Table Of ContentFormation of regular magnetic domain patterns with alternating uniaxial and biaxial
anisotropy in epitaxial Fe films on BaTiO
3
Tuomas H. E. Lahtinen,1 Yasuhiro Shirahata,2 Lide Yao,1 K´evin J. A. Franke,1
Gorige Venkataiah,2 Tomoyasu Taniyama,2 and Sebastiaan van Dijken1∗
1NanoSpin,DepartmentofAppliedPhysics,AaltoUniversitySchoolofScience,P.O.Box15100,FI-00076Aalto, Finland.and
2Materials and Structures Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, Japan.
(Dated: October 25, 2012)
We report on domain formation and magnetization reversal in epitaxial Fe films on ferroelectric
BaTiO substrateswithferroelastica−cstripedomains. TheFefilmsexhibitbiaxialmagnetocrys-
3
talline anisotropy on top of c domains with out-of-plane polarization, whereas the in-plane lattice
2 elongation of a domains induces uniaxial magnetoelastic anisotropy via inverse magnetostriction.
1 Thelargemodulationofmagneticanisotropysymmetryresultsinfullimprintingofthea−cdomain
0 pattern in the Fe films. Exchange and magnetostatic interactions between neighboring magnetic
2 stripes further influence magnetization reversal and pattern formation within the a and c domains.
t
c
O
Ferromagnetic pattern formation via efficient coupling films with a 5 nm Au capping layer were grown onto
to ferroelectric domain structures has recently been single-crystal BaTiO substrates using molecular beam
4 3
demonstrated.1–6 Directcorrelationsbetweeninteracting epitaxy.7,8 Filmgrowthat300◦Cinanultrahighvacuum
2
ferromagnetic and ferroelectric domains and its persis- chamberresultedinepitaxialFewithanin-planeFe[110]
] tence during ferroelectric polarization reversal open up (cid:107) BaTiO [100] alignment at room temperature as con-
3
i
c promising ways for electric-field control of local mag- firmedbytransmissionelectronmicroscopy(Fig. 1). The
s netic switching1–5 and the motion of magnetic domain ferroelasticdomainpatternoftheBaTiO substratecon-
- 3
l walls.6 In systems based on interlayer strain transfer, sistedofalternatingaandcstripedomainswithanaver-
r
t the ferroelastic domain structure of a ferroelectric ma- agewidthof6µmand3µm,respectively. Theevolution
m
terial induces local magnetoelastic anisotropies in a fer- ofthemagneticdomainstructurewithin-planemagnetic
. romagneticfilmviainversemagnetostriction. Withinthe
t
a ferromagneticsub-system,themagnetoelasticanisotropy
m competes with intrinsic magnetic properties including
(a)
- magnetocrystalline anisotropy and exchange and mag-
d a-domain c-domain
netostatic interactions between domains. Consequently,
n
the evolution of the magnetic microstructure in an ap-
o
c plied magnetic or electric field depends critically on the [110] 4.036 Å 3.992 Å
Fe
[ two ferroic materials, the ferromagnetic layer thickness, Å Å
1 and the ferroelastic domain size. a c a c a [100]BTO 3.992 3.992
v In a previous study, full pattern transfer from ferro-
H, ω
3 electric BaTiO substrates with alternating a −a fer- θ
3 1 2
3
roelastic domains to polycrystalline Co Fe thin films
5 60 40
wasanalyzed.4–6 Theuniaxialmagnetoelasticanisotropy
6 (b) (c) (002)
axis of this system rotates by 90◦ at domain boundaries Fe
0. and since the magnetocrystalline anisotropy of Co Fe Au
1 isnegligible,itfullydominatesthelocalmagneticp6r0ope4r0- (001)BTO
2 (-110)
ties. Here, we report for the first time on full imprinting Fe
1 Fe
v: otafxfiearlroFeeleficltmrisc aBsasTcihOe3maat−icaclldyoimlluasintraptaetdteirnnsFiign.to1e(ap)i-. (020)BTO
Xi Magneto-optical Kerr effect (MOKE) microscopy mea- 2nm c BaTiO
surements indicate that the magnetic anisotropy is lat- 3 [100] //[110]
r BTO Fe
a erally modulated by the alternating in-plane structural
symmetry of the BaTiO lattice. Moreover, it is shown FIG. 1: (a) Schematic illustration of the domain configura-
3
that magnetic switching in neighboring a and c domains tion in the Fe/BaTiO3 system. The arrows in the BaTiO3
is strongly coupled via exchange and magnetostatic in- substrate indicate the direction of ferroelectric polarization
and the double-headed arrows in the Fe film represent the
teractions. The demonstrated ability to initialize a rich
magnetic easy axes. The schematic on the right illustrates
variety of micromagnetic configurations in Fe/BaTiO
3 thein-planelatticestructureandpolarizationdirectionofthe
supports the design of electric-field controlled magnetic
BaTiO substrate in the a and c domains. A cross-sectional
3
structuresincludingmagnoniccrystalsandspintronicde-
TEM image and a selected area electron diffraction (SAED)
vices. pattern of a 10 nm thick epitaxial Fe film on BaTiO (001)
3
are shown in (b) and (c).
