], together with the review by Meiklejohn [3],anticipated virtually all the features of subsequentexperimental observations and models for ex-change anisotropy.

Fig. 1a shows hysteresis loops at 77 K of acompact of "ne partially oxidized Co particles(10}100 nm). The shifted loop (curve 1) was mea-sured after cooling in a "eld of 10 kOe; the symmet-ric loop (curve 2) was measured after cooling inzero "eld. M}B showed that the loop shift wasequivalent to the assumption of a unidirectionalanisotropy energy in the expression for the freeenergy at ¹"0 K of a single-domain sphericalparticle with uniaxial anisotropy, aligned with itseasy axis in the direction of the "eld, H, which isapplied anti-parallel to the particle's magneti-zation, M

4, i.e.,

F"HM4cos H!K

6cos H#K

1sin2 H,

where H is the angle between the easy direction andthe direction of magnetization, and K

6and K

1are

the unidirectional and uniaxial anisotropy energyconstants, respectively. Solutions of this equationare readily expressed in terms of an e!ective "eld

H@"H!K6/M

4,

which gives the hysteresis loop displaced by K6/M

4,

on the H-axis. Thus, an explanation of the loopshift is equivalent to explaining the unidirectionalanisotropy.

AFM materials, such as CoO, magnetically orderbelow their NeH el temperatures, ¹

N, with the spins of

the Co2` cations parallel to each other on (1 1 1)planes, and with anti-parallel spin directions inalternate (1 1 1) planes, i.e., zero net moment. How-ever, at the interface with a FM, there are localizednet moments which arise from several sources (dis-cussed in the Models and theories section). The

most obvious case is where there are AFM grainswith parallel spin planes at the interface as depictedin Fig. 2. Alternatively, even in AFM grains withcompensated interfacial spin planes, there can beunequal numbers of parallel and anti-parallel spinsat the surface of the grain, due to grain size, shape,or roughness. These various origins of localized net

A.E. Berkowitz, K. Takano / Journal of Magnetism and Magnetic Materials 200 (1999) 552}570 553

G A Basheed

Highlight

Fig. 2. Schematic of the ideal FM/AFM interface. The FM andAFM layers are single crystal and epitaxial with an atomicallysmooth interface. The interfacial AFM spin plane is a fullyuncompensated spin plane. For this ideal interface, the cal-culated value of the full interfacial energy density is about twoorders of magnitude larger than the experimentally observedvalues.

Fig. 3. Interfacial complexities of a polycrystallineFM(metal)/AFM(oxide) interface. In this "gure, the interfacialspins prefer to align ferromagnetically. The X marks identifythe frustrated exchange bonds, i.e. the interfacial spins that arecoupled antiferromagnetically. The interfacial region can havea high degree of stress since metals and oxides often have verydi!erent lattice parameters. Dislocations (represented by thedashed line) can form during "lm growth to relieve the stress.

AFM moments are depicted in Fig. 3. Since the FMis ordered at its Curie temperature, ¹

C, which is

greater than ¹N

of the AFM, a "eld applied tocoupled FM}AFM systems at ¹'¹

Nwill align

the FM magnetization in the "eld direction, while

the AFM spins remain paramagnetic. As the tem-perature is lowered through ¹

N, the ordering net

localized AFM spins will couple to the aligned FMspins, sharing their general spin direction. For highAFM magnetocrystalline anisotropy, if the inter-facial AFM spins are strongly coupled to the AFMlattice, they will not be substantially rotated out oftheir alignment direction by "elds applied at tem-peratures below ¹

N. This is also a consequence of

the fact that the generally compensating anti-paral-lel arrangement of the AFM spins does not result ina strong torque on the spin system when a "eld isapplied (i.e., low susceptibility). However, since thelocalized uncompensated AFM spins are coupledto FM spins at the interface, they exert a strongtorque on these FM spins, tending to keep themaligned in the direction of the cooling "eld, i.e.,a unidirectional anisotropy. This model explainsthe shift in curve 1 in Fig. 1a, for the "eld-cooledparticles. When the particles are cooled in zero"eld, there is still a unidirectional bias in eachparticle, but since the moments of the particles arerandomly arranged, there is no net bias, and curve2 in Fig. 1a is symmetric.

M}B anticipated and considered all of the ex-change anisotropy issues dealt with in more detailbelow. These include: (a) how the relative strengthsof the interfacial exchange coupling and the AFMmagnetocrystalline anisotropy determine whethera unidirectional anisotropy dominates, or whetherthe AFM spin system is switched as the FM rotates,producing high-"eld rotational hysteresis; (b) howwalls in either the FM or AFM can in#uence theobserved behavior; (c) how the "eld-cooling para-meters in#uence the resulting unidirectional anisot-ropy; and (d) the temperature dependence of thebias "eld.

1.2. Other early work

The 1962 review by Meiklejohn [3] discussesa number of two-phase systems in which variousproperties could plausibly be attributed to ex-change anisotropy. These include not only FM}AFM, but also ferrimagnetic}AFM, and ferrima-gnetic}FM combinations. Rotational hysteresis(=

R) is the integrated displacement of torque

curves measured with the "eld rotated in the

554 A.E. Berkowitz, K. Takano / Journal of Magnetism and Magnetic Materials 200 (1999) 552}570

plane of the sample in clockwise and counterclock-wise directions, as shown in Fig. 1b. Meiklejohnpresented an expanded model for the existence of=

Rin FM}AFM systems for "elds '2K

1/M

4of

the FM. Above ¹N

of the CoO coating, the single-domain particles of Co with uniaxial anisotropywere shown to exhibit =

Ronly for "elds between

K1/M

4and 2K

1/M

4. However, with an AFM-or-

dered CoO shell, Co particles have "nite =R

in"elds H<2K

1/M

4. Meiklejohn showed this occurs

when the exchange anisotropy constant, K6'

KAFM

. This high "eld=Ris due to the discontinuous

switching of the AFM spin system twice each cycleas the FM is rotated 3603 by the applied "eld.This is a consequence of the torque exerted on theAFM spin system by the FM to which it is coupled.The magnitude of=

Rdepends on K

6/K

AFM, and on

the AFM thickness (i.e., net AFM magnetocrystal-line energy). The additional interaction of the AFMspin system with the applied "eld was described byBerkowitz and Greiner [6].

Meiklejohn called attention to the ideal manifes-tations of unidirectional anisotropy in the atomi-cally disordered Mn alloys investigated by Kouvel[7]. In these alloys, the Mn atoms have either FMor AFM exchange interactions, depending onwhether they are nearest or next-nearest neighbors,respectively. Accordingly, Kouvel ascribed the uni-directional anisotropy to adjacent exchangecoupled FM and AFM regions which were presentas localized composition #uctuations. Satoh et al.[8] used high "eld measurements to determine themagnitude of the coupling "eld in Mn}Ni alloys ofthis type.

