On the exchange bias in single and polycrystalline ferro/antiferromagnetic bilayersZhanjie Li and Shufeng Zhang Citation: Journal of Applied Physics 89, 7272 (2001); doi: 10.1063/1.1358830 View online: http://dx.doi.org/10.1063/1.1358830 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/89/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Influence of magnetic anisotropy on hysteresis behavior in the two-spin model of a ferro/antiferromagnet bilayerwith exchange bias Low Temp. Phys. 38, 937 (2012); 10.1063/1.4758774 Magnetization depth dependence in exchange biased thin films Appl. Phys. Lett. 89, 072504 (2006); 10.1063/1.2336742 Magnetic hysteresis loop tuning in antiferromagnetically coupled bilayer structures Appl. Phys. Lett. 85, 1571 (2004); 10.1063/1.1787161 Metastable antiferromagnetic domain configurations in exchange biased bilayers J. Appl. Phys. 93, 8606 (2003); 10.1063/1.1557792 Rotational hysteresis of torque curves in polycrystalline ferro/antiferromagnetic systems J. Appl. Phys. 89, 7546 (2001); 10.1063/1.1358833

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On the exchange bias in single and polycrystalline ferro Õantiferromagneticbilayers

Zhanjie Li and Shufeng Zhanga)

Department of Physics and Astronomy, University of Missouri-Columbia, Columbia, Missouri 65211

By incorporating a random interfacial exchange interaction into the Landau–Lifshitz–Gilbertequation, a unified picture of exchange bias for single crystals, textured crystals, twin structures, andpolycrystals of antiferromagnets is presented. It is found that the lateral interaction in theantiferromagnet is a key element governing the exchange bias and magnetization reversal of theferromagnet. ©2001 American Institute of Physics.@DOI: 10.1063/1.1358830#

In modeling exchange bias of a ferromagnetic/antiferromagnetic~F/AF! bilayer, one has to necessarily as-sume the antiferromagnet with certain crystal and magneticstructures, for example, one usually assumes either a poly-crystalline AF layer with an average domain sizeD1,2 or asingle crystal structure with compensated/uncompensated in-terface magnetic configurations.3–5 Aside from the abovetwo cases, there are textured oriented crystal structures witha preferred anisotropic direction and a single crystal twinstructure6 separated by twin boundaries. While most of thesefilms show a shifted hysteresis and enhanced coercivity, themodeling of the magnetic properties seems quite different. Inthis article, we present a unified picture to understand ex-change bias in all these realizations.

We start by constructing a macroscopic magnetic Hamil-tonian. The bilayer film is laterally divided into meshes. Fol-lowing the standard micromagnetic approach each mesh isassumed in a single domain state. For a polycrystalline AFfilm, we take the mesh size same as the grain size~the an-isotropic direction of each grain is random!. This choice isvalid as long as the grain size is less than the characteristicmagnetic length in AF and F layers, e.g., the domain wallwidth. In our calculations below, we choose the grain sizeless than 100 Å, and the anisotropic constant of the AF layeris small so that the domain wall width of the AF layer islarger than the grain size. For the single crystal, we choosethe same mesh size as the polyscrystal film in order to obtainquantitative comparison between the crystal structure and ex-change bias. There are two essential differences betweenpoly and single crystal films. The former has random aniso-tropic axis among grains and intergrain interaction is weak.1

The latter has fixed anisotropic directions throughout the filmand the interaction between meshes are strong. We model theinteraction between neighboring meshes for different crystalstructures by a single parameterJmesh. For the polycrystalfilm, we assume there is no magnetic interaction betweengrains,1 i.e., Jmesh50. For a single crystal AF layer, the ex-change interaction between meshes isJmesh5JAF /D2 per sitewhereJAF is the exchange constant of the AF film andD isthe mesh size. For the textured AF layer, we again setJmesh50 but the anisotropic direction of each mesh is alonga fixed direction. For a twin structure, the neighboring

meshes have two mutually perpendicular anisotropic axisand they interact byJmesh5gJAF /D2 whereg characterizesexchange coupling at the twin boundary. With these differentinteraction parameters and anisotropic directions of themeshes, we develop a unified picture to understand exchangebias of the different AF films and to access what the keycomponents of exchange bias are.

The rest of the terms in our Hamiltonian includes: aferromagnetic exchange interaction between the neighboringmeshes, a magnetostatic energy, and a random interaction ofthe spins at the interface of the F and AF layer. Since we areinterested in F and AF exchange coupling induced exchangeshift and coercivity, we take the magnetostatic energy asimple 4pMz

2 where Mz is the out-of-plane component ofthe magnetization of the F layer and neglect the anisotropyof the F layer. We refer the details of the these terms toRef. 7.