In the experiments, 10 nm and 20 nm thick Fe
2
-22mT 0mT 1mT 2mT 3mT 22mT
a
c
ω H
0º
=
θ a
H c
ω H a
c
5º
4
=
θ
H a
c
ca
ω H
0º
9
=
θ
H
20μm
FIG. 2: Kerr microscopy images of a20 nm thick epitaxialFe filmon BaTiO for different magneticfield angles (θ) andfield
3
strength. The white arrows indicate the direction of magnetization within the domains as inferred from a set of two images
with orthogonal optical contrast axes (ω).
field was analyzed using MOKE microscopy. The same fromtheslopeandsaturationfieldofhard-axishysteresis
setupwasusedtomeasuremagnetichysteresiscurveson curves is K =5±2×104 J/m3.
me
single a and c stripe domains for different magnetic field Magnetization reversal in the c domains of the Fe film
angles (θ). isstrikinglydifferent. Thepolarplotoftheremnantmag-
Figure 2 shows MOKE microscopy images of a 20 netization in Fig. 4(a) clearly illustrates that the mag-
nm thick Fe film on top of BaTiO for three mag- netic anisotropy of the c domains exhibits fourfold sym-
3
netic field directions. The regular magnetic stripes di- metry. TheeasymagnetizationaxesarealignedalongFe
rectly correlate with the ferroelastic a − c pattern of [100] and Fe [010], in agreement with the magnetocrys-
the BaTiO substrate. The magnetic domain walls are talline anisotropy of bulk Fe. The BaTiO substrate
3 3
stronglypinnedontotheferroelectricdomainboundaries is in the cubic paraelectric phase during film growth
by abrupt changes in local magnetic anisotropy6,9. As a and the in-plane lattice remains cubic when c domains
result, the overall stripe pattern does not alter in an ap- form upon cooling through the ferroelectric Curie tem-
pliedmagneticfield(untilthepatternvanishesinsatura- perature (T = 120◦C). The lattice misfit between Fe
C
tion)andmagneticswitchingintheaandcdomainsdif- (a = 2.870 ˚A) and BaTiO (a = 3.992 ˚A) at
Fe 3 BaTiO3
fersconsiderably. Foramagneticfieldangleofθ=0◦,the room temperature induces a biaxial compressive strain
magnetization of the a domains rotates coherently while of 1.7%, which alters the magnitude but not the symme-
abrupt switching is observed for θ = 90◦. This uniaxial try of the crystalline anisotropy. From the experimental
symmetry is also confirmed by the local magnetic hys- data,themagnetocrystallineanisotropyofthecdomains
teresiscurvesofFig. 3andthepolarplotoftheremnant is estimated as K =5±2×104 J/m3.