NeH el [9] considered in detail the behavior ofpartially oxidized FM "lms in which the oxide wasAFM (e.g., Co}CoO, Ni}NiO), and was assumed tobe in the form of small grains. He discussed theissues of high "eld =

Rin these "lms in much the

same spirit as Meiklejohn did for the partially oxi-dized particles. NeH el focused particularly on thebehavior of these "lms under repetitive cycling ofthe "eld. He described how the loop shift, and itsdependence on the amplitude of the cycled applied"eld, varied with the number of "eld cycles. Hedistinguished among three types of hysteresis loss:AC loss, where the "eld varies between #H and!H; rotational hysteresis, in which a "xed "eld is

rotated through complete cycles; and oscillatoryhysteresis, in which a "xed "eld is rotated betweentwo "xed directions. NeH el also considered the still-open question of the nature of the exchange inter-action at the FM}AFM interface on an atomiclevel. Yelon's review [5] includes a useful summaryof NeH el's work in this area. Charap and Fulcomer[10,11] extended the consideration of the magneti-zation dynamics of this type of oxidized "lm withexperimental observations and models. They ob-served viscous domain wall motion, as well asfrequency- and temperature-dependent loop dis-placements which they modeled by consideringthermally induced #uctuations of the spin systemsof the small AFM grains coupled to the FM "lm.Their papers contain references to the other signi"-cant investigations in similar systems. Bostanjogloet al. [12,13] reported some of the "rst Lorentzmicrographs of domain wall structures taken atvarious stages of magnetization reversal in NiFe}NiFeMn couples after one or more "eld cycles.They concluded that the decreasing loop shift withprogressive "eld cycling was accompanied by a ro-tation of the unidirectional anisotropy axis by 903.The investigations noted above point to a growingawareness of the extraordinary complexity and thesigni"cance of the chemical and magnetic structureat the FM}AFM interface.

2. More recent investigations

During the past several decades, the pace ofactivity involving FM}AFM exchange couples hasgreatly increased. The reason is that the e!ectivebias "eld, H

E, on a FM thin "lm produced by the

interfacial exchange with an AFM "lm, has foundan extremely useful application in the informationstorage industry. The digital data in current high-density magnetic storage disks is sensed by read-heads which employ thin FM "lm devices whoseresistance varies with the magnitude and directionof the stray "elds above the stored bits [14]. This isthe phenomenon of magnetoresistance (MR). Tolinearize the bipolar MR signal, and to minimizethe noise produced by discontinuous jumps of do-main walls (Barkhausen noise), the FM "lms mustbe biased by a magnetic "eld. Coupling the FM


Fig. 4. Chemical and magnetic structure of NixCo

(1~x)O anti-

ferromagnetic materials. The shaded spheres represent the mag-netic metal atoms, and the un"lled spheres represent the oxygenatoms.

"lm to an AFM "lm provides a substantial fractionof the required bias in all current high-densityread-heads. All of the initial AFM "lms used forthis purpose were metallic Mn alloys, particularlyFe}Mn. Recently, read-heads using the more ro-bust insulating AFM bias "lms such as NiO havebeen appearing. Since the exchange interactionsand spin structures are quite di!erent in metallicand insulating AFM materials, the behavior of ex-change couples with these two types of AFMs areconsidered separately below.

By the mid-1970s virtually all of the most signi"-cant static and dynamic features of FM}AFM ex-change coupling had been recognized, andplausible qualitative models had been developedfor a number of issues. What was lacking, and isstill missing, was adequate characterization of thechemical states and the exchange interactions at theFM}AFM interface on an atomic scale. Until thisextremely complex information becomes available,there can be no rigorously reliable explanations forthe salient features of exchange anisotropy inFM}AFM couples. Therefore, the papers discussedbelow were primarily selected with the hope thatthey o!ered signi"cant clues to a basic understand-ing by virtue of their (i) careful sample preparation;(ii) useful interfacial characterization; or(iii) unique exchange properties. In all these cases,the FM}AFM exchange couples are thin "lms.

2.1. Exchange couples with insulating AFM xlms

Almost all the reported investigations with insu-lating AFMs involve the monoxides NiO, CoO,and Ni

xCo

(1~x)O. An important exception is FeF

2.

Detailed work with other oxides such as a-Fe2O

3and orthoferrites are preliminary and still in pro-gress. The monoxides have an FCC structure above¹

N, with a slight distortion below ¹

N[15]; rhom-

bohedral contraction along S1 1 1T in NiO, tetrag-onal contraction along S1 0 0T in CoO. The bulk¹

Nfor CoO is 293 K; for NiO, it is 525 K. For

NixCo

(1~x)O, ¹

Nvaries linearly with x [16]. Above

¹N, the monoxides are paramagnetic. Below ¹

N,

they order with parallel spins on (1 1 1) planes, andwith anti-parallel spin directions on adjacentplanes (i.e., the spins of next nearest neighborsalong S1 0 0T are anti-parallel due to the superex-

change interaction via an intervening oxygenatom). This is depicted in Fig. 4. The four di!erentS1 1 1T axes for spin ordering combined with thenon-cubic distortions below ¹

N, make for a rich

variety of AFM domain structures, which was de-scribed in detail by Roth and Slack [17}19]. AnAFM domain is identi"ed by its NeH el axis, thedirection along which the spins are either parallelor anti-parallel. Since it is di$cult to preparesingle-domain samples, it has not been possible toaccurately measure the magnetocrystalline con-stants of the AFM monoxides. The spins can berotated much more easily within the coherentlymagnetized (1 1 1) planes than out of these planes.Thus, two anisotropy constants can be identi"ed,K

1for rotation out of the (1 1 1) spin plane, and

K2

for rotation within this plane. The unquenchedorbital momentum of Co2` gives CoO a very highmagnetocrystalline anisotropy. Kanamori has cal-culated K

1+2.7]108 erg/cm3 [20]. At 4.2 K,

K2(2]105 was obtained [21]. For NiO, values

reported for K1

are 1 to 5]106 [22}25]; K2

hasbeen variously measured [26}29], and calculated[30] from 0.1 to &5% of K

1. Although there is

considerable uncertainty as to the correct values ofK

1and K

2, there is no doubt that both are much

higher for CoO than for NiO.


In a general sense, the recent (1990s) investiga-tions of exchange couples with monoxide AFM andmetallic FM "lms have served to con"rm the initialsuggestions of Meiklejohn, Bean, and NeH el, albeitwith more sensitive and re"ned experimental andanalytical methods. The principal achievementshave been: (1) demonstrating that the uncompen-sated AFM interfacial spin density determines H

E;

(2) HC

increases with lower AFM anisotropy ener-gies; (3) thermally activated aftere!ects are fre-quently observed. Furthermore, a quantitativelypredictive model for H

Ehas been developed for

CoO-permalloy couples.Carey and Berkowitz [31] reported the prepara-

tion, by reactive sputtering, of AFM "lms of CoO,NiO, and Ni

xCo

(1~x)O. When coupled to permal-

loy, the blocking temperatures, ¹B

(and, by infer-ence, ¹

Nalso) of the Ni

xCo

(1~x)O varied linearly

with x from the CoO to the NiO values. HE

andH

Cwere determined as functions of x; for x'20

vol%, HE/H

Cwas '1, a necessary condition for

biasing read-heads. The same authors measuredH

E(¹) of CoO}NiO superlattices exchange coupled

to permalloy [32]. These data indicated a su$-ciently strong exchange interaction at CoO}NiOinterfaces such that when the superlattice repeatdistance was )2 nm, a single ordering temper-ature existed, and ¹

Nwas the same as an alloy with

the same vol% of CoO and NiO. This was latercon"rmed by neutron di!raction [33]. H

E(¹) also

depended on whether a CoO or NiO layer wasadjacent to the permalloy. Generally, this workpointed to several potential options for control ofH

E(¹). However, the de"nitive aspects of this work

primarily focus on the magnetic ordering within theAFM. The results pertaining to exchange biasingare only suggestive since it still remains to modeland establish de"nitively the AFM superlattices'e!ectiveness for exchange biasing.

