Effect of interfacial coupling on the magnetic ordering in ferro-antiferromagnetic bilayers

4 Pages·0.12 MB·English

by  Shan-Ho Tsai

1
Effect of interfacial coupling on the magnetic ordering in ferro-antiferromagnetic
bilayers
3 Shan-Ho Tsaia,c, D. P. Landaua, and Thomas C. Schulthessb
0 a Center for Simulational Physics, University of Georgia, Athens, GA 30602
0 b Center for Computational Sciences and Computer Science & Mathematics Division,
2 Oak Ridge National Laboratory, Oak Ridge TN 37831
c Enterprise Information Technology Services, University of Georgia, Athens, GA 30602
n
a
Monte Carlo simulations have been used to study magnetic ordering in coupled anisotropic
J
ferro/antiferromagnetic (FM/AFM) films of classical Heisenberg spins. We consider films with
7
flat interfaces that are fully uncompensated as well as rough interfaces that are compensated on
2
average. Forboth typesof interfaces above the“N´eel temperature”we observed order in theAFM

with the AFM spins aligning collinearly with the FM moments. In the case of rough interfaces
]
h thereisatransitionfromcollineartoperpendicularalignmentoftheFMandAFMspinsatalower
c temperature.
e
m
- Ferromagnetic/antiferromagnetic (FM/AFM) bilayers −JA X Sr·Sr′ −KA X (Sry)2
at have been shown to exhibit a unidirectional shift in the hr,r′i∈AFM r∈AFM
t hysteresisloop(exchangebias)andasignificantincrease
.s of the coercivity [1]. Magnetic properties of FM/AFM −JI X Sr·Sr′ (1)
at bilayers can also be drastically different from those of hr,r′i∈FM/AFM
m
free FM and AFM films. For example, even though in where hr,r′idenotes nearest-neighborpairsof spins cou-
- most exchange bias systems the blocking temperature is
d pled with exchange interactions JF > 0 in the FM film,
lower than the N´eeltemperature of the antiferromagnet,
n JA <0 in the AFM film, and JI at the FM/AFM inter-
orderintheAFMhasbeenobservedabovetheN´eeltem-
o face. Spins in the AFM film have a uniaxial single-site
c perature due to the coupling to the ferromagnet [2]. anisotropy K > 0, whose easy axis is along the y axis.
[ A
Earliertheoreticalwork [3, 4]has shownthat for com- The demagnetizing field on the FM film is modeled with