mc
magnetization in Fig. 4(a). The magnetic easy axis of Besides the strong lateral modulation of magnetic
theadomainsintheepitaxialFefilmisorientedparallel anisotropy, local magnetization reversal in Fe/BaTiO
3
tothemagneticdomainwallsand,thus,perpendicularto also depends on the coupling between neighboring mag-
the in-plane lattice elongation and polarization direction netic stripe domains. This is clearly illustrated by the
of the ferroelectric BaTiO substrate. This qualitatively double switching events in the hysteresis curves of the
3
agrees with the magnetostriction of single-crystalline Fe. a and c domains and the close agreement in switching
IntetragonalBaTiO ,theadomainsprovideamaximum fields (Fig. 3). Double switching has been observed for
3
anisotropiclatticestrainof1.1%inthe[100]directionat epitaxialFewireswithbiaxialanisotropyandfieldangles
room temperature. The Fe film is thus stretched along nearthemagneticeasyaxes,11 buttheoccurrenceoftwo
[110] and, since the magnetostriction coefficient of Fe is consecutivereversaleventsintheuniaxialadomainscan
negative for this direction (λ = −10×10−6)10, an onlyberationalizedwhenmagneticinteractionsbetween
[110]
uniaxial magnetic easy axis is induced along [1-10]. The neighboringdomainsaretakenintoaccount. Toillustrate
strength of the magnetoelastic anisotropy as determined the coupling between the Fe stripe domains and the na-
3
10..050º a-domain 45º 90º (a1).0 3 3 0 0 30 (b)5.0 3 3 0 0 30 (c)
M/MS0.0 0.5 300 60 T)2.5 300 60
--10..05 M/MS0.0 270 90 H (m0.0 270 90
10..050º c-domain 45º 90º 0.5 240 120 μ02.5 240 120
MS0.0 1.0 210 180 1 5 0 5.0 210 18 0 1 5 0
M/
-0.5
-1.0 FIG.4: Experimentalpolarplotsof(a)theremnantmagne-
-10 0 10 -10 0 10 -10 0 10 tization and (b) the magnetic switching fields of the a (black
μH (mT)
0 solidlines)andc(reddashedlines)magneticstripedomains.
(c) Polar plot of the switching fields for isolated uniaxial a
FIG.3: Magnetichysteresiscurvesofsingleaandcdomains and biaxial c domains as determined by micromagnetic sim-
measuredatdifferentmagneticfieldangles. Theredlinesand ulations using OOMMF.12 For both domains, an anisotropy
arrowsinthecircularsymbolsindicatetheeasymagnetization constant of K =5×104 J/m3 was used in the simulations.
axesandthedirectionofmagnetizationduringdifferentstages
ofthereversalprocess. Theverticalreddashedlinesillustrate
simultaneous magnetic switching in the a and c domains.
short-range exchange interactions.
Finally,forθ=45◦,themagnetizationofthecdomains
tureofthemagneticinteractions,thehysteresiscurvesof reverses by two separate 90◦ switches. In this case, both
Fig. 3 are analyzed in detail. coupling effects are observed. At small magnetic field,
Forθ =0◦,themagneticfieldisalignedalongtheuni- magnetic switching in the biaxial c domains induces a
axial magnetic hard axis of the a domains. However, in small abrupt magnetization rotation in the uniaxial a
addition to coherent magnetization reversal, an abrupt domains. Thesecondswitchinthecdomainsistriggered
magneticswitchisobservedinthehysteresiscurve. This by instantaneous 180◦ magnetization reversal in the a
switch is induced by 90◦ magnetization rotation in the domains. Both exchange and magnetostatic interactions
neighboringcdomainsat0.6mT.Becauseferromagnetic might contribute to domain coupling in this case.
coupling between the a and c domains reduces the mag- The polar plot of Fig. 4(b) summarizes the switching
netization angle just prior and after this reversal event, fields of the a and c domains as a function of magnetic
the magnetization of the a domains instantaneously ro- field angle. Strong coupling between neighboring stripe
tates when the c domains switch. The induced magneti- domains results in identical switching fields for both do-
zationrotationintheadomains,asestimatedfromlocal mains irrespective of field direction. The vertical lines
MOKE hysteresis curves, is about 20◦. Since exchange representmagneticswitchingeventsthataretriggeredby
andmagnetostaticinteractionsbothreducethemagneti- uniaxial a domains. The shape of these curves deviates
zation angle between domains in this configuration, it is significantly from the Stoner-Wohlfarth astroid,13 which
notpossibletodistinguishbetweenbothmagneticeffects. is obtained when the switching fields of isolated uniax-
For θ = 90◦, the magnetization of the a domains is ial domains are simulated (Fig. 4(c)). In the Stoner-
aligned along the uniaxial magnetic easy axis through- Wohlfarth case, a maximum switching field is obtained
out the reversal process. In this case, one single switch- when the field is applied along the uniaxial magnetic
ing event is observed at 2.0 mT in both stripe domains. easy axis (θ = 90◦). In our Fe/BaTiO3 samples, strong
The increase of switching field compared to θ = 0◦ in- couplingbetweenneighboringstripedomainsrotatesthe
dicatesthatferromagneticcouplingbetweenneighboring magnetization of the a domains away from its magnetic
