Electric-field-driven domain wall dynamics in perpendicularly magnetized multilayers
Diego López González, Yasuhiro Shirahata, Ben Van de Wiele, Kévin J. A. Franke, Arianna Casiraghi, Tomoyasu Taniyama, Sebastiaan van Dijken
EElectric-field-driven domain wall dynamics in perpendicularly magnetizedmultilayers
Diego L´opez Gonz´alez, Yasuhiro Shirahata, Ben Van de Wiele, K´evin J. A. Franke, Arianna Casiraghi, Tomoyasu Taniyama, and Sebastiaan van Dijken NanoSpin, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto,Finland. Materials and Structures Laboratory, Tokyo Institute of Technology, Yokohama,Japan. and Department of Electrical Energy, Systems and Automation, Ghent University, Ghent B-9000,Belgium. (Dated: 7 September 2018)
We report on reversible electric-field-driven magnetic domain wall motion in a Cu/Ni multilayer on a fer-roelectric BaTiO substrate. In our heterostructure, strain-coupling to ferroelastic domains with in-planeand perpendicular polarization in the BaTiO substrate causes the formation of domains with perpendicularand in-plane magnetic anisotropy, respectively, in the Cu/Ni multilayer. Walls that separate magnetic do-mains are elastically pinned onto ferroelectric domain walls. Using magneto-optical Kerr effect microscopy,we demonstrate that out-of-plane electric field pulses across the BaTiO substrate move the magnetic andferroelectric domain walls in unison. Our experiments indicate an exponential increase of domain wall ve-locity with electric field strength and opposite domain wall motion for positive and negative field pulses.Magnetic fields do not affect the velocity of magnetic domain walls, but independently tailor their internalspin structure, causing a change in domain wall dynamics at high velocities.Controlled motion of domain walls in perpendicularlymagnetized layers forms the basis of spintronic memoryand logic device concepts. The technological relevanceof materials with perpendicular magnetic anisotropy(PMA) stems from the stability and small width of theirdomain walls. Domain walls in PMA nanowires are effi-ciently driven by electrical currents via spin-orbit inducedeffects.
Motivated by the prospect of low-power con-sumption and the ability to tailor magnetic propertieslocally, electric-field control of domain walls in PMA sys-tems is also pursued. In previous studies, electric fieldsare either applied across a gate dielectric, an ionicconductor, or a piezoelectric transducer. These ap-proaches manipulate the strength of PMA. As a result,the velocity or pinning of magnetic domain walls thatare driven by a magnetic field or electrical current is de-liberately tuned. Since the underlying physics relies onthe variation of PMA, electric field control is most pro-nounced for thermally activated creep motion.ln this letter, we report on a PMA system wherein do-main walls are actively driven by an electric field. Ourapproach differs from previous work in that the electricfield does not modify the strength of PMA. Instead, elec-tric fields are used to move domain walls in a ferroelectriccrystal onto which magnetic domain walls in a neighbor-ing PMA multilayer are strongly pinned. The magneticdomain walls are thus driven by an electric field withoutthe assistance of a magnetic field or electrical current.Reversible motion of domain walls and an exponential in-crease of domain wall velocity with electric field strengthare demonstrated. a) sebastiaan.van.dijken@aalto.fi V E- E + FIG. 1. Illustration of domain correlations in our experimen-tal sample. The ferroelectric polarization of the BaTiO sub-strate alternates between in-plane and perpendicular direc-tions (white arrows). Strain transfer from these domains tothe [Cu (9 nm)/Ni (2 nm)] /Cu (9 nm) multilayer causes themagnetization to rotate from perpendicular to in-plane (blackmarks). The magnetic domain walls are strongly pinned ontothe domain walls in the ferroelectric substrate, enabling re-versible motion in positive and negative out-of-plane electricfields. We consider a [Cu (9 nm)/Ni (2 nm)] /Cu (9 nm) mul-tilayer on a single-crystal ferroelectric BaTiO substrate.The Cu and Ni layers are grown by molecular beam epi-taxy at room temperature onto a 1 nm Fe buffer layerand capped by 5 nm Au. Before sample preparation,the polarization of the BaTiO substrate is oriented in-plane. Despite a lattice mismatch of more than 10% be-tween the metal layers and BaTiO , the Cu/Ni multi-layer grows epitaxially with a (001) orientation. Instantstrain relaxation during MBE, decouples the Cu/Ni mul- a r X i v : . [ c ond - m a t . m t r l - s c i ] F e b -1.0-0.50.00.51.0 -20 -10 0 10 20 M z / M S µ H(mT) -1.0-0.50.00.51.0 -100 -50 0 50 100 M / M S µ H(mT)
H DWH DW (a) (b) (c) µ m FIG. 2. (a) MOKE microscopy image of the Cu/Ni multi-layer. (b) Polar MOKE hysteresis curves for two neighboringdomains. The rectangles in (a) illustrate the area of data col-lection. The measurements indicate that one of the domainsexhibits PMA (domain with red rectangle), while the mag-netization of the other domain is oriented in-plane (domainwith black rectangle). (c) Local longitudinal MOKE hystere-sis loops for the domain with in-plane magnetic anisotropy,i.e., both curves are measured in the black rectangle. Theorientation of in-plane magnetic field is parallel (blue curve)and perpendicular (black curve) to the domain wall. Themagnetic domain wall does not move in a magnetic field be-cause of strong elastic pinning to a ferroelectric domain wallin the BaTiO substrate. tilayer from the BaTiO substrate. As a result, the Nilayers are strained only by the lattice mismatch with Cu.The growth-induced tensile strain in Ni amounts to 1.9%,which is sufficient to induce PMA via a strong magnetoe-lastic effect. For more details on the crystallographicstructure of the Cu/Ni multilayer on BaTiO , we refer toRef. 15, which reports on magnetization switching. Here,we focus on the dynamics of electric-field-driven domainwall motion.Domain walls are created in the Cu/Ni multilayerby the application of a strong out-of-plane electric fieldacross the ferroelectric BaTiO substrate. After the fieldis turned off, the BaTiO crystal relaxes into stripe do-mains with alternating perpendicular and in-plane polar-ization. Since the strain in Ni layers on top of ferroelec-tric domains with in-plane polarization does not changeby this procedure, PMA is preserved in these areas. Ontop of domains with perpendicular polarization, this isnot the case. Polarization switching from in-plane toperpendicular coincides with a 90 ◦ rotation of the tetrag-onal BaTiO unit cell. In the substrate plane, this corre-sponds to a uniaxial lattice compression of 1.1%. Nowthat the multilayer is clamped to the substrate, voltage-induced strain effects are efficiently transferred to theCu/Ni multilayer. The growth-induced tensile strain inNi layers on domains with perpendicular polarization isthus considerably reduced and this causes the magneti-zation to rotate into the film plane. Figure 1 illustratesthe ferromagnetic and ferroelectric domain configurationafter the application of a strong out-of-plane electric field.We use magneto-optical Kerr effect (MOKE) mi-croscopy to characterize the sample. In Fig. 2, we focuson an area of the Cu/Ni multilayer with one magneticdomain wall. Local polar MOKE microscopy data (Fig. 2(b)) confirm that one of the domains exhibits PMA(bright domain in Fig 2(a)). Using vibrating sample mag-netometry with large in-plane magnetic field (not shown),we derive an effective PMA of K eff = 2 . × J/m forthis domain type. The polar MOKE hysteresis curve ofthe other domain is completely closed (black curve inFig. 