Alternating domains with uniaxial and biaxial magnetic anisotropy in epitaxial Fe films on BaTiO3
Tuomas H. E. Lahtinen, Yasuhiro Shirahata, Lide Yao, Kévin J. A. Franke, Gorige Venkataiah, Tomoyasu Taniyama, Sebastiaan van Dijken
AAlternating domains with uniaxial and biaxial magnetic anisotropy in epitaxial Fefilms on BaTiO Tuomas H. E. Lahtinen, Yasuhiro Shirahata, Lide Yao, K´evin J. A. Franke, Gorige Venkataiah, Tomoyasu Taniyama, and Sebastiaan van Dijken ∗ NanoSpin, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland. and Materials and Structures Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, Japan. (Dated: June 4, 2018)We report on domain formation and magnetization reversal in epitaxial Fe films on ferroelectricBaTiO substrates with ferroelastic a − c stripe domains. The Fe films exhibit biaxial magneticanisotropy on top of c domains with out-of-plane polarization, whereas the in-plane lattice elongationof a domains induces uniaxial magnetoelastic anisotropy via inverse magnetostriction. The strongmodulation of magnetic anisotropy symmetry results in full imprinting of the a − c domain patternin the Fe films. Exchange and magnetostatic interactions between neighboring magnetic stripesfurther influence magnetization reversal and pattern formation within the a and c domains. Ferromagnetic pattern formation via efficient cou-pling to ferroelectric domain structures has recentlybeen demonstrated.
Direct correlations between fer-romagnetic and ferroelectric domains and its persis-tence during ferroelectric polarization reversal open uppromising ways for electric-field control of local mag-netic switching and the motion of magnetic domainwalls. In systems based on interlayer strain transfer,the ferroelastic domain structure of a ferroelectric ma-terial induces local magnetoelastic anisotropies in a fer-romagnetic film via inverse magnetostriction. Within theferromagnetic sub-system, the magnetoelastic anisotropycompetes with intrinsic magnetic properties includingmagnetocrystalline anisotropy and exchange and mag-netostatic interactions between domains. Consequently,the evolution of the magnetic microstructure in an ap-plied magnetic or electric field depends critically on thetwo ferroic materials, the ferromagnetic layer thickness,and the ferroelastic domain size.In a previous study, full pattern transfer from ferro-electric BaTiO substrates with alternating ferroelastic a − a domains to polycrystalline Co Fe thin filmswas analyzed. The strain-induced uniaxial magnetoe-lastic anisotropy axis of this system rotates by 90 ◦ at do-main boundaries and this fully dominates the local mag-netic properties since the magnetocrystalline anisotropyof Co Fe is negligibly small. Here, we report forthe first time on full imprinting of ferroelectric BaTiO a − c domain patterns into epitaxial Fe films as schemat-ically illustrated in Fig. 1(a). Magneto-optical Kerreffect (MOKE) microscopy measurements indicate thatthe magnetic anisotropy is laterally modulated by thealternating in-plane structural symmetry of the BaTiO lattice. Moreover, it is shown that magnetic switchingin neighboring a and c domains is strongly coupled viaexchange and magnetostatic interactions. The demon-strated ability to initialize a rich variety of micromag-netic configurations in Fe/BaTiO supports the designof electric-field controlled magnetic structures includingmagnonic crystals and spintronic devices.In the experiments, 10 nm and 20 nm thick Fe films with a 5 nm Au capping layer were grown ontosingle-crystal BaTiO substrates using molecular beamepitaxy . Film growth at 300 ◦ C in an ultrahigh vacuumchamber resulted in epitaxial Fe with an in-plane Fe [110] (cid:107)
BaTiO [100] alignment as confirmed by transmissionelectron microscopy (Fig. 1(b) and (c)). The ferroelastic FeAuc (002) Fe (001) BTO (-110) Fe (020) BTO [100]