Since the bulk ¹N

of CoO is approximately roomtemperature, and its magnetocrystalline anisotropyis high, CoO}FM is a very useful model systemsince magnetic characterization is convenientlyperformed using a SQUID magnetometer. A sys-tematic study of polycrystalline CoO}permalloyexchange couples by Takano et al. [34,35] clearlydemonstrated that the AFM interfacial uncompen-sated spin density determines H

E, independent of

compensation considerations, and a model wasdeveloped that provided the "rst quantitative pre-dictions of H

Efor a given system. That work is

discussed in detail below in the section on Modelsand Theories. It was demonstrated experimentallyand analytically that the density of AFM uncom-pensated interfacial spins was inversely propor-tional to the average interfacial grain diameter.Although smaller interfacial grains produced high-er H

Eat low temperatures, H

Ewas signi"cantly

temperature dependent if the grain had a corre-spondingly small volume [36]. This is a conse-quence of the fact that the anisotropy energies ofthe AFM grains are proportional to their volumes;therefore, su$ciently small grains can be subject tothermally activated #uctuations of their spin sys-tems, analogous to superparamagnetism in FMnanoparticles, but modi"ed by the coupling to theFM. Accordingly, Martien et al. [37] showed thattextured AFM Co

0.5Ni

0.5O "lms in which the in-

terfacial grain diameters were small but elongatednormal to the interface, yielded increased H

Ewith

minimal decrease in thermal stability.Two investigations have emphasized the com-

plex atomic scale chemical and spin distributions atthe CoO interface with a FM material. Moran et al.[38] used bulk CoO (1 1 1) crystals which weremechanically roughened to various degrees. Per-malloy was deposited on these surfaces, and H

Eand

HC

were measured after "eld-cooling from above¹

N. H

Eregularly increased with roughness, which

seemed counterintuitive at the time, but is consis-tent with the quite plausible notion of an uncom-pensated spin density increasing with roughness.Spagna et al. [39] reported the properties ofCo}CoO bilayers and Co}CoO}Co trilayers inwhich the CoO was formed by partially oxidizingthe Co "lms. A depth pro"ling technique, usingAuger electron spectroscopy in conjunction with1 keV Ar` ion sputter etching, showed a lineardecrease of both Co and oxygen over a distance of2.3 nm from the 100% Co surface of a "lm that wasinitially 8 nm of Co. In spite of this strong evidencefor a lack of a sharp interface, H

Ewas +1 kOe at

20 K. HEvanished at &150 K, presumably because

the spin system in the non-uniform 2.3 nm oxidelayer became thermally unstable. However, Abarraet al. [40] found ¹

Nof a 2.3 nm "lm of CoO was


+270 K, and Takano [36] determined that ¹"

tobe one-half ¹

Nonly in cases where the sizes of the

oxide grains were extremely small * i.e., whendeposited on cryogenically cooled substrates. Thenature of the interfacial exchange interaction,whether superexchange or direct exchange, is notknown at present. A start in elucidating this ques-tion was made by Takano and co-workers [36].They deposited a number of di!erent FM "lms onCoO underlayers, and measured the low-temper-ature H

E. A mean "eld analysis of these values

permitted discrimination between direct and super-exchange. At a metal}oxide interface, one mightexpect superexchange to dominate; however, theanalysis suggested direct exchange as the limitinginterfacial exchange.

In the exchange couples with CoO discussedabove, the FM layer was a metal. Several importantstudies have been made in which CoO was coupledto Fe

3O

4, a ferrimagnet (FIM) which has two FM

sublattices of unequal magnetization oriented anti-parallel. The net magnetization of Fe

3O

4vanishes

at its Curie temperature, ¹C"858 K. Since the

lattice constant of Fe3O

4is twice that of CoO, and

the FCC oxygen lattice has very similar dimensionsin both materials, they can be grown epitaxially.This was demonstrated by Terashima and Bando[41], who grew multilayers of CoO}Fe

3O

4pairs

with various "lm thicknesses and numbers of bi-layer repeats, on (1 0 0) cleaved NaCl. X-ray struc-ture analysis con"rmed epitaxial growth for thicker(&5.0}10.0 nm) Fe

3O

4, with evidence of cation

disorder in thinner "lms. A surprising result wasthe existence of a hysteresis loop shift forCoO(2.2 nm)}Fe

3O

4(9.0 nm) at room temperature,

since such thin CoO was expected to be paramag-netic or at least superparamagnetic at that temper-ature.

van der Zaag et al. [42,43] have prepared epi-taxial bilayers of CoO and Fe

3O

4with (1 0 0) and

(1 1 1) orientations. They examined the CoO thick-ness (t

C0) dependence of H

Eand ¹

B. They found

that ¹B

was +¹N

of CoO for tC0*8.0 nm.

HE(0 K) was maximum for 2.0 nm(t

C0(5.0 nm.

Ijiri et al. [44,45] used neutron di!raction to inves-tigate spin con"gurations in (0 0 1)[Fe

3O

4(10 nm)}

CoO(30 nm)]50

and [Fe3O

4(10 nm)}CoO(10 nm)]

50superlattices prepared by van der Zaag and Wolf.

The most remarkable result was the observation,after "eld-cooling, that the CoO spins aligned per-pendicular to the Fe

3O

4net moment. The two

samples also exhibited very high HE

(550 and1300 Oe), H

C(6000 and 3200 Oe), and ¹

N(450 and

325 K), respectively. These values suggest a highlycomplex interfacial spin structure, with the likeli-hood of propagation of anomalous magnetic orderthroughout the superlattices, evidenced by the ex-tension of the AFM coherence across the bilayers.Another possible factor might be the presence offerrimagnetic Co-ferrite-like magnetic order, withan enormous magnetocrystalline anisotropy. Alongthese lines, Kleint et al. [46] found shifted loopsin Fe

3O

4}Co

xFe

(3~x)O

4bilayers, and ascribed H

Eto the reversal of the softer Fe

3O

4without chan-

ging the magnetization direction of the harderCo

xFe

(3~x). This study emphasized the extremely

complex interfacial magnetic structure.The relatively high ¹

Nof NiO makes it attractive

for commercial applications. However, its low mag-netocrystalline anisotropy (1) limits H

E, and (2) in-

creases HC, when the interfacial exchange exceeds

the magnetic energy of the AFM grain. A numberof studies have con"rmed this behavior. Lee et al.[47] compared epitaxial NiO}NiFe bilayersprepared on (1 0 0), (1 1 0), and (1 1 1)MgO to poly-crystalline NiO}NiFe. They also measured rough-ness. They concluded that texture did not playa signi"cant role in determining H