2(b)). Local longitudinal MOKE microscopy mea-surements on this domain (Fig. 2(c)) indicate that the in-plane magnetization aligns perpendicular to the domainwall. From the slope of the hard-axis hysteresis curve,we estimate an uniaxial in-plane magnetic anisotropy of K u = 1 . × J/m . The magnetic domain wall in theCu/Ni multilayer is pinned onto a ferroelectric domainwall in the BaTiO substrate, separating domains within-plane and perpendicular polarization. This strong pin-ning effect, which prevents any domain wall displacementin an applied magnetic field, is caused by the abruptchange in magnetoelastic anisotropy.Next, we discuss the magnetic response to out-of-planeelectric field pulses. In the experiments, the Cu/Ni mul-tilayer is grounded and square voltage pulses are appliedto a metallic electrode on the back of the BaTiO sub-strate. Positive pulses generate an electric field ( E + )favoring ferroelectric domains with polarization pointingupward. As a result, these domains grow at the expenseof neighboring domains with in-plane polarization. A re-versal of the voltage polarity (i.e. negative voltages or E − ) causes ferroelectric domains with upward polariza-tion to shrink. Alternating positive and negative volt-age pulses thus reversibly move the ferroelectric domainwalls in the BaTiO substrate. Figure 3(a) shows themagnetic response of the Cu/Ni multilayer to this elec-tric field effect. Positive electric field pulses (indicated byblack numbered dots) displace the magnetic domain walldownward. In this case, the domain with in-plane mag-netization grows at the expense of the magnetic domainwith PMA. Negative out-of-plane electric field pulses (rednumbered dots), in turn, move the magnetic domain wallback up. Reversible motion of the domain wall is causedby strong strain coupling between magnetic domains inthe Cu/Ni multilayer and ferroelectric domains in theBaTiO substrate. Correlations between the different fer-roic domains are preserved in an applied electric field, aspreviously demonstrated for magnetic films with in-planemagnetic anisotropy. Consequently, the magnetic andferroelectric domain walls move in unison. Electric-field-driven motion of the magnetic domain wall does not re-quire any assistance from a magnetic field or electricalcurrent.The domain wall velocity ( v ) varies with the strengthof applied electric field. To extract the v − E dependence,we adjust the duration of the voltage pulses (∆ t ) to thestrength of the applied electric field, so that the dis-placement of domain walls is accurately measured (typ-ically ∆ x ≈ µ m). From the data, the velocity ( v )of electric-field-driven magnetic domain walls is derived( v = ∆ x /∆ t ). Figure 3(b) summarizes the results forpositive and negative out-of-plane field pulses. For both (b)(a) µ m FIG. 3. (a) Sequence of MOKE microscopy images demon-strating reversible electric-field-driven magnetic domain wallmotion in the Cu/Ni multilayer. Images with black (red) dotsare recorded after the application of a positive (negative) fieldpulse across the BaTiO substrate. The strength of the elec-tric field is ± pulse polarities, the domain wall velocity increases byfive orders of magnitude when the electric field is en-hanced from 2 kV/cm to 15 kV/cm. The exponentialvariation of v with E is explained by thermally assisteddepinning of the ferroelectric domain wall in the BaTiO substrate. The maximum domain wall velocity in ourproof-of-concept experiments is 1 cm/s. Despite beingrelatively small compared to current-driven magnetic do-main wall motion, it is three orders of magnitude fasterthan our previous result on 20-nm-thick Fe films within-plane magnetic anisotropy. This observation demon-strates that exponential scaling of the domain wall ve-locity persists up to large electric field. Further enhance-ments of the maximum velocity would require the use ofultrashort and even stronger field pulses. An extrapola-tion of the data in Fig. 3(b) suggests that E ≈