First, we examine the postulation made by Malozemoff.8

By simply considering the interfacial random energy and theexchange energy of the AF film Malozemoff argued that alateral domain in the AF layer should be formed and thesedomains are responsible for the exchange bias. The criticalassumption in this argument is that these random field in-duced AF domains are frozen upon the reversal of the Flayer. In Fig. 1, we show the calculated AF lateral domainstructure for the single crystal~two left panels! and polycrys-tal ~two right panels! films at the large external fields whichsaturates the magnetization of the F layer in the field coolingdirection ~upper panels! and in the reverse field direction~lower panels!. For the single crystal AF layer, the domainformation is driven by the competition of the exchange en-ergy between meshes of the AF layer and the random energy,see upper left of Fig. 1. Indeed the interfacial interactionbreaks the AF layer into lateral domains; this agrees withMalozemoff. However, these domains in single crystal AFlayer are not stable upon the reversal of the magnetization ofthe F layer. Rather than the random field contributes to thehysteresis shift as Malozemoff postulated, it in fact makesthe domains of the AF layer reversed during the reversal ofthe F layer. This is clearly seen by comparing two left panelsof Fig. 1 with two opposite directions of the F layer. There-fore, the AF lateral domains are not frozen during the hys-teresis cycle of the F layer and we conclude that theserandom-field induced domains are not responsible for thea!Electronic mail: zhangshu@missouri.edu

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hysteresis shift of F/AF bilayers. The reason for the switch ofthe AF domains lies on the fact that single crystal AF meshesare strongly coupled and the reversal of the random fieldtriggers reversal of the AF domains. Thus, the lateral domainformation alone cannot explain the hysteresis loop shift. Forthe polycrystal film, the domain is primarily set by each in-dividual grain since there is no interaction between grains ormeshes. The reversal of the F magnetization will not lead tothe complete reversal of the magnetization of AF grains.Comparing the two right panels of Fig. 1, we clearly see thatsome AF grains switch when the local random field exceedsthe anisotropy of the grains and some grains do not switchwhen the random fields are smaller. Since each grain is notexchange coupled, they respond to the random field locallyand independently. Those pinned AF domains contribute tothe hysteresis loop shift.

Since most of experimental AF layers, CoO, possess thecubic symmetry, we wish to examine whether our conclusionof the zero hysteresis loop shift for the single crystal AFlayer remains valid. In the two left panels of Fig. 2, we showthe domain structure of the AF layer with cubic symmetry,i.e., the anisotropic easy axis is at 0° and 90°. In this case,the magnetization direction of the AF layer is almost perpen-dicular to the F layers, thus it has no lateral domains whenthe F layer is saturated. This perpendicular alignment be-tween the field cool direction and the AF moment can be

understood the following way: the random interaction be-tween spins at the interface of the AF and F layer is similarto the compensated F/AF interface structure4 and the mini-mum energy occurs at the spin-flop state of the AF layer, i.e.,perpendicular alignments. This is only true, of course, whenthe AF meshes are strongly coupled as in the case of thesingle crystal AF layer. By comparing the AF pattern for theF aligned in the positive and the negative directions in Fig. 2,it becomes obvious that there is no hysteresis loop shift forthe AF single crystal with a cubic symmetry.

The question arises: what is the cause for the observedhysteresis loop shift in experimental single crystal AFfilms?9 To address this issue we need to distinguish a truesingle crystal where the interaction between the meshes isJmesh5JAF /D2 ~as we modeled in Fig. 1! with that of thetextured ‘‘single crystal’’ where the anisotropic direction isoriented mostly in a given direction but the coupling betweenthe meshes behave like a polycrystal, i.e., there is very smallcoupling between AF meshes. These two types of singlecrystals would be almost identical when one carries the ex-periment of the structure characterization via x-ray diffrac-tion or neutron diffraction. However, they are quite differentin contributing to the exchange bias. In the two small panelsof Fig. 2, we show the AF magnetization pattern for a cubictextured AF layer by turning off the interaction betweenmeshes. In this case, since each mesh is independent, somemeshes will orient parallel to the random field. The domainsof these meshes will not switch during the reversal of therandom field, i.e., part of the AF domains are frozen. A siz-

FIG. 1. Interface magnetization pattern~one sublattice! of the antiferromag-netic layer for a single crystal~two left panels! whose anisotropic directionis along the external field and for a polycrystal~two right panels! with grainsizeD580 Å where the easy axis of each grain is also shown by a dottedline. The upper two panels are for the F layer magnetization saturated in theright direction @Hext54000~Oe!# and the lower two panels are forHext524000~Oe!. The axis of units represents the positions of the meshes takenfrom 30330 meshes. The parameters are similar to those in Ref. 8, i.e.,tF

580 Å, tAF530 ML, JF516 meV, JAF54 meV, KAF50.005 meV, andJs

is a random number between22 and 2 meV.

