4 0 0 2 n a J Phasetransitionsinferro-antiferromagneticbilayerswithastepped 2 interface ] h c D.P.Landaua,∗,Shan-Ho Tsaia,c,Thomas C. Schulthessb e m aCenterforSimulational Physics, Universityof Georgia, Athens, GA 30602 bCenterforComputational Sciencesand Computer Science& MathematicsDivision, Oak RidgeNational Laboratory, - Oak Ridge, TN 37831 at cEnterprise ITServices, Universityof Georgia, Athens, GA 30602 t s . t a m Abstract - d We have studied magnetic ordering in ferro/antiferromagnetic (F/AF) bilayers using Monte Carlo simulations n of classical Heisenberg spins. For both flat and stepped interfaces we observed order in the AF above the N´eel o temperature,withtheAFspinsaligningcollinearlywiththeFmoments.Inthecaseofthesteppedinterfacethere c is atransition from collinear toperpendicularalignment of theFand AFspinsat alower temperature. [ 1 v Keywords: Ferromagnetic-antiferromagnetic bilayer, classicalspin, anisotropy, Monte Carlosimulation 4 PACS: 75.70.-i,75.10.Hk, 75.40.Mg 1 0 1 Magnetic properties of ferro/antiferromagnetic causeofthebccstructure)layersofclassicalspins 0 4 (F/AF)bilayerscanbeverydifferentfromthoseof |Sr|=1,whichinteractviathe Hamiltonian 0 freeFandAFfilms.Thesecoupledsystemsexhibit t/ a shift in the hysteresis loop (exchange bias) and H=−JFXSr·Sr′ −KFX(Srz)2− a larger coercivity than the free F film [1]. Other hr,r′i∈F r∈F m effects of the F/AF coupling include the order in d- the AF observed above the N´eel temperature[2] −JAX Sr·Sr′−KAX(Sry)2−JI X Sr·Sr′ n and the perpendicular orientation of the F with hr,r′i∈AF r∈AF hr,r′i∈F/AF o theAFmoments[3,4].Understandingtheseeffects where hr,r′i denotes nearest-neighbor pairs of c and the nature of the F/AF interfaces remains a v: challenge. spins coupled with exchange interactions JF = 5J > 0 in the F film, J = −J < 0 in the AF i In this paper we use Monte Carlo simulations A X film,andJ =−J attheF/AFinterface.Spinsin to study the effect of the interfacialexchange and I r the AF film have a uniaxial single-site anisotropy a roughnessonthemagneticorderinginF/AFbilay- K = J, whose easy axis is along the y axis. The ers. The work is motivated by recent experiments A demagnetizingfield onthe F film is modeledwith forFe3O4/CoOmultilayers[2].Weconsideraferro- a hard-axis (K = −0.5J) along the z direction, magnetic(F)filmcoupledtoanantiferromagnetic F which is perpendicular to the F/AF interfacial (AF) film where the lattice is coherent across the plane. No external magnetic field is applied. We F/AFinterface.Eachfilmisabcclattice,withlin- use periodic boundary conditions along the x and earsizesL =L =L≤96and12staggered(be- x y y directions and free boundary conditions along ∗ the z direction. We model flat interfaces that Corresponding author. Tel +1 (706) 542 2908, Fax +1 are fully uncompensated as well as uniformily (706) 5422492 Email address: [email protected] (D.P.Landau). stepped ones that are compensated on average. Preprintsubmitted toElsevier Science 2February2008 The stepped interface has 6, L, and one spin per observedeitherbeloworaboveT resultfromthe N terracein the x,y,andz directions,respectively. exchangecouplingto the AF film. The F and AF order parameters are the