1 pensated interfacial exchange (i.e. zero net exchange in- ahard-axis(K <0)alongthez direction,whichisper-
F
v teraction across the FM/AFM interface) the FM aligns pendicular to the FM/AFM interfacial plane. No exter-
9
perpendicular to the AFM easy axis. Although similar nal magnetic field is applied. We use periodic boundary
2
5 perpendicularorientationhasbeenobservedinnumerous conditionsalongthexandydirectionsandfreeboundary
1 FM/AFM systems [5], understanding the nature of the conditions along the z direction.
0 interfacial coupling and roughness in FM/AFM bilayers We consider interaction and anisotropy parameters
3 remains a challenge. J = 5J > 0, J = −J, J = −J, K = J, and
F A I A
0
/ InthispaperweuseMonteCarlosimulationstostudy KF =−0.5J. Wemodelflatinterfacesaswellas“rough”
at the effect of interfacial exchange interaction and rough- oneswhicharecomprisedofuniformlyspacedsteps,with
m ness on transitions from ordered to disordered states in 6,L,andonespinperterraceinthex,y,andzdirections,
- FM/AFM bilayers. The work is motivated by recent ex- respectively. The terrace sizes along the x and z direc-
d periments of Ijiri et. al. [6], which show for CoO/Fe3O4 tions are kept fixed for the different film cross sections
n multilayers,thatthetransitiontoperpendicularordering used. For both types of interfaces the exchange coupling
o
c takes place at temperatures considerably lower than the across the interface is uniform (JI =−J); therefore, the
: FM and AFM ordering temperatures. flat interfaces are fully uncompensated while the rough
v
ones are compensated on average.
i The model studied here consists of a ferromagnetic
X The FM and AFM order parameters are the uni-
(FM) film coupled to an underlying antiferromagnetic
r formand staggeredmagnetizationper spin, respectively.
a (FAMF/MA)FMfilmintewrhfaecree. Tthheeslatrtuticcteuriesocfothheerfienlmtsaicsraosbsodthye- These are defined as m = |PrSr|/NF and ms =
centeredcubic(BCC)lattice,withlinearsizesL =L = |Pr∈ISr − Pr∈IISr|/NA, where I and II denote the
x y two simple cubic sublattices of the BCC lattice and N
L≤96. Each film is composed of 12 staggered (because F
and N denote the number of spins on the FM and on
oftheBCCstructure)layersofclassicalunitlengthspins A
the AFM films, respectively. The summations here are
Sr =(Srx,Sry,Srz), which interact via the Hamiltonian
performedoverallsitesonbothtypesoffilms. Themag-
nitude of the two components of the uniformmagnetiza-
H = −JF X Sr·Sr′ −KF X (Srz)2 tionparalleltotheinterfacialplaneisdenotedasmx and
hr,r′i∈FM r∈FM my. Our simulations were carried out using importance
2
samplingMonteCarlomethods[7],withMetropolisalgo- 1.0
5
rithm, at fixed temperature T. Typically 2×10 Monte (a) L=96, rough interface
Carlo Steps/site (MCS) were used for computing aver- 0.8
ages after about 3 ×105 MCS were first discarded for m
m
thermalization. Whenever not shown, error bars in the
0.6 s
figures are smaller than the symbol sizes. m
x
Fig.1 shows the uniform and staggered magnetization m
y
as a function of T for systems with a rough (stepped) 0.4
interface. At low T, both m and m tend to unity, in-
s
0.2
1.0
L=24 0.0
0 2 4 6 8 10 12
0.8
L=48 k T/J
B
L=96 1.0
0.6
(b) L=48, flat interface
m 0.8
0.4 m
m
s m
0.6 s
m
0.2 x
m
y
0.4
0.0
0 2 4 6 8 10 12
k T/J
B 0.2
FIG. 1: Uniform and staggered magnetization as a function
0.0
of temperature for L = 24, 48, and 96, with rough interface 0 2 4 6 8 10 12
and parameters JF = 5J > 0, JA = JI = −J, KA = J, and k T/J
KF =−0.5J. B
FIG. 2: Temperature dependence of the uniform and stag-
dicating ordered FM and AFM films. At very high T, geredmagnetizationandofthemagnitudeofthecomponents
both m andms decayto zero,indicating disorderedspin oftheuniformmagnetizationmx andmy for(a)L=96,with
configurations on both films. Finite-size effects are illus- rough interface and for (b) L=48, with flat interface. Both
tratedusing films with crosssections L=24,48,and96, cases are for JF = 5J > 0, JA = JI = −J, KA = J, and
where the number of spins per terrace along the x di- KF =−0.5J.
rection is constant. These data suggest the existence of
a FM transition between ordered and disordered states
at T ≈ 9.3J/k and a possible N´eel temperature at haveglobalrotationsymmetryinthe x-y plane, whichis
c B
T ≈ 2.2J/k , which coincides with the N´eel temper- theeasyplaneforspinsonthisfilm. Thepreferentialori-
N B
ature of a free 12-atomic-layerAFM film [8]. entations of the FM spins observed here either below or
aboveT resultfromthe exchangecouplingto the AFM
Temperature dependences of m and m are shownin N
x y
film.
Figs.2a and 2b for systems with a rough and a flat in-
terface, respectively. For both types of interfaces, the Instudying thin films, itis alsointeresting to examine
spins onthe FMfilmorientpredominantlyina direction the layer magnetization since this can vary significantly
collinear with the easy axis of the AFM at high temper- dependingontheproximitytotheinterfaceortothefree
atures, even above T . This is an indication that there boundaries. Figs.3a and 3b show the layer magnetiza-
N
is still order in the AFM above T due to the coupling tionand the magnitude of its y-component,respectively,