BTO //[110] Fe a a ac cH, ωθ (a)(b) (c) [110] Fe [100] BTO Fe - . % -1.6%-0.6% - . % [110] Fe [-110] Fe a-domain c-domainBTO . Å . Å [100] BTO [010]
BTO
FIG. 1: (a) Schematic illustration of the domain configura-tion in the Fe/BaTiO system. The arrows in the BaTiO substrate indicate the direction of ferroelectric polarizationand the double-headed arrows in the Fe film represent themagnetic easy axes. The schematics on the right illustratethe in-plane lattice structure and polarization direction of theBaTiO substrate and the orientation of the Fe film in the a and c domains. The room-temperature lattice parameters ofthe BaTiO substrate and the in-plane strains of the Fe filmare indicated. The strains are calculated relative to the Febulk lattice parameter on the basis of full strain transfer be-tween substrate and film. A cross-sectional TEM image anda selected area electron diffraction (SAED) pattern of a 10nm thick epitaxial Fe film on BaTiO (001) are shown in (b)and (c). a r X i v : . [ c ond - m a t . m t r l - s c i ] J a n -22mT 0mT 1mT 2mT 3mT 22mT θ = º H ω H ω θ = º H ω H ω θ = º H ω H ω acacac acac 20 μ m FIG. 2: Kerr microscopy images of a 20 nm thick epitaxial Fe film on BaTiO for different magnetic field angles ( θ ) and fieldstrength. The direction of magnetic field was altered by sample rotation in the Kerr microscope while the electromagnet wasfixed. Negative fields point down and positive fields point up in the above images. The white arrows indicate the direction ofmagnetization within selected a and c domains as inferred from a set of two images with the magneto-optical contrast axis ( ω )along the vertical and horizontal direction, respectively. domain pattern of the BaTiO substrates consisted of al-ternating a and c stripe domains with an average widthof 6 µ m and 3 µ m at room temperature. This regular do-main structure was formed upon sample cooling throughthe ferroelectric Curie temperature ( T C = 120 ◦ C) afterFe film growth. At T C , the structure of BaTiO changesfrom cubic to tetragonal. The ferroelastic a and c do-mains in tetragonal BaTiO impose different local strainson the epitaxial Fe films. For full strain transfer, the in-plane lattice of the Fe films is compressed by − .
6% and − .
6% with respect to that of the bcc Fe bulk structure( a F e = 2 .
870 ˚A) as illustrated in Fig. 1(a). On top ofthe ferroelastic c domains, the Fe lattice remains cubic.However, due to different shear strains in the [110]Fe and[-110]Fe directions, the in-plane structure of the Fe filmschanges into a diamond shape on top of the BaTiO a domains. MOKE microscopy was used to analyze mag-netization reversal in the a and c domains as a func-tion of in-plane magnetic field. Images were recordedwith two orthogonal magneto-optical contrast axes ( ω )by rotation of the optical plane of incidence using anadjustable diaphragm. From these two images, the lo-cal magnetization direction was extracted. The MOKEmicroscope setup was also used to measure magnetic hys-teresis curves on single a and c stripe domains for differ-ent in-plane magnetic field angles ( θ ).Figure 2 shows MOKE microscopy images of a 20nm thick Fe film on top of BaTiO for three mag-netic field directions. The regular magnetic stripes di- rectly correlate with the ferroelastic a − c pattern ofthe BaTiO substrate. The magnetic domain walls arestrongly pinned onto the ferroelectric domain boundariesby abrupt changes in local magnetic anisotropy. As aresult, the overall stripe pattern does not alter in an ap-plied magnetic field (until the film is saturated) and mag-netic switching in the a and c domains differs consider-ably. For a magnetic field angle of θ = 0 ◦ ( H perpendic-ular to the domains), the magnetization of the a domainsrotates coherently as indicated by the white arrows in theimages