RESEARCH ARTICLE | MARCH 17 2022 Zero-field routing of spin waves in a multiferroic heterostructure  Weijia Zhu ; Huajun Qin  ; Lukáš Flajšman ; Tomoyasu Taniyama ; Sebastiaan van Dijken  Appl. Phys. Lett. 120, 112407 (2022) https://doi.org/10.1063/5.0086430 CrossMark   View Export Online Citation 11 December 2023 10:43:47 Applied Physics Letters ARTICLE scitation.org/journal/apl Zero-field routing of spin waves in a multiferroic heterostructure Cite as: Appl. Phys. Lett. 120, 112407 (2022); doi: 10.1063/5.0086430 Submitted: 25 January 2022 . Accepted: 7 March 2022 . Published Online: 17 March 2022 Weijia Zhu,1 Huajun Qin,1,a) s Flajsman,1 Luka Tomoyasu Taniyama,2 and Sebastiaan van Dijken1,a) AFFILIATIONS 1 NanoSpin, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland 2 Department of Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan a) Authors to whom correspondence should be addressed: huajun.qin@aalto.fi and sebastiaan.van.dijken@aalto.fi ABSTRACT We report zero-field routing of spin waves in a multiferroic heterostructure comprising a ferromagnetic Fe film and a ferroelectric BaTiO3 substrate with fully correlated strain-coupled domains. In the Fe film, a regular alternation of magnetic anisotropy produces a back-and-forth rotation of uniform magnetization in zero magnetic field. Spin waves propagating across this domain structure are refracted at the magnetic domain walls because of abrupt changes in the dispersion relation and phase velocity. Using super-Nyquist sampling magneto-optical Kerr 11 December 2023 10:43:47 effect microscopy, we image the routing of spin waves and analyze the dependence of the effect on frequency and the propagation direction. We find that spin waves are routed efficiently by angles up to 60 without measurable loss in amplitude. The experimental results are reproduced by micromagnetic simulations and calculations based on the modified Snell’s law for magnonics. Published under an exclusive license by AIP Publishing. https://doi.org/10.1063/5.0086430 Magnonics, using spin waves as information carriers for data spin-wave dispersion relation. The heterostructure can, therefore, be processing, transport, and storage, offers perspectives for low-power considered as an experimental demonstration of a refractive-index wave-like computing.1–6 Low-loss interconnects enabling the redirec- grating. Using super-Nyquist sampling magneto-optical Kerr effect tion of propagating spin waves are crucial for integrated magnonic cir- (SNS-MOKE) microscopy, we image zigzag-like routing of spin waves cuits. Curved waveguides have been considered as the prime candidate across multiple domains and gauge its dependence on the spin-wave to fulfill this function,7–11 but the steering of spin waves through bends frequency and the propagation direction. Our results are a step toward is complicated by scattering and inefficient mode conversion. Being the realization of voltage-controllable refractive-index gratings for inspired by optics, magnonic elements with a graded refractive index magnonics. have been proposed for the redirection and focusing of spin waves The Fe/BaTiO3 multiferroic heterostructure consists of fully cor- with low loss.12–18 In theory, a smooth spatial variation of the refrac- related ferroelectric/ferromagnetic domains, as illustrated in Fig. 1(a). tive index requires a gradual change of the saturation magnetization, Two strain-coupled domains alternate in the sample with a period of magnetic anisotropy, film thickness, or external magnetic field. 