FIG. 2. Interface magnetization~one sublattice! of the antiferromagneticlayer for a single crystal with the cubic symmetry~two left panels! and fora textured single crystal with anisotropic axis along the directions at 0° and90° with respect to the external fields~two right panels!. Note the texturedfilm establishes the hysteresis loop shift as labeled. The parameters are thesame as in Fig. 1.

7273J. Appl. Phys., Vol. 89, No. 11, 1 June 2001 Z. Li and S. Zhang

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able hysteresis shift is thus established, in similitude with thepolycrystalline AF layer.

Another class of AF layers is a twin structure where theanisotropic axis of the neighboring twins is perpendicular toeach other and the twins are separated by twin boundaries. Ithas been estimated, for example, for FeF2, that the size of thetwin is of the order of 80 Å.10 Again, we found that there isno hysteresis shift if we assume that the neighboring twinsare strongly coupled (g51), and one obtains large shiftswhen one turns off the interaction at the twin boundaries(g50). In Fig. 3, we show the hysteresis loop of the bilayerwithout the interaction between the twin boundaries. Withthese reasonable parameters for FeF2, we reproduced thegross features of the experimental hysteresis loop for twodifferent twin orientations.

Finally, we briefly address the coercive behavior of thesestructures. All the structures we have modeled, perfect and‘‘textured’’ single crystals, polycrystals, and twin structures,show enhanced coercivity. The enhanced coercivity comesfrom two sources: one is from the spin-flop type reversalmode as pointed out earlier,2,5 the other comes from the spa-tial variation of the random field such that the different do-mains of the ferromagnetic layer during hysteresis cycle re-

verse at different external fields.8 These two mechanisms areoften entangled together and they depend on the detail of thedomain structures of the ferromagnetic layers induced by theinterface coupling between F and AF layers.

In conclusion, we have demonstrated that ‘‘ideal’’ singlecrystal AF layers are unable to produce a unidirectional an-isotropy of the F layer due to strong exchange couplingwithin the AF layers. To observe the exchange bias of thesingle crystal AF layer, one either restricts the interface in-teraction extremely small in an uncompensated AFsurface,3,11 or involves ‘‘textured’’ or ‘‘imperfect’’ singlecrystals, i.e., the exchange coupling in the AF layer has to bereduced by ‘‘grain boundary’’ or ‘‘twin boundary.’’ The firstproposition seems contradictory with many other properties,for example, the enhanced coercivity in the single crystallayers. This indicates that the interaction at F/AF interface isstrong but contains some degree of randomness, which is themodel we have based on. Thus, we conclude that the termi-nation of the interaction in the AF layer is the key to under-stand exchange bias in this random field model. We expectthat, up until now, experimental systems, whether they arepolycrystalline, or textured single crystals and twin struc-tures, have a necessary ingredient to reduce AF coupling inthe AF films.

This work is partially supported by Defense AdvancedResearch Projects Agency~DARPA-ONR No. N00014-96-1-1207! and NSF~No. DMR-0076171!.

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9C. H. Lai, H. Matsuyama, R. L. White, and T. C. Anthony, IEEE Trans.Magn. 31, 2609 ~1995!; C. H. Lai, H. Matsuyama, R. L. White, T. C.Anthony, and G. G. Bush, J. Appl. Phys.78, 6389~1996!; R. P. Michel,A. Chaiken, C. T. Wang, and L. E. Johnson, Phys. Rev. B58, 8566~1998!.

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FIG. 3. The hysteresis loops of twin structures for two different perpendicu-larly oriented twins. Each twin size is assumed 80 Å. The closed circlesrepresent the easy axis of the twin along645° with respect to the externalfield. The open circles are those twins along the directions at 0° and 90°with respect to the external field. The parameters are indicated in the figure.Both exchange shift and coercivity are different for the two cases as indi-cated in the figure.

7274 J. Appl. Phys., Vol. 89, No. 11, 1 June 2001 Z. Li and S. Zhang

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