E, but that

roughness seemed to increase HC. Han et al. [48]

concluded that low interfacial roughness was thekey to low H

Cin NiO}Ni

81Fe

19exchange couples,

and that HE

was insensitive to texture. Michel et al.[49] compared the behavior of epitaxial (0 0 1) andpolycrystalline NiO}NiFe bilayers. They foundthat the polycrystalline couples had larger H

Ethan

the epitaxial ones. They suggested that a staticsurface anisotropy with reversible interfacial NiOspin dynamics could account for a large part of theobserved behavior. However, they noted that thepresence of high-"eld rotational hysteresis in-dicated some irreversible AFM spin dynamics.They also called attention to the possibility that theexistence of interfacial roughness, stress, and do-mains in the AFM layer could produce frustrationin the interfacial layer, a spin-glass like situationpreviously suggested by Stoecklein et al. [50] and


by Schlenker et al. [51]. MoK ssbauer studies byTakano and Parker [36] would tend to providesupport for such a topologically disordered spincon"guration. Their data suggest that the inter-facial atoms occupy a variety of valence states andchemical environments. In a study of spin valves,Chopra et al. [52] used high-resolution TEM toshow how the atomic structure of a NiO}Co inter-face varied with the O

2sputtering pressure during

reactive deposition of the NiO onto the Co "lm,and how the resulting pinning "eld re#ected theinterfacial structure. These authors emphasize thattheir pinning is primarily accomplished by the highH

Cat the NiO}Co interface. Observation of do-

main con"gurations during reversal of Ni(50 nm)}NiFe(10 nm) bilayers grown on (0 0 1)MgO werereported by Nikotenko et al. [53], using a mag-neto-optical indicator. At the resolution of thismethod (+several lm), they observed that domainnucleation was responsible for magnetization re-versal when the "eld was applied along H

E, but that

incoherent reversal occurred in transverse "elds.Another interesting observation was that the wallnucleation initiated at "lm edges with "elds anti-parallel to H

E, but nucleation occurred at disloca-

tion slip planes and their intersections for applied"elds parallel to H

E.

Although ¹N

is relatively high in NiO, its lowK

2can lead to thermal instability if the grain size is

small, since the energy barrier against thermallyactivated reversal is JK

2<. Soeya et al. [54]

examined HE

of exchange-coupled 40 nm Ni81

Fe19

"lms after "eld-cooling from above ¹N, and then

cooling from ¹)¹N

in both 500 Oe DC "eldsopposite to the initial cooling-"eld direction or anAC "eld of 40 Oe perpendicular to the cooling "eldin the plane of the "lms. In both cases, H

Ede-

creased monotonically with higher starting temper-atures. They interpreted this behavior as indicatingthe presence of a distribution of di!erent ex-change-coupling paths at the interface, each withdi!ering ¹

Bs. This is certainly a plausible model,

which was initially introduced by Tsang and Lee[55], and by Speriosu et al. [56] for FeMn}Ni

81Fe

19. Similar results were reported by Oh-

shima et al. [57]. They investigated Ni80

Fe20"lms

coupled to both NiO and FeMn. They applied"elds perpendicular to the direction of H

%in the

"lm plane at temperatures of 323 and 373 K forvarious times. They examined the phase shift of theunidirectional component of the torque curve afterthe thermal treatments. The shifts increased and thetorque amplitudes decreased linearly with log time,leading them to ascribe this behavior to a thermal#uctuation aftere!ect, in the spirit of NeH el [9] andFulcomer and Charap [10,11]. Similar results werereported by van der Heijden et al. [58] forNiO}Ni

66Co

18Fe

16bilayers. They concluded that

the AFM grains were not single domains. Thuswalls were likely important in these structures.They also noted that the AFM grains could havea small moment due to uncompensated spins, en-abling a direct coupling of these grains to the ap-plied "eld.

A very unique exchange anisotropy situation hasbeen reported for the Fe}FeF

2system. FeF

2has

a body-centered tetragonal structure with the Fe2`cations located at the cube corners and center [59].At 78.4 K, AFM ordering puts the Fe2` spinsalong the c-axis, with the cube corner spins anti-parallel to those at the body-center position, withan accompanying uniaxial magnetocrystalline an-isotropy [60,61]. The remarkable fact is that whenFeF

2(+90 nm)}Fe(+13 nm) bilayers grown on

(0 0 1)MgO are "eld-cooled below ¹N, the magni-

tude and sign of HEdepend on the magnitude of the

cooling "eld [62]. Thus, after cooling in positive"elds, H

Eincreases from &!200 Oe to #200 Oe

monotonically with increasing applied cooling"elds up to 70 kOe, and the sign of H

Eremains

constant until ¹B"¹

Nis reached. The authors'

model for this behavior is that high "elds beginmoving AFM interfacial spins into the "eld direc-tion, and these spins couple antiferromagneticallywith the interfacial FM spins. Several other papersby the same group have considered a variety ofaspects of this system [63}65]. An important "nd-ing was that the exchange-bias e!ects can be quitelarge (&1.1 erg/cm2), and that the magnitude of theexchange bias "eld increases with interfacial rough-ness.

2.2. Exchange couples with metallic AFM xlms

Since almost all of the current applications ofexchange anisotropy for "lm biasing use metallic


AFMs, it might be expected that reliable modelingof exchange biasing with these systems would bemore extensive than for the insulating AFMs. How-ever, although many more investigations have beenreported for exchange couples using metallic AFM"lms than for insulating ones, it seems that there isactually less understanding of the basic phenomenawhen metallic AFM "lms are involved. There areseveral likely reasons for this situation. The crystalstructures of metallic AFMs often deviate morestrongly from cubic symmetry than do the struc-tures of the insulating AFMs. This makes it moredi$cult to grow suitable epitaxial "lms, whetherbilayer or multilayer. The spin structures are gener-ally more complex in metallic AFM; i.e. multi-spinsublattices, as well as temperature-dependent spinphases. The ¹

Ns of the metallic AFMs are usually

higher than for insulating AFMs. This means thatit is not always possible to "eld-cool through¹

Nwithout risking irreversible structural changes

such as grain growth and interdi!usion. Thus, it isnot as convenient to work with model systems aswith insulating AFM.

Virtually all of the metallic AFM materials inves-tigated for exchange-biasing have been Mn alloys.The seminal paper in this connection was byHempstead et al. [66], in which it was reported thatdepositing c-phase FeMn (&50% Mn) "lms ontoNi

80Fe

20"lms produced larger loop shifts and

higher HE/H

Cratios than were obtained for couples

consisting of either annealed Ni80

Fe20

/Mn orNi

80Fe

20/a-Fe

2O

3. They noted that although the

c-phase of Mn was not stable at room temperaturein the bulk, the c-phase of FeMn in "lms was stable,and could be deposited on the Ni

80Fe

20, even with-

out annealing. They suggested a number of ternaryadditions to further stabilize the c-phase, andpointed out that bulk binary alloys of Mn with Fe,Ni, Rh, Pt and ternary alloys with Ni and Fe arec-phases, and exhibit unidirectional properties.They also noted that unidirectional anisotropy wasproduced in their Ni

80Fe

20/FeMn couples without

cooling from above ¹N, and that the direction of

the exchange bias could be moved into the direc-tion of a "eld applied at temperatures much lowerthan ¹

N. Finally, they stressed the importance of

the nature of the FM/AFM interface. These pointsmade by Hempstead et al. have consistently re-

appeared in the extensive subsequent work on ex-change couples with metallic AFMs.