30 lm. Ferroelectric BaTiO3 domains with perpendicular polariza- Experimental proof-of-concepts of graded-index steering effects tion couple to Fe domains with biaxial magnetic anisotropy. The easy have been demonstrated using shape anisotropy12 and laser-induced axes of magnetization in these domains and the domain walls make an heating.19,20 Another means of redirecting spin waves is through an angle of 45 . Hereafter, we refer to them as c domains. BaTiO3 interface refraction effect, which is described by a modified version of domains with in-plane polarization couple to Fe domains with uniax- Snell’s law.21–26 Refraction in magnonics occurs when the dispersion ial magnetic anisotropy. The easy magnetization axis of these so-called relation of spin waves changes abruptly. In experiments, the effect has a domains aligns parallel to the domain walls. Because of the regular been demonstrated in magnetic films with a thickness step21,22 or a alternation of magnetic anisotropy, the magnetic domain walls in the magnetic domain wall.26 Fe film are pinned onto the ferroelectric boundaries of BaTiO3.27 In this Letter, we report on spin-wave refraction in a Fe/BaTiO3 In our experiments, the fully correlated multiferroic domain pat- multiferroic heterostructure. In our composite material system, strain- tern is formed during molecular beam epitaxy of a 26-nm-thick Fe coupling between the ferroelectric substrate and ferromagnetic film film onto a BaTiO3 substrate, as described elsewhere.28,29 Strain produces a regular alternation of magnetic anisotropy and the coupling of ferroelectric and ferromagnetic domains has been used to Appl. Phys. Lett. 120, 112407 (2022); doi: 10.1063/5.0086430 120, 112407-1 Published under an exclusive license by AIP Publishing Applied Physics Letters ARTICLE scitation.org/journal/apl FIG. 1. (a) Schematic of the sample and measurement geometry. Strain coupling between a BaTiO3 substrate and a Fe film produces a fully correlated multiferroic domain structure. In the Fe film, domains with biaxial and uniaxial magnetic anisotropy alternate. Spin waves are excited by a microwave antenna in a c domain, and their transport is imaged using SNS-MOKE microscopy in zero magnetic field. (b) MOKE microscopy image of the magnetic domain structure in the Fe film and the position of a microwave 11 December 2023 10:43:47 antenna patterned on top. The red arrows depict the direction of magnetization in the a and c domains. The dashed red box indicates the imaging area in SNS-MOKE micros- copy measurements. (c)–(e) SNS-MOKE microscopy images of spin-wave transport across a c  a  c domain structure recorded at 9.5 GHz (c), 10.5 GHz (d), and 11.5 GHz (e). The solid lines mark the location of magnetic domain walls. Arrows depict the direction of spin-wave propagation. Transport of spin waves across the magnetic domains is characterized by the incident angle a ¼ 45 , the refraction angle b, and the routing angle c, as illustrated in (c). b and c depend on the spin-wave frequency. control magnetic domain-wall motion29 and spin-wave propagation30 the magnetization direction [Damon–Eshbach (DE) transport geome- by an applied electric field. Here, we utilize the multiferroic hetero- try]. The angle of incidence, a, with respect to the domain wall is structure to investigate the redirection of spin waves when they propa- therefore 45 . The wavelength shortens and the propagation direction gate across a c  a  c domain pattern. Spin waves are excited by rotates when the spin waves enter the a domain. To quantify the redi- 3.5-lm-wide microwave antennas with a 3 nm Ta/120 nm Au struc- rection of spin waves, we define a refraction angle, b, and a routing ture, which are patterned onto the sample using laser-writing lithogra- angle, c ¼ a  b. The routing angle is largest just above the FMR fre- phy and liftoff. A 20-nm-thick insulating TaOx layer separates the quency of the c domain [c ¼ 41 at 9.5 GHz in Fig. 1(c)], and it microwave antennas from the Fe film. Spin-wave transport is imaged decreases at higher frequency [c ¼ 29 at 11.5 GHz in Fig. 1(e)]. After using SNS-MOKE microscopy. In this technique, the laser frequency transport across the 6-lm-wide a domain, the spin waves revert to comb down-converts the excited GHz magnetization dynamics to an their original wavelength and propagation direction when entering the intermediate frequency e, allowing tuning of the excitation signal to second c domain. The zigzag-like routing of spin waves that we any frequency fexc ¼ n  frep þ e. At non-zero e and with the excita- observe in our multiferroic