Phase transitions in ferro-antiferromagnetic bilayers with a stepped interface

0.1 MB·English

by  D. P. Landau

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 [phone], 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