30 kV/cmcould possibly increase the domain wall velocity to 100m/s. For reasonably small voltages, this is only achievedwhen the thickness of the BaTiO layer is reduced from500 µ m (this study) to < µ m. Since it is not obvioushow downscaling affects the dynamics of ferroelectric do-main walls, this open question needs to be addressed infuture studies.To assess domain wall dynamics at high velocities, we performed micromagnetic simulations using MuMax3. In the simulations, a 2-nm-thick Ni layer is discretizedinto 2 . × . M s = 4 . × A/m, an exchange constant A = 7 . × − J/m, anda damping parameter α = 0.015. The application of anout-of-plane electric field is mimicked by fast lateral mo-tion of an anisotropy boundary that separates domainswith perpendicular and in-plane magnetization. Domainwall motion at velocity v is implemented by shifting theanisotropy boundary over one discretization cell (∆ x =2.5 nm) during each time window ∆ t = ∆ x / v of the sim-ulation. Two-dimensional periodic boundary conditionsare used. The micromagnetic simulations thus reflect thedynamic response of a continuous Ni/Cu multilayer ontop of BaTiO .Figure 4 shows an overview of simulation results. Un-der static conditions and zero magnetic field (Fig. 4(a)),the simulations reproduce the domain configuration inthe MOKE microscopy images of Figs. 2 and 3, i.e., onedomain with in-plane magnetization pointing towards thedomain wall and another domain with PMA. The 90 ◦ magnetic domain wall that separates the two domains isof the N´eel type. At high domain wall velocities v , themagnetization within the wall tilts towards the y -axis.The tilt angle depends on the direction of domain wallmotion and steadily grows with v . Above a critical veloc-ity v crit , here corresponding to the velocity at which themagnetization points along + y or − y , the spins withinthe magnetic domain wall start to precess continuously.This dynamic behavior, which is similar to Walker break-down in magnetic domain walls that are driven by a mag-netic field or electric current, results in the emissionof spin waves. Figure 4(d) shows an example.The application of a magnetic field does not move themagnetic domain wall, in agreement with experiments,but it changes its spin structure (Fig. 4(c)). Besides, amagnetic field either stabilizes or destabilizes the domainwall at high velocities, depending on the directions of ap-plied magnetic field and domain wall motion. In general,external magnetic fields that suppress magnetization tilt-ing towards the y -axis enhance the critical velocity. Thesimulated variations of v crit with in-plane magnetic fieldsalong the x - and y -axes are summarized in Fig. 4(e).In summary, we have demonstrated reversibleelectric-field-driven motion of magnetic domain wallsin perpendicularly magnetized Cu/Ni multilayers onferroelectric BaTiO substrates. The driving mechanismis based on strong elastic coupling between magnetic andferroelectric domains and does not require assistancefrom a magnetic field or electrical current. The velocityof the magnetic domain walls is fully determined bythe electric field strength. While not affecting magneticdomain wall motion, magnetic fields allow for versatiletuning of their internal spin structure. Electric andmagnetic fields can thus be used to independently moveand tailor magnetic domain walls in Cu/Ni multilayers. -30 -20 -10 0 10