on the top rows of Fig. 2. On the other hand,abrupt switching is observed for θ = 90 ◦ ( H parallel tothe domains). In the images on the bottom rows of Fig.2, this switching event can be clearly seen at 2 mT. Thedifference in magnetization reversal mechanism reflectsthe uniaxial magnetic symmetry of the a domains, whichis also confirmed by the local magnetic hysteresis curvesof Fig. 3 and the polar plot of the remnant magnetizationin Fig. 4(a). The magnetic easy axis of the a domains inthe epitaxial Fe films is oriented parallel to the magneticdomains ([-110]Fe direction) and, thus, perpendicular tothe in-plane lattice elongation and polarization directionof the ferroelectric BaTiO substrate. This qualitativelyagrees with the symmetry of magnetoelastic anisotropyin Fe/BaTiO as illustrated in the next paragraph.The magnetoelastic anisotropy energy density ( K me )of Fe films on top of BaTiO can be written as K me = B ( e xx α x + e yy α y ) + B e xy α x α y (1) -10 0 100º0º 45º45º 90º90ºa-domain M / M S M / M S -10 0 10 10μ H (mT) -10 0 c-domain
FIG. 3: Magnetic hysteresis curves of single a (top row)and c (bottom row) domains measured at different magneticfield angles. The red lines and arrows in the circular sym-bols indicate the easy magnetization axes and the directionof magnetization during different stages of the reversal pro-cess. The vertical red dashed lines illustrate simultaneousmagnetic switching in the a and c domains. Here, B and B are the magnetoelastic coupling coeffi-cients, e xx and e yy are the strains along the cubic axes([100]Fe and [010]Fe), e xy is the shear strain along thediagonal [110]Fe direction, and α x and α y are the direc-tional cosines with respect to [100]Fe and [010]Fe. Ontop of the ferroelastic a domains, the in-plane Fe lat-tice exhibits a diamond shape due to a shear strain along[110]Fe. Relative to the [-110]Fe direction, the magnitudeof this strain amounts to +1 .
0% for full strain transfer.The change in magnetoelastic anisotropy that this straineffect induces is given by the second term of Eq. 1. Us-ing B = 7 . × J/m , e xy = 1 . α x = α y =1 / √
2, this calculation yields ∆ K me = 3 . × J/m .Since ∆ K me is positive, the [110]Fe direction is magnet-ically hard. Consequently, the uniaxial magnetic easyaxis is oriented along the orthogonal [-110]Fe direction,i.e. parallel to the magnetic domains and perpendicularto the BaTiO ferroelectric polarization. The strengthof the magnetoelastic anisotropy as determined from theslope and saturation field of hard-axis hysteresis curves is K me = 5 ± × J/m . The close agreement between thecalculated and experimentally measured uniaxial magne-toelastic anistropy indicates that the ferroelastic strainof the BaTiO substrates is fully transferred to the epi-taxial Fe films when the samples are cooled after MBEgrowth.Magnetization reversal in the c domains of the Fe filmis strikingly different. The polar plot of the remnant mag-netization in Fig. 4(a) clearly illustrates that the mag-netic anisotropy of the c domains exhibits fourfold sym-metry. The easy magnetization axes are aligned along[100]Fe and [010]Fe, in agreement with the magnetocrys-talline anisotropy of bulk Fe. Moreover, the in-planelattice of BaTiO remains cubic when c domains formduring sample cooling through T C . The lattice misfit be-tween Fe ( a F e = 2 .
870 ˚A) and BaTiO ( a BaT iO = 3 . μ H ( m T ) M / M S (a) (b) (c) FIG. 4: Experimental polar plots of (a) the remnant mag-netization and (b) the magnetic switching fields of the a (black solid lines) and c (red dashed lines) magnetic stripedomains. (c) Polar plot of the switching fields for isolateduniaxial a and biaxial c domains as determined by micromag-netic simulations. For both domains, an anisotropy constantof K = 5 × J/m was used in the simulations. pressive strain of − .