2.2.1. Fe}MnAFM Fe}Mn "lms with various additions are

currently in use in most exchange-biased MRread-heads. The AFM c-phase is FCC, and extendsfrom about 30}55 at% Mn at room temperature[67]; ¹

Nincreases from about 425}525 K with in-

creasing Mn concentration in this range. Most in-vestigations use alloys with 50% or more Mn toachieve the higher ¹

N(and, hence, ¹

B). The Mn and

Fe atoms occupy the lattice sites randomly. Theatoms at the (0, 0, 0), (0, 1

2, 12), (1

2, 0, 1

2), and (1

2, 12, 0)

form a tetrahedron, and the spins on these atomsare directed along the four S1 1 1T directions to-wards the center of this tetrahedron [67]. WhenFCC permalloy (Ni

81Fe

19) is the FM, lower H

Cis

achieved when the FeMn is deposited on the per-malloy than when the deposition order is reversed,and the substrate is not FCC.

The issues of deposition order and of the in#uenceof FeMn thickness were explored by Kung et al.[68], who characterized trilayers of NiFe(60 nm)/FeMn(4}40 nm)/NiFe(30 nm)/Ta(20 nm). The lowerand upper interface coupling behavior could bereadily distinguished by hysteresis loop measure-ments. The interfacial unidirectional energy den-sity, *p (erg/cm2) is commonly de"ned by

HE"*p/M

FMtFM

,

where tFM

is the thickness of the FM "lm. For thelower interface, *p and ¹

Bboth increase initially

with FeMn thickness, but become constant forFeMn thicknesses beyond 8 and 16 nm, respective-ly. For the upper interface, *p and ¹

Bboth increase

initially, but start to decrease for FeMn thicknessesabove 12 and 36 nm, respectively. Kung et al. foundthat the FeMn grain size increased with thickness,and suggest that the initial increase in *p and¹

Bare due to an average increase in grain size and

that the decrease for thick FeMn are due to rough-ness and the loss of the c-phase. Although this isa plausible explanation, it is simpler to explain thedecrease in *p at the upper interface as re#ectinga decreasing density of uncompensated spins withincreasing interfacial AFM grain size as the FeMn


G A Basheed

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thickness increases, as was found for the CoO}Ni

81Fe

19system [34,35].

Jungblut et al. [69] investigated the in#uence ofinterfacial orientation on H

Eand H

Cin epitaxial

Ni80

Fe20

/Fe50

Mn50

bilayers. They described thevery di!erent spin structures terminating the (0 0 1),(1 1 1), and (1 1 0)Fe

50Mn

50surfaces, and grew

wedge-shaped bilayers in these orientations withvarying thicknesses of the FM and AFM layers.They discussed their "ndings in terms of variousmodels and structural features. The general con-clusions were that while H

Eand H

Cand their

ratios depended strongly on interfacial orienta-tion, there was no indication that the compensatedor uncompensated nature of an &ideal' interfaceplayed a signi"cant role in determining theseproperties.

A number of papers have interpreted the temper-ature dependence of H

E, H

C, and ¹

Nin terms of

several interfacial issues, e.g., interfacial magneticdisorder [51], varieties of exchange paths [70],directional distributions of pinning "elds due to thepolycrystalline interface [71] or interfacial struc-tural features [72,73]. These considerations areevidence of the growing recognition that detailedatomic scale magnetic and structural characteriza-tion of the FM}AFM interface is the key to under-standing exchange anisotropy phenomena.

2.2.2. Ni}MnThe search for higher ¹

Band a more corrosion-

resistant AFM has led to the characterization ofa number of other Mn-based alloys. The orderedFCT #-phase of Ni}Mn extends from &43 to&53 at%Mn [74]. The Mn atoms, with moments+3.8 l

B, and the Ni atoms, with virtually no mo-

ment ((0.2 lB), are alternately placed on (0 0 2)

planes [74,75]. The nearest-neighbor Mn atoms arecoupled AFM, with the next-nearest-neighborsFM. At temperatures '&1050 K, the #-phasetransforms to a disordered BCC phase, and themagnetic order disappears [74]. Lin et al. [76]compared H

Eand H

Cof Ni

50Mn

50and Fe

46Mn

54bilayers with Ni

81Fe

19. After annealing at 240 and

2553C for 240 and 255 h, respectively, the bilayerswith Ni

50Mn

50had *p values of 0.27 erg/cm2,

three times that of the Fe46

Mn54

biased "lms.¹

Bwas '4003C for the Fe

46Mn

54"lm, as com-

pared to &1503C for the Fe46

Mn54

biased "lm.Corrosion resistance was also superior for theNi

50Mn

50/Ni

81Fe

19bilayer. However, the anneal-

ing to produce the AFM FCT phase increasedH

Cto 47 Oe, as compared to 5 Oe for the

Fe46

Mn54

/Ni81

Fe19

bilayer.

2.2.3. Ir}MnIn the disordered FCC (c) phase from &10 to

&30 at% Mn, ¹N

increases from &600 to&750 K [77]. The average spins on each (0 0 2)plane are aligned parallel along the c-axis withalternating signs on neighboring (0 0 2) planes[77,78]. The average moments per atom are&2.5 l

Bup to &20 at% Mn, and drop to 0.8 l

Bat

&25.6 at% Mn [58]. Fuke et al. [79]. character-ized spin valves in which Ir

20Mn

80"lms were used

to bias Co90

Fe10"lms. H

Evaried inversely with the

Co90

Fe10

thickness, and *p was 0.19 erg/cm2 atroom temperature for the as-deposited couples, anddecreased to about 0.16 erg/cm2 after annealing at2803C for 5 min in an applied "eld. *p decreasedmonotonically with temperature, and ¹

Bwas

&2653C before and after the anneals. HC

for theas-deposited "lms was +100 Oe.

2.2.4. Pt}MnChemically ordered Pt}Mn alloys are AFM with

¹N

ranging from 485 K for 66 at% Mn to a max-imum value of 975 K at the equiatomic composi-tion, decreasing to 815 K at 41 at% Mn [80,81].Utilizing these high ¹

Nvalues requires achieving

the ordered structure in "lms. Farrow et al. [82]prepared a number of polycrystalline an epitaxialcouples of Mn

xPt

(1~x)with permalloy using a var-

iety of substrates and underlayers to encouragegrowth of an ordered structure. Their X-ray di!rac-tion data were generally consistent with an orderedstructure for "lms grown at 2003C. The best resultswere obtained on an MgO(0 0 1) substrate witha 18.6 nm Mn

56Pt

44"lm. *p was 0.032 erg/cm2 at

room temperature, and HC

was 19 Oe for the10.9 nm permalloy "lm. *p decreased monotoni-cally from 77 K, and extrapolated values from MRdata suggested a ¹

B'500 K. However, heating the

"lm to 1803C for the MR measurements decreased*p, possibly due to interdi!usion.


2.2.5. Rh}MnOrdered Mn

3Rh has a triangular spin arrange-

ment below its ¹N

of 850 K. Velosa et al. [83] haveinvestigated spin valves with Mn

78Rh

22"lms bias-

ing Co90

Fe10

. *p was +0.19 erg/cm2, and ¹B

was&2503C.