domains delays magnetization reversal in the biaxial c easy axis during magnetization reversal and this drasti-
domains until the a domains switch by 180◦. This do- cally reduces the switching field for θ = 90◦. Similarly,
main coupling effect can be rationalized by considering thehorizontallinesinFig. 4(b)indicatemagneticswitch-
the magnetic energy of the Fe/BaTiO system. If the c ing events that areinduced by biaxial c domains. Again,
3
domainswouldswitchpriortotheadomains,themagne- theshapeoftheseexperimentalcurvesdifferscompletely
tizationanglebetweenbothdomainswouldincreasefrom from the simulated polar plot of isolated domains with
about 45◦ to 135◦ (see circular symbols in Fig. 3). This biaxial anisotropy (Fig. 4(c)). The measured polar plot
wouldenhanceboththeexchangeandmagnetostaticen- of the switching fields in Fe/BaTiO3 is unique. Both the
ergy. Simultaneous switching in both domains is there- vertical and horizontal curves have no analogue in sys-
fore energetically more favorable because it limits the tems with uniform magnetic anisotropy. We also note
maximum magnetization angle between neighboring do- that our microscopic observation of a small intrinsic c-
mains to 45◦ throughout the reversal process. Since the domain switching field agrees with previous macroscopic
magnetization of the a domains is parallel to the stripe studies demonstrating a reduction of magnetic switch-
pattern, their stray field hardly influences the magneti- ing field after the application of an out-of-plane electric
zation direction in the c domains. Hence, ferromagnetic field.7,14
coupling between both stripe domains is dominated by Finally, we show that efficient coupling between a and
4
c domains influences the magnetic pattern within the a on the competition between the strain-induced magne-
and c stripe domains of the Fe films. If both domains toelastic anisotropy and the intrinsic magnetocrystalline
would switch independently, the evolution of the mag- anisotropy of the magnetic film. Moreover, magnetic
netic microstructure of the biaxial c domains would be interactions between neighboring domains strongly in-
similar for θ = 0◦ and θ = 90◦. The MOKE microscopy fluence local magnetization reversal. Pattern formation
images of Fig. 2 clearly show that this is not the case. in epitaxial Fe films on ferroelectric a − c domains of
For θ = 0◦, the magnetization of the a domains coher- BaTiO is particularly rich. In this system, magnetic
3
ently rotates clockwise and, due to ferromagnetic inter- stripe domains with biaxial and uniaxial anisotropy al-
actions between domains, this forces the magnetization ternate. Moreover, depending on the direction of the
of the c domains to reverse in the same direction. In applied magnetic field, highly mobile or robust magnetic
small magnetic field, 90◦ domains nucleate within the c patternsformwithinthecdomains,apropertythatcould
stripes. These domains are highly mobile and their size be exploited in magnetic devices.
increasesrapidlywithappliedfieldstrength. Asaresult,
themagneticuniformityofthecdomainsisre-established
at a field of about 3 mT. For θ = 90◦, the magnetiza-
tion of the a domains remains fixed along its uniaxial
Acknowledgments
magnetic easy axis. In this case, exchange interactions
with neighboring c domains do not favor a particular re-
versal direction. The c domains therefore split up into This work was supported by the Academy of Finland
a regular stripe pattern with alternating clockwise and (Grant Nos. 127731 and 260361), the European Re-
anti-clockwise magnetization rotation. Due to negligible search Council (ERC-2012-StG 307502-E-CONTROL),
domain wall motion within the c domains under these the Industrial Technology Research Grant Program in
conditions, the stripe pattern is robust until it abruptly 2009 from NEDO of Japan, JSPS KAKENHI (Grant
changes during simultaneous magnetic switching in both No. 2200077), the Advanced Materials Development
domains. In this case, a large magnetic field is required and Integration of Novel Structured Metallic and Inor-
to fully remove the stripe pattern from the c domains. ganic Materials Project of MEXT, and the Collabora-
In summary, the results of this paper clearly demon- tive Research Project of the Materials and Structures
stratethatmagneticdomainscanbeimprintedintocon- Laboratory, Tokyo Institute of Technology. T.H.E.L. is
tinuous magnetic films via efficient coupling to ferroe- supported by the National Doctoral Program in Materi-
lastic domains of a ferroelectric material. The magne- als Physics and K.J.A.F. acknowledges support from the
tization reversal mechanism in such domains depends Finnish Doctoral Program in Computational Sciences.
∗ Electronic address: sebastiaan.van.dijken@aalto.fi 8 Y. Shirahata, T. Nozaki, G. Venkataiah, H. Taniguchi,
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