6% along the cubic axes. From thefirst term in Eq. 1 and e xx = e yy − . α x = 1, α y = 0, and B = − . × J/m , the magnetoelas-tic anisotropy along [100]Fe can be estimated. This gives K me = − . × J/m . The same result is obtainedfor [010]Fe with α x = 0 and α y = 1. Thus, the biaxialcompressive strain along [100]Fe and [010]Fe lowers themagnetoelastic anisotropy energy along these directions,which agrees with the experimentally observed orienta-tion of the easy magnetization axes in the c domains (Fig.4).Besides the strong lateral modulation of magneticanisotropy, local magnetization reversal in Fe/BaTiO also depends on the coupling between neighboring mag-netic stripe domains. This is clearly illustrated by thedouble switching events in the hysteresis curves of the a and c domains and the close agreement in switchingfields (Fig. 3). Double switching has been observed forepitaxial Fe wires with biaxial anisotropy and field anglesnear the magnetic easy axes, but the occurrence of twoconsecutive reversal events in the uniaxial a domains canonly be rationalized when magnetic interactions betweenneighboring domains are taken into account. To illustratethe coupling between the Fe stripe domains and the na-ture of the magnetic interactions, the hysteresis curves ofFig. 3 are analyzed in detail.For θ = 0 ◦ , the magnetic field is aligned along the uni-axial magnetic hard axis of the a domains. However, inaddition to coherent magnetization reversal, an abruptmagnetic switch is observed in the hysteresis curve. Thisswitch is induced by 90 ◦ magnetization rotation in theneighboring c domains at 0.6 mT. Because ferromagneticcoupling between the a and c domains reduces the mag-netization angle just prior and after this reversal event,the magnetization of the a domains instantaneously ro-tates when the c domains switch. The induced magneti-zation rotation in the a domains, as estimated from localMOKE hysteresis curves, is about 20 ◦ . Since exchangeand magnetostatic interactions both reduce the magneti-zation angle between domains in this configuration, it isnot possible to distinguish between both magnetic effects.For θ = 90 ◦ , the magnetization of the a domains isaligned along the uniaxial magnetic easy axis through-out the reversal process. In this case, one single switch-ing event is observed at 2.0 mT in both stripe domains.The increase of switching field compared to θ = 0 ◦ in-dicates that ferromagnetic coupling between neighboringdomains delays magnetization reversal in the biaxial c domains until the a domains switch by 180 ◦ . This do-main coupling effect can be rationalized by consideringthe magnetic energy of the Fe/BaTiO system. If the c domains would switch prior to the a domains, the magne-tization angle between both domains would increase fromabout 45 ◦ to 135 ◦ (see circular symbols in Fig. 3). Thiswould enhance both the exchange and magnetostatic en-ergy. Simultaneous switching in both domains is there-fore energetically more favorable because it limits themaximum magnetization angle between neighboring do-mains to 45 ◦ throughout the reversal process. Since themagnetization of the a domains is parallel to the stripepattern, their stray field hardly influences the magneti-zation direction in the c domains. Hence, ferromagneticcoupling between both stripe domains is dominated byshort-range exchange interactions.Finally, for θ = 45 ◦ , the magnetization of the c domainsreverses by two separate 90 ◦ switches. In this case, bothcoupling effects are observed. At small magnetic field,magnetic switching in the biaxial c domains induces asmall abrupt magnetization rotation in the uniaxial a do-mains. The second switch in the c domains is triggered by180 ◦ magnetization reversal in the a domains. Both ex-change and magnetostatic interactions might contributeto domain coupling in this case.The polar plot of Fig. 4(b) summarizes the switchingfields of the a and c domains as a function of magneticfield angle. Strong coupling between neighboring stripedomains results in identical switching fields for both do-mains irrespective of field direction. The vertical linesrepresent magnetic switching events that are triggered byuniaxial a domains. The shape of these curves deviatessignificantly from the Stoner-Wohlfarth astroid, whichis obtained when the switching fields of isolated uniax-ial domains are simulated (Fig. 4(c)). In the Stoner-Wohlfarth case, a maximum switching field is obtainedwhen the field is applied along the uniaxial magneticeasy axis ( θ = 90 ◦ ). In our Fe/BaTiO samples, strongcoupling between neighboring stripe domains rotates themagnetization of the a domains away from its magneticeasy axis during magnetization reversal and this drasti-cally reduces the switching field for θ = 90 ◦ . Similarly,the horizontal lines in Fig. 4(b) indicate magnetic switch-ing events that are induced by biaxial c domains. Again,the shape of these experimental curves differs completelyfrom the simulated polar plot of isolated domains withbiaxial anisotropy (Fig. 4(c)). The measured polar plotof the switching fields in Fe/BaTiO is unique. Both thevertical and horizontal curves have no analogue in sys-tems with uniform magnetic anisotropy. We also notethat our microscopic observation of a small intrinsic c - domain switching field agrees with previous macroscopicstudies demonstrating a reduction of magnetic switch-ing field after the application of an out-of-plane electricfield. Finally, we show that efficient coupling between a and c domains influences the magnetic pattern within a and c stripe domains of the Fe films. If both domains wouldswitch independently, the evolution of the magnetic mi-crostructure of the biaxial c domains would be similarfor θ = 0 ◦ and θ = 90 ◦ . The MOKE microscopy imagesof Fig. 2 clearly show that this is not the case. For θ =0 ◦ , the magnetization of the a domains coherently rotatesclockwise and, due to ferromagnetic interactions betweendomains, this forces the magnetization of the c domainsto reverse in the same direction. In small magnetic field,90 ◦ domains nucleate within the c stripes. These domainsare highly mobile and their size increases rapidly with ap-plied field strength. As a result, the magnetic uniformityof the c domains is re-established at a field of about 3mT. For θ = 90 ◦ , the magnetization of the a domains re-mains fixed along its uniaxial magnetic easy axis. In thiscase, exchange interactions with neighboring c domainsdo not favor a particular reversal direction. The c do-mains therefore split up into a regular stripe pattern byalternating clockwise and anti-clockwise magnetizationrotation. Due to negligible domain wall motion withinthe c domains under these conditions, the stripe patternis robust until it abruptly changes during simultaneousmagnetic switching in both domains. In this case, a largemagnetic field is required to fully remove the stripe pat-tern from the c domains.In summary, the results of this paper clearly demon-strate that magnetic domains can be imprinted into con-tinuous magnetic films via efficient coupling to ferroe-lastic domains of a ferroelectric material. The magne-tization reversal mechanism in such domains dependson the symmetry of the strain-induced magnetoelasticanisotropy and the applied field angle. Moreover, ferro-magnetic coupling between neighboring domains stronglyinfluences local magnetic switching events. Pattern for-mation in epitaxial Fe films on ferroelectric a − c domainsof BaTiO is particularly rich. In this system, magneticstripe domains with biaxial and uniaxial anisotropy al-ternate. Moreover, depending on the direction of theapplied magnetic field, highly mobile or robust magneticpatterns form within the c domains, a property that couldbe exploited in magnetic devices. Acknowledgments
This work was supported by the Academy of Finland(Grant Nos. 127731 and 260361), the European Re-search Council (ERC-2012-StG 307502-E-CONTROL),the Industrial Technology Research Grant Program in2009 from NEDO of Japan, JSPS KAKENHI (GrantNo. 2200077), the Advanced Materials Developmentand Integration of Novel Structured Metallic and Inor-ganic Materials Project of MEXT, and the Collabora-tive Research Project of the Materials and StructuresLaboratory, Tokyo Institute of Technology. T.H.E.L. is supported by the National Doctoral Program in Materi-als Physics and K.J.A.F. acknowledges support from theFinnish Doctoral Program in Computational Sciences. ∗ Electronic address: sebastiaan.van.dijken@aalto.fi Y.-H. Chu, L. W. Martin, M. B. Holcomb, M. Gajek, S.-J.Han, Q. He, N. Balke, C.-H. Yang, D. Lee, W. Hu, et al.,Nature Materials , 478 (2008). D. Lebeugle, A. Mougin, M. Viret, D. Colson, andL. Ranno, Physical Review Letters , 257601 (2009). J. T. Heron, M. Trassin, K. Ashraf, M. Gajek, Q. He,S. Y. Yang, D. E. Nikonov, Y.-H. Chu, S. Salahuddin, andR. Ramesh, Physical Review Letters , 217202 (2011). T. H. E. Lahtinen, J. O. Tuomi, and S. van Dijken, Ad-vanced Materials , 3187 (2011). T. H. E. Lahtinen, J. O. Tuomi, and S. van Dijken, IEEETransactions on Magnetics , 3768 (2011). T. H. E. Lahtinen, K. J. A. Franke, and S. van Dijken,Scientifc Reports , 258 (2012). G. Venkataiah, Y. Shirahata, M. Itoh, and T. Taniyama,Applied Physics Letters , 102506 (2011). Y. Shirahata, T. Nozaki, G. Venkataiah, H. Taniguchi,M. Itoh, and T. Taniyama, Applied Physics Letters ,022501 (2011). K. J. A. Franke, T. H. E. Lahtinen, and S. van Dijken,Phys. Rev. B , 094423 (2012). R. C. O’Handley,
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