2.2.6. Other Mn-based AFM xlmsSeveral ternary AFM Mn-based alloys have been

examined. These include Pd}Pt}Mn [84,85] andCr}Mn}Pt [86]. A particularly comprehensivecomparison of the properties of FeMnRh, IrMn,RhMn, PdPtMn, NiMn, and CrPtMn has beenreported by Lederman [87].

3. Models and theories

3.1. Ideal interfaces

The "rst simple model of exchange anisotropyexamined the exchange coupling across an idealinterface as shown in Fig. 2. The FM and AFMlayers are both single crystalline and epitaxialacross an atomically smooth FM/AFM interface.AFM materials have no net moment. The AFMmonoxides are composed of atomic planes of fer-romagnetically oriented spins with anti-parallelalignment between adjacent planes. In Fig. 2, theinterfacial AFM spin plane is fully uncompensated.During the reversal of the FM magnetization inthis ideal model, the spins of the FM layer rotatecoherently, while the spins of the AFM layerremain "xed. The energy cost is equal to the inter-facial exchange energy. The phenomenological for-mula of the exchange "eld is

HE"

*pM

FMtFM

"

2J%9

SFM

)SAFM

a2MFM

tFM

, (1)

where *p is the interfacial exchange energy density,J%9

is the exchange parameter, SFM

and SAFM

are thespins of the interfacial atoms, and a is the cubiclattice parameter. In the Ni

xCo

(1~x)O system, an

atomically smooth S1 1 1T oriented single crystalshould result in a fully uncompensated interfacialspin plane as depicted in the ideal model. Therefore,

one may expect a FM layer coupled to a S1 1 1Toriented Ni

xCo

(1~x)O single crystal to exhibit an

exchange "eld magnitude as predicted by Eq. (1).Using reasonable parameters, one obtains values of*p&10 erg/cm2. However, as discussed above, theobserved exchange "elds for single- and polycrys-talline AFM "lms of all types are two-to-threeorders smaller. Clearly, this simple ideal modeldoes not realistically represent the FM/AFM inter-facial environment.

Phenomena such as interfacial contamination orroughness have been invoked to account for thereduction of interfacial coupling strength. Rough-ness in the form of interfacial atomic steps couldproduce neighboring antiparallel spins and therebyreduce the number of interfacial uncompensatedspins. Other experimental studies have raised otherquestions. If only the S1 1 1T spin planes are fullyuncompensated, one may expect that single crystalsof any other crystalline orientation would exhibitsmall or no exchange "eld due to a compensatedinterfacial spin plane. Polycrystalline "lms arecomposed of subunits or grains which possess adistribution of orientations, predominantly notS1 1 1T. Yet FM "lms coupled to polycrystallineAFM "lms often have higher exchange "elds thanFM "lms coupled to single crystal S1 1 1T "lms.Perhaps the uncompensated spins originate fromthe disordered regions within the grain boundaries.These are simply qualitative explanations and donot provide for quantitative analysis and compari-son with experimental observations. A model of theexchange bias mechanism must resolve the follow-ing discrepancies and questions:

1. What structural and magnetic parameters areresponsible for the drastic reduction of the inter-facial exchange energy density from the idealcase?

2. What are the origin and role of the interfacialuncompensated AFM spins?

3. How is the magnitude of the exchange "elddependent upon the AFM grain structure?

4. What determines the temperature dependence ofthe exchange "eld?

5. What are the roles of interfacial exchangeJ%9

and AFM magnetocrystalline anisotropyK

AFMin unidirectional anisotropy?


G A Basheed

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G A Basheed

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G A Basheed

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In the past decade, a number of models and the-ories have been proposed to provide qualitativeand quantitative descriptions of the exchange bias-ing mechanism.

3.2. Interfacial AFM domain wall

To explain the discrepancy between the exchange"eld value predicted by simple theory and experi-mental observations, Mauri et al. [88] proposeda mechanism that would e!ectively lower the inter-facial energy cost of reversing the FM layer withoutremoving the condition of strong interfacialFM/AFM coupling. They proposed the formationof a planar domain wall at the interface with thereversal of the FM orientation. The domain wallcould be either in the AFM or FM, wherever theenergy is lower. They examined the case where thedomain wall forms in the AFM side of the interface.With the magnetization reversal of the FM layer,the increase in interfacial exchange energy wouldbe equal to the energy per unit area of an AFM

domain wall 4JAAF

KAF

, where AAF

and KAF

arethe exchange sti!ness (&J

AF/a) where J

AFis the

AFM exchange integral parameter, and a is theAFM lattice parameter) and AFM magnetocrystal-line anisotropy, respectively. Thus, the modi"edexpression for the exchange "eld would be

HE"

2JAAF

KAF

MFM

tFM

. (2)

By spreading the exchange energy over a domain

wall width &pJAAF

KAF

instead of a single atomi-cally wide interface, the interfacial exchange energy

is reduced by a factor of pJAAF

KAF

/a, +100,which would provide the correct reduction to beconsistent with the observed values. Smith andCain [89] "tted the magnetization curves of per-malloy/TbCo bilayer "lms using a similar modelwith strong interfacial coupling.

Mauri et al. assume that: (i) an AFM domaincan form at the interface; (ii) the AFM layer isin"nitely thick (no restrictions for the AFM do-main wall formation due to thickness); and (iii) thespins within the FM rotate coherently (for the caseof the FM layer thickness less than the thickness ofa domain wall). They use a Hamiltonian that ac-

counts for AFM domain wall energy, interfacialexchange energy, FM anisotropy energy, anda magnetostatic energy term. Magnetization curveswere calculated by minimizing the energy with twofree parameters: a (which represents the angulardisplacement of the interfacial AFM spins from theAFM NeH el axis), and b (the angular displacement ofthe coherent FM spins from the easy-axis). TheAFM NeH el axis and the FM easy-axis are parallel.A numerical calculation over a range of interfacialexchange energies yields the following two limitingcases:

Strong interfacial coupling

NH%9"!2A

JAAF

KAF

MStFM

B, (3)

Weak interfacial coupling

NH%9"!A

J%9

MStFMB, (4)

where J%9

is the e!ective interfacial coupling energy,and t

FMand M

Sare the thickness and saturation

magnetization of the FM, respectively. In the caseof strong interfacial exchange coupling (J

%9<

JAAF

KAF

), H%9

saturates at energies far less thanthe fully uncompensated interfacial exchange coup-ling case due to the formation of an interfacialAFM domain wall. In the case of weak interfacial

exchange coupling (J%9;JA

AFK

AF), H

%9is limited

by the strength of the interfacial exchange couplingJ%9. The model o!ers no insight as to the origins of

the reduced interfacial coupling, nor does it addressthe origin of the coupling with compensated spinplanes. This model highlights the formation of anAFM planar domain wall in the limit of stronginterfacial exchange; however, most experimentalstudies indicate the presence of weak interfacialexchange. Thus, this model does not shed light onthe mechanism responsible for the reduced inter-facial exchange coupling energy density.

3.3. Random xeld model

Malozemo! rejects the assumption of an atomi-cally perfect uncompensated boundary exchange.