uni- Fig.2 shows m versus T for different L for s form (m) and staggered (m ) magnetization per stepped and flat interfaces. In the former case s spin, respectively[6]. m and m denote the two the decay to zero of m at T ≈ 2.2J/k becomes x y s B components ofm inthe interfacialplane.We per- sharper for larger L (see the inset), suggesting an formMonteCarlosimulationswithMetropolisal- AFphasetransitionatT .Incontrast,withaflat N gorithmatfixedtemperatureT.Typicallywedis- (uncompensated) interface there is no finite-size card 3 × 105 Monte Carlo Steps/site (MCS) for dependencyofm nearT ,suggestingtheabsence s N thermalization and then use about 2×105 MCS ofanAFphase transitionthere. for averages. Whenever not shown, error bars in 1.0 the figuresaresmallerthanthe symbolsizes. The T-dependenceofm showninFigs.1(a)and ms0.8 1(b) plus finite-size analysis (not shown) indicate n, a1n2-aFtoomrdice-rlianygertrAanFsifitlimonuantdTercg≈oes9.a3Jp/hkaBse.tArafnrseie- netizatio 0.6 L 0.1 g tionattheN´eeltemperature[5]TN ≈2.2J/kB.For d ma 0.4 2448}stepped gere 9468} 0 2.2 2.4 2.6 1.0 ag 0.2 60 flat (a) stepped interface st m 0.0 m 0 1 2 3 4 0.5 ms kBT/J x m y Fig.2.Staggered magnetization as afunctionoftempera- tureforstepped andflat interfaces. 0.0 Research partially supported by NSF grant 1.0 DMR-0094422 and DOE-OS/ASCR through the (b) flat interface Laboratory Technology Research Program under m m contract DE-AC05-00OR22725with UT-Battelle, s m 0.5 x LLC. Simulations performed on the IBM SP at m y NERSCandORNL. 0.0 0 2 4 6 8 10 12 k T/J B References Fig.1.Temperaturedependenceofm,ms,mx,andmy(see text) forL=60, with(a) stepped and (b) flatinterface. [1] Seee.g.,J.Nogu´esandI.K.Schuller,J.Magn.Magn. Mater.192(1999)203;A.E.BerkowitzandK.Takano, ibid. 200 (1999) 552; M. Kiwi, ibid. 234 (2001) 584; bothflatandsteppedinterfaces,thespinsontheF R.L.Stamps, J.Phys. D 33(2000) R247. film orient predominantly in a direction collinear [2] P.J.vanderZaag,Y.Ijiri,J.A.Borchers,L.F.Feiner, withtheeasyaxisoftheAFathighT (seeFig.1), R.M. Wolf, J.M. Gaines, R.W. Erwin, and M.A. evenabove T . This is anindication that there is Verheijen, Phys. Rev. Lett. 84(2000) 6102. N stillorderintheAFaboveTN duetothecoupling [3] N.C. Koon, Phys. Rev. Lett. 78 (1997) 4865; T.C. to the ferromagnet.As T is loweredin the case of Schulthess and W.H.Butler, ibid. 81(1998) 4516. thesteppedinterfacetheFspinsswitchtoorientin [4] T.J.MoranandI.K.Schuller,J.Appl.Phys.79(1996) a direction that is perpendicular to the AF spins. 5109; Y. Ijiri, J.A. Borchers, R.W. Erwin, S.-H. Lee, Our results suggest that the onset of this perpen- P.J. van der Zaag, and R.M. Wolf, Phys. Rev. Lett. 80 (1998) 608; T.J. Moran, J. Nogu´es, D. Lederman, dicular orientation is very sharp and it occurs at and I.K.Schuller, Appl.Phys. Lett. 72(1998) 617. a temperature below T . The z-components ofm N [5] S.-H. Tsai, D.P. Landau, T.C. Schulthess, J. Appl. and ms are very small for all T. In the absence of Phys. 91(2002) 6884. the AF film, spins on the F film have global rota- [6] S.-H. Tsai, D.P. Landau, T.C. Schulthess, J. Appl. tionsymmetryinthex-yplane,whichistheireasy Phys. 93(2003) 8612. plane.The preferentialorientationsofthe Fspins 2