20 30 -300-200-1000100200300 v c r i t ( m / s ) B y (mT) v = 0 m/sv = -240 m/sv = 240 m/s v= -400 m/sv = 0 m/sv = 400 m/s v = 295 m/sv = -190 m/sv = 0 m/s v = -295 m/sv = 0 m/sv = 190 m/sB x = 0 mTB y = 0 mT B x = 25 mTB y = 0 mT B x = 0 mTB y = 25 mT B x = 0 mTB y = -25 mT250 nm -400-300-200-1000100200300400 v c r i t ( m / s ) B x (mT) (d)(a) (b) (c) (e) y xzB x = 0 mT ; B y = 0 mT v = 260 m/s FIG. 4. (a)-(c) Micromagnetic simulations of the magnetic domain wall for zero and non-zero magnetic fields along the x - and y -axis. Colored arrows indicate the in-plane orientation of magnetization. The magnetization is oriented out-of-plane in whiteareas. In (a)-(c), v < v crit . (d) Spin wave emission from a moving domain wall for v > v crit . The double-headed arrow indicatesthe scale of all micromagnetic simulations. (e) Variation of critical domain wall velocity with magnetic bias field along the x -and y -axis. This work was supported by the European Re-search Council (ERC-2012-StG 307502-E-CONTROLand ERC-2014-PoC 665215-EMOTION), JSPS KAK-ENHI (Grant Nos. 15H01998, 15H01014, 16K14381),the Creation of Life Innovation Materials for Inter-disciplinary and International Researcher DevelopmentProject of MEXT, and the Collaborative ResearchProject of the Materials Structures Laboratory, TokyoInstitute of Technology. J. A. Currivan, Y. Jang, M. D. Mascaro, M. A. Baldo, and C. A.Ross, IEEE Magnetics Letters , 3000104 (2012). S. Parkin and S.-H. Yang, Nature Nanotechnology , 195(2015). I. M. Miron, T. Moore, H. Szambolics, L. D. Buda-Prejbeanu,S. Auffret, B. Rodmacq, S. Pizzini, J. Vogel, M. Bonfim,A. Schuhl, and G. Gaudin, Nature Materials , 419 (2011). S. Emori, U. Bauer, S.-M. Ahn, E. Martinez, and G. S. D. Beach,Nature Materials , 611 (2013). K.-S. Ryu, L. Thomas, S.-H. Yang, and S. Parkin, Nature Nan-otechnology , 527 (2013). A. J. Schellekens, A. van den Brink, J. H. Franken, H. J. M.Swagten, and B. Koopmans, Nature Communications , 847(2012). D. Chiba, M. Kawaguchi, S. Fukami, N. Ishiwata, K. Shima-mura, K. Kobayashi, and T. Ono, Nature Communications ,888 (2012). A. Bernand-Mantel, L. Herrera-Diez, L. Ranno, S. Pizzini, J. Vogel, D. Givord, S. Auffret, O. Boulle, I. M. Miron, andG. Gaudin, Applied Physics Letters , 122406 (2013). J. H. Franken, Y. Yin, A. J. Schellekens, A. van den Brink,H. J. M. Swagten, and B. Koopmans, Applied Physics Letters , 102411 (2013). U. Bauer, S. Emori, and G. S. D. Beach, Nature Nanotechnology , 411 (2013). U. Bauer, L. Yao, A. J. Tan, P. Agrawal, S. Emori, H. L. Tuller,S. van Dijken, and G. S. D. Beach, Nature Materials , 174(2015). P. M. Shepley, A. W. Rushforth, M. Wang, G. Burnell, andT. A. Moore, Scientific Reports , 7921 (2015). M. T. Johnson, P. J. H. Bloemen, F. J. A. den Broeder, andJ. J. de Vries, Reports on Progress in Physics , 1409 (1996). N. A. Pertsev, Physical Review B , 212102 (2008). Y. Shirahata, R. Shiina, D. L´opez Gonz´alez, K. J. A. Franke,E. Wada, M. Itoh, N. A. Pertsev, S. van Dijken, andT. Taniyama, NPG Asia Materials , e198 (2015). T. H. E. Lahtinen, K. J. A. Franke, and S. van Dijken, ScientificReports , 258 (2012). T. H. E. Lahtinen, J. O. Tuomi, and S. van Dijken, AdvancedMaterials , 3187 (2011). T. Mitsui and J. Furuichi, Physical Review , 193 (1953). K. J. A. Franke, B. Van de Wiele, Y. Shirahata, S. J. H¨am¨al¨ainen,T. Taniyama, and S. van Dijken, Physical Review X , 011010(2015). A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. Garcia-Sanchez, and B. Van Waeyenberge, AIP Advances , 107133(2014). C. Kittel, Reviews of Modern Physics , 541 (1949). H. Lassri, H. Ouahmane, H. E. Fanity, M. Bouanani,
F. Cherkaoui, and A. Berrada, Thin Solid Films , 245 (2001). N. L. Schryer and L. R. Walker, Journal of Applied Physics ,5406 (1974). A. Thiaville, Y. Nakatani, J. Miltat, and Y. Suzuki, Europhysics Letters , 990 (2005). J. Shibata, G. Tatara, and H. Kohno, Journal of Physics DApplied Physics , 384004 (2011). B. Van de Wiele, L. Laurson, K. J. A. Franke, and S. van Dijken,Applied Physics Letters104