G A Basheed

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G A Basheed

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G A Basheed

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G A Basheed

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He proposed a random-"eld model [90}92] inwhich an interfacial AFM moment imbalance orig-inates from features such as roughness and struc-tural defects. Thus, the interfacial inhomogeneitiescreate localized sites of unidirectional interfacialenergy by virtue of the coupling of the net uncom-pensated moments with FM spins. For interfacialroughness that is random on the atomic scale, thelocal unidirectional interface energy p

lis also ran-

dom, i.e.

pl"$z

J

a2, (5)

where J is the interfacial exchange parameter, a iscubic lattice parameter, z is a number of orderunity. Random-"eld theory argues that a net aver-age non-zero interfacial energy will exist, parti-cularly when the average is taken over a smallnumber of sites. Statistically, the average p in an

area of ¸2 will decrease as p+(pl/JN) where

N"(¸2/a2) is the number of sites projected ontothe interface plane. Given the random "eld andassuming a single domain FM "lm, the AFM "lmwill divide into domain-like regions to minimize thenet random unidirectional anisotropy. UnlikeMauri et al.'s model, the AFM domain walls inMalezemo!'s model are normal to the interface.Initiation of the AFM domain pattern occurs as theFM/AFM bilayer is cooled through ¹

N.

Although expansion of the domain size ¸ wouldlower the random "eld energy, in-plane uniaxialanisotropy energy K in the AFM layer will limit thedomain size. Anisotropy energy con"nes the do-

main wall width to pJA/K ((¸), and creates anadditional surface energy term of the domain wall

4JAK (surface tension in bubble domain). Thebalance between exchange and anisotropy energy is

attained when ¸+pJA/K. Therefore, the averageinterfacial exchange energy density *p becomes

*p"4zJ

pa¸. (6)

Accordingly, the exchange "eld due to the inter-facial random-"eld energy density is

HE"

*p2M

FMtFM

"

2zJAK

p2MFM

tFM

(7)

using the equilibrium domain size expression for ¸.This equation is very similar to the strong inter-facial exchange case (Eq. (3)) of Mauri et al.'s planarinterfacial AFM domain wall model. Thus, quantit-atively, the random-"eld model also accounts forthe 10~2 reduction of the exchange "eld from theideal interface model case.

In addition to the reduction of the interfacialexchange energy, Malozemo!'s model attempts toexplain the following magnetic behavior associatedwith exchange anisotropy: (1) approximately linearfallo! (1!¹/¹

#3*5) of exchange "eld, (2) the mag-

netic training e!ect [9] (as the unwinding of do-main state and the annihilation of domains with"eld cycling), and (3) critical AFM thicknesses forexhibiting an exchange "eld. Malozemo! has triedto account for a number of the key experimentalobservations associated with exchange biasing.Malozemo!'s model is speci"cally formulated forsingle crystal AFM systems and does not clearlypropose how the model can be extended to poly-crystalline systems. The argument of a statisticalbasis for the density of uncompensated spins isintriguing but not explicitly convincing.

3.4. &Spin-yop' perpendicular interfacial coupling

The &spin-#op' model introduced by Koon [93]presents a novel solution to a particular issue ofexchange biasing. On the basis of his micromag-netic numerical calculations, Koon proposed theexistence and stability of unidirectional anisotropyin thin "lms with a fully compensated AFM inter-face. His calculations indicate the stability of inter-facial exchange coupling with a perpendicularorientation between the FM and AFM axes direc-tions. He refers to the perpendicular interfacialcoupling as &spin-#op' coupling. One limitation ofKoon's model is that he examines a very speci"csystem. To observe perpendicular interfacial coup-ling, his model speci"es the structure and orienta-tion of the AFM layer, and the relative orientationbetween the AFM and FM layer. His results aresuggestive but di$cult to apply to other systems.The model utilizes a single-crystal body centeredtetragonal (BCT) AFM structure as shown inFig. 5a. The BCT structure can be oriented to havea fully uncompensated interfacial spin plane (1 0 0)


Fig. 5. (a) Magnetic structure of a S1 1 0T oriented AFM bodycentered tetragonal crystal. The exchange bonds are representedby the dashed lines. (b) Lowest energy spin con"guration nearthe interface plane. The interfacial AFM plane (L15) is fullycompensated, and the interfacial FM plane (F16) is orientedperpendicular (903 coupling). The angles are approximately toscale. From Ref. [93].

or a fully compensated interfacial spin plane (1 1 0)(shown in Fig. 5a). He included uniaxial anisotropyin the AFM crystal along the (0 0 1) axis, and theFM layer was modeled with no intrinsic anisotropy.

Koon applied his model to two di!erent cases ofthe AFM interfacial spin plane: (1) a fully compen-sated interface and (2) a fully uncompensated inter-face. For both cases, he calculated the interfacialenergy density as a function of the angle betweenthe FM spins and the NeH el axis of the AFM spins.The fully uncompensated interface gives the ex-pected results of collinear coupling, a minimum ath"03. However, the fully compensated interfacegives the surprising result of an energy minimum ath"903 indicating perpendicular interfacial coup-ling between the FM and AFM spins. Fig. 5b showsthe spins con"guration near the interface plane,illustrating the perpendicular orientation of theFM and AFM axes.

In his published work, Koon hypothesizes thatroughness would reduce frustration and reduce bi-asing from the fully compensated case. However,his unpublished work suggested that the introduc-tion of roughness into his model resulted in thetransition from perpendicular to collinear coupling.The transition may be attributed to the increasingdensity of uncompensated interfacial AFM spins.The issue of perpendicular interfacial coupling inFM/AFM bilayers may be more relevant in smoothsingle crystals than in polycrystalline "lms.

The recent work by Schulthess and Butler [94]yielded "ndings contrary to Koon's calculations.They adopted Koon's spin con"gurations but im-plemented a classical micromagnetic approach us-ing the Landau}Lifshitz equation of motion withthe Gilbert}Kelley form for a damping term. Theirwork yielded the interfacial spin-#opped state sim-ilar to Koon's, but had contrary conclusions withrespect to exchange biasing. Their calculations in-dicated enhanced uniaxial anisotropy or enhancedcoercivity, but not a shifted magnetization curve.The di!erence is attributed to an additional degreeof freedom which creates a lower energy barrier.However, the introduction of interfacial defectsshifts the energy minima of the two spin-#oppedstates. The asymmetry in the energy minima resultsin the observation of an exchange bias. They notedthat the unidirectional shift results from the coup-ling of the FM to the uncompensated defects on theAFM interface, and spin-#op coupling is not a re-quirement for observing exchange bias.