N
totheferromagnet. Asthetemperatureisloweredinthe as a function of the film layer for a system with rough
case of the rough interface the FM spins switch to ori- interface and L = 96. In our notation, layers 1 to 12
ent in a directionthat is perpendicular to the AFM easy comprise the AFM film, layer 13 has uniform terraces
axis,whichisthedirectionoftheAFMspins. Ourresults belonging alternately to the AFM and FM films, and
suggest that the onset of this perpendicular orientation layers14 to 24 form the FM film. For each temperature,
is very sharp and it occurs at a temperature below the theslightlylowermagnetizationonthesurfacelayersisa
N´eeltemperature. Thez-componentsoftheuniformand consequence of the free boundary condition along the z-
staggered magnetization are very small for all T. Note axis. In addition, the compensated exchange on average
thatintheabsenceoftheAFMfilm,spinsontheFMfilm across the interfacial plane reduces the layer magnetiza-
3
1.0 1.0
T/J= T/J=
0.8 0.8
0.6 0.6
n n
o 2.2 o 2.2
ati 8.0 ati 8.0
z 0.6 z 0.6
eti eti
n n
g g
a (a) a
m 0.4 m 0.4
r r
e e
y y
a a
l l
0.2 0.2
L=96, rough interface L=48, flat interface
0.0 0.0
0 4 8 12 16 20 24 28 0 4 8 12 16 20 24 28
AFM layers FM layers AFM layers FM layers
interface interface
n | 1.0
atio T/J= FIG.4: Layermagnetizationasafunctionofthefilmlayer,for
gnetiz 0.8 01..64 flJAat=inJteIrf=ac−eJa,ndKAL==J48,.anPdarKamFe=ter−s0u.5seJd. are JF =5J >0,
a
m 1.8
r 0.6 2.2
e
of lay 0.4 48..00 JpAerp=en−diJc,ulJaIr =ori−enJta,tKioFn o=f t−h0e.5FJM, aannddKAAFM= sJp)i,nsthies
nt present throughout the FM phase.
e
n
po 0.2 Besides the usual critical slowing down near critical
m
o (b) points, studies of phase transitions in thin films are fur-
c
| y- 0.00 4 8 12 16 20 24 28 tlahyeerrcboymlpalyicear,teadsbilylutshteraftaecdtathbaotveo.rdTehreirnetfohreefi,ldmetsevramriines-
AFM layers FM layers ing the nature of phase transitions may require a layer
interface
order parameter. However, the goal of our current work
FIG. 3: (a) Layer magnetization and (b) the magnitude of is not to study the thermodynamic limit of these bilay-
its y-component as a function of the film layer, for rough ers, but rather to understand experimental observations
interface and L = 96. Parameters used are JF = 5J > 0, of finite systems.
JA =JI =−J, KA =J, and KF =−0.5J. Monte Carlo simulations have been used to study a
system of coupled FM/AFM films, with flat interfaces
that are fully uncompensated as well as rough interfaces
tion for the layers near the interface. The perpendicular that are compensated on average. For both types of in-
orientation of the FM spins with the AFM spins at low terfaces above the N´eel temperature we observed order
T canalsobe seeninFig.3b,wheree.g. forT =0.6J/kB intheAFMwiththeAFMspinsaligningcollinearlywith
the magnetization on the FM layers has a very small y- the FM moments. As the temperature is lowered in the
component. At a higher T, e.g. T = 1.8J/kB < TN the caseoftheroughinterface,wehaveseenatransitionfrom
magnetizationontheFMlayershasalargey-component. collineartoperpendicularalignmentoftheFMandAFM
When the interfaceis flat with uncompensatedexchange spins.
acrossit,thereductionofthemagnetizationonthelayers
This research was partially supported by NSF grant
near the interface is not very large, at low T (see Fig.4,
DMR-0094422 as well as DOE-OS through BES-DMSE
where layers 1 to 12 comprise the AFM film and layers
and OASCR-MICS under Contract No. DE-AC05-
13 to 24 the FM film).
00OR22725withUT-BattelleLLC.Simulationswereper-
Simulations using J =5J > 0, J = −J, J = −2J, formed on the IBM SP at NERSC.
F A I
K = J, and K = −0.5J (i.e. with a stronger in-
A F
terfacial coupling) with rough interface suggest that the
onset of the perpendicular orientation of the FM with
the AFMeasyaxis occursata lowerT when the interfa-
[1] See the recent reviews, J. Nogu´es and I. K. Schuller, J.
cial coupling increases in magnitude. We also find that
Magn. Magn. Mater. 192, 203 (1999); A. E. Berkowitz
for a film with a rough interface that is compensated
and K. Takano, J. Magn. Magn. Mater. 200, 552 (1999);
on average,when the interaction and anisotropy param- M. Kiwi, J. Magn. Magn. Matter. 234, 584 (2001); R.
eters are such that the AFM becomes disordered at a L. Stamps, J. Phys. D 33, R247 (2000); and references
higher temperature than the FM (e.g. with JF = J, therein.
4
[2] P.J.vanderZaag,Y.Ijiri,J.A.Borchers,L.F.Feiner,R. 608 (1998); T. J. Moran, J. Nogu´es, D. Lederman, and I.
M.Wolf,J.M.Gaines,R.W.Erwin,andM.A.Verheijen, K. Schuller,Appl. Phys.Lett. 72, 617 (1998).
Phys. Rev.Lett. 84, 6102 (2000). [6] Y. Ijiri, et. al.,to be published.
[3] N. C. Koon, Phys. Rev.Lett. 78, 4865 (1997). [7] See e.g., D. P. Landau and K. Binder, A Guide to Monte
[4] T. C. Schulthess and W. H. Butler, Phys. Rev. Lett. 81, Carlo Simulations in Statistical Physics, Cambridge Uni-
4516 (1998). versity Press, 2000.
[5] T. J. Moran and I. K. Schuller, J. Appl. Phys. 79, 5109 [8] S.-H.Tsai,D.P.Landau,T.C.Schulthess,J.Appl.Phys.
(1996); Y. Ijiri, J. A. Borchers, R. W. Erwin, S.-H. Lee, 91, 6884 (2002)
P. J. van der Zaag, and R. M. Wolf, Phys. Rev.Lett. 80,