3.5. Uncompensated interfacial AFM spins

Meiklejohn and Bean originally suggested thatunidirectional exchange anisotropy was a conse-quence of the presence of interfacial uncompen-sated AFM spins. The experimental correlationbetween the interfacial uncompensated CoO spinsand the exchange "eld in polycrystalline CoO/per-malloy bilayer "lms was only recently demon-strated by Takano et al. [34,35]. They measured theuncompensated spins on the surfaces of antifer-romagnetic CoO "lms as a thermoremanent mag-netization (TRM) after "eld-cooling a series ofCoO/MgO multilayers from ¹'¹

N. The temper-

ature dependence of the TRM was similar to the


Fig. 6. Schematic of interface cross section. Film normal is n( , p( is the normal to the parallel spin plane (1 1 1) of the AFM, and e( is theAFM spin axis (in this case N

3084"4). From Refs. [34,35].

temperature dependence of the sublattice magneti-zation for bulk CoO materials as determined byneutron di!raction [95]. These measurementsshowed that the spins responsible for this uncom-pensated AFM moment are interfacial and consti-tute &1% of the spins in a monatomic layer ofCoO. This low density is consistent with the lowexchange "elds observed compared to the valuespredicted by the ideal interface model (see Eq. (1)).The uncompensated AFM TRM also has the sametemperature dependence as the exchange "eld ofNi

81Fe

19/CoO bilayers after "eld-cooling. Thus,

the uncompensated interfacial AFM spins appearto be the spins responsible for unidirectional an-isotropy. Takano et al. determined that a linearrelationship exists between the strength of the ex-change "eld and the inverse of the CoO crystallitediameter, i.e., H

EJ¸~1, where ¸ is the grain dia-

meter. This suggests a structural origin for thedensity of uncompensated spins.

The magnitude and the temperature dependenceof the exchange "eld in FM/CoO bilayers correlatewith the density of uncompensated interfacial CoOspins, but what are the structural origins of theuncompensated spins in polycrystalline AFM"lms? To answer this question, Takano et al. cal-culated the density of interfacial uncompensatedspins as a function of grain size, orientation, andinterfacial roughness of polycrystalline AFM "lms.Each CoO crystallite was assumed to be a singleAFM domain. Fig. 6 is a view of the interfacialcross section of an AFM crystal showing that theorientation of the AFM determines the periodicity

with which the (1 1 1) ferromagnetic spin planesintercept the interface. Fig. 7a is a plan view of thesame AFM crystal. The crystalline orientation isre#ected in the periodic alternating pattern of fourrows. In Fig. 7a, an elliptical sampling region simu-lating a grain with a major axis length ¸ has beensuperimposed onto the spin map. The number ofuncompensated spins S*NT for a model crystallitewas computed by simply adding the total numberof spins in each direction contained within theboundaries of the model grain. The fundamentalorigin of uncompensated AFM moment is scale.Although the large spin map may represent com-pensated spin regions, one observes small densitiesof uncompensated spins when sampling small areaswithin the spin map. Thus, one will observe anexchange bias with polycrystalline AFM "lmsregardless of whether the preferred orientation sug-gests that the interfacial plane is completely com-pensated. Interfacial roughness was incorporatedonto the spin maps by superimposing elliptical&islands' of monatomic thickness on the spinmap. The e!ect of adding one atomic layer is toreverse the direction of the spin at each site coveredby the island, since successive layers of CoO spinshave opposite direction (see Fig. 7b). Takano et al.created a series of large spin maps several timeslarger than the model grain sizes to be sampled.Fig. 8 is an example of one of the large spin mapscontaining the topographical roughness features.Statistical averages were obtained from sampling106 model crystallites by varying the position, ori-entation of the major axis, and aspect ratio of the


Fig. 7. (a) Topographical representation of the interfacial plane.Periodic pattern of N

3084"4 (as in Fig. 6) with a sample region

representing a model crystallite. (b) Topographical representa-tion of the interfacial plane. Elliptical &islands' of monatomiclayer thickness were superimposed on the spin map to simulateroughness. Note that adding one atomic layer reverses thedirection of the underlying spin. From Refs. [34,35].

Fig. 8. Topographical map containing overlapping &islands'.The islands have a feature diameter of 20 lattice parameters andcoverage equal to the total area of the map. The legend corre-lates the di!erent shades of gray with the height of interfacialelevation above the base spin pattern [see Fig. 7a]. From Refs.[34,35].

model crystallite. Two primary results of these cal-culations are: (1) a perfectly regular interface with-out any roughness features results in S*NTJ¸0.5;(2) the addition of roughness results inS*NTJ¸0.90F1.04. Since the exchange "eld is pro-portional to S*NT/¸2, the rough case givesH

EJ¸~1, in agreement with the experimental re-

sults. Using realistic and experimental values, theobserved exchange "eld for a 10 nm CoO biasing"lm was consistent with interfacial roughness ofonly a few &extra' atomic steps across the face ofeach crystallite. Thus, the model correctly predictsthe inverse dependence of the uncompensated spinson grain size and the correct magnitude of H

E. The

model indicates that the origins of the uncompen-sated AFM interfacial moment are (i) the dimen-sions of the AFM grain boundaries and (ii) thepresence of interfacial roughness features.

The combination of the experimental results andthe model is very comprehensive in explainingmany of the issues and questions concerning themechanism behind exchange biasing. The origin ofthe exchange biasing mechanism is indeed the un-compensated interfacial AFM spins. The magni-tude and temperature dependence of the exchange"eld can be explained from the measurementsof the magnetic properties of the uncompensatedAFM spins. The model has demonstrated thestructural origins of the uncompensated AFMmoment in polycrystalline "lms. Neither the ex-perimental results nor the model shed any lighton the type of interfacial coupling, i.e. collinear


versus perpendicular coupling. CoO has very highmagnetocrystalline anisotropy which results ina direct correlation of the uncompensated momentand the exchange "eld. Other AFM materials withlower anisotropy, such as NiO, do not exhibit thiscorrelation due to complications not included inthis model. Future models can attempt to modelthe complex behavior for AFM systems with lowbulk or surface anisotropy.

4. Concluding comments

Using the rather demanding criterion of majortechnological application, it is clear that substantialprogress has been made in elucidating some quali-tative details concerning the phenomenon of ex-change anisotropy. However, in common withmost other magnetic phenomena in which surfaceand/or interfacial properties are important, thereexists no basic, generally applicable, predictive the-ory/model. The reason for this state of our know-ledge in exchange anisotropy is that the essentialbehavior depends critically on the atomic-levelchemical and spin structure at a buried interface,and the tools to uncover this type of information* e.g., atomic level chemical and spin-selectivephoto-emission, MoK ssbauer spectroscopy, neutrondi!raction, chemically resolved TEM imaging* are just beginning to be applied to this problem.Even if this atomic level information becomes avail-able, it is likely that the interfacial chemical andspin structures are too complex for ab initiomodeling.

A more promising view is that considerable pro-gress has been achieved. The interfacial complexityhas been recognized as the major factor and isbeing investigated. The hitherto puzzling low *phas been convincingly explained in at least one caseas arising from the low density of the uncompen-sated interfacial AFM spins. Hopefully, this willturn out to be a general conclusion. This is just oneof several explanations of exchange anisotropy phe-nomenon proposed by Meiklejohn and Bean, andby NeH el, that have been made more quantitative orhave been reinforced by experiment. Other exam-ples are the signi"cance of the AFM magnetocrys-talline anisotropy as compared to the interfacial

exchange interaction, and the various viscosity ef-fects. This signi"cant progress, the increasing avail-ability of methods for examining buried interfaces,and the technological demand for higher H

Eand

¹B, are probably reason enough to be optimistic

about achieving a continually better understandingof this fascinating phenomenon.

Acknowledgements

The preparation of this paper was partially sup-ported by the NSF.

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