heterostructure is analogous to the optical tion synchronized to a laser repetition rate of frep ¼ 80 MHz, the phase beam path in multilayers with alternating refractive indices. In mag- of the spin waves relative to the excitation signal is preserved by lock- nonics, a similar effect has been calculated in Refs. 13 and 14. In our in demodulation at e.31 Our home-built SNS-MOKE microscope uses experiments, the back-and-forth redirection of spin waves is caused a 515 nm laser with a spot size of 500 nm. Images are recorded by by a regular modulation of magnetic anisotropy induced by strain cou- scanning the Fe/BaTiO3 sample in front of the fixed laser spot with a pling to ferroelectric domains. piezo-controlled stage. In all experiments, the magnetization in the a We note that the 45 magnetic domain walls in our multiferroic and c domains is initialized by applying a magnetic field along the y heterostructure are transparent to propagating spin waves at axis. After the magnetic field is turned off, the magnetization aligns at 9:5–11:5 GHz. Using a different initialization process, the magnetiza- a 45 angle [see red arrows in Fig. 1(b)]. Spin-wave transport is imaged tion of neighboring domains can also align at a 135 angle in zero field. for this configuration in zero magnetic field. In this magnetization configuration, the pinned magnetic domain Figures 1(c)–1(e) show SNS-MOKE microscopy images of prop- walls partially reflect the incoming spin waves. Spin-wave reflection is agating spin waves at a frequency of 9.5 GHz [Fig. 1(c)], 10.5 GHz explained by the excitation of a domain-wall resonance, as previously [Fig. 1(d)], and 11.5 GHz [Fig. 1(e)]. In the experiments, spin waves reported for 90 magnetic domain walls in another multiferroic are excited within a c domain where they propagate perpendicular to heterostructure.32 Appl. Phys. Lett. 120, 112407 (2022); doi: 10.1063/5.0086430 120, 112407-2 Published under an exclusive license by AIP Publishing Applied Physics Letters ARTICLE scitation.org/journal/apl We performed micromagnetic simulations in MuMax333 to ana- angles b, as this parameter changes with frequency. Using the data in lyze the transport of spin waves across the c  a  c domain structure. Fig. 2(e), we also derive the frequency dependence of the phase veloc- Figure 2(a) illustrates the simulation geometry. We consider a 26-nm- ity in the two magnetic domains for a ¼ 45 and b ¼ 0 , i.e., for DE thick Fe film and an area of 115  115 lm2, discretized into spin waves in the c and a domains [Fig. 2(f)]. Clearly, the difference in 4  4  26 nm3 cells. In the simulations, a 10-lm-wide a domain sepa- phase velocity diminishes at higher frequency. rates two larger c domains. The uniaxial and biaxial anisotropy values Transport of spin waves across the magnetic domains of our are set to Ka ¼ 15  103 and Kc ¼ 44  103 J/m3, which we experi- multiferroic heterostructure is described by a modified version of mentally derived from ferromagnetic resonance measurements on sin- Snell’s law.21–26 For spin waves traveling from a c domain into an a gle a and c domains.30 Saturation magnetization Ms ¼ 1705 kA/m and domain across a pinned magnetic domain wall, Snell’s law postulates Gilbert damping parameter a ¼ 0:002, also extracted from experi- that the incident angle and wave vector in the c domain and the refrac- ments,30 and exchange constant Aex ¼ 21 pJ/m34 are the other input tion angle and wave vector in the a domain relate as parameters. Spin waves are excited locally by a 1 mT in-plane sinusoi- dal magnetic field applied over a 400-nm-wide area in the c domain, sin a krefr ¼ : (1) as indicated by the yellow bar in Fig. 2(a). No magnetic field is applied sin b kin in the simulations. The wave vectors in this expression can be calculated using the spin- Figures 2(b)–2(d) show simulated spatial maps of propagating wave dispersion relation, which is given by Ref. 35, spin waves at a frequency of 9.5 GHz [Fig. 2(b)], 10.5 GHz [Fig. 2(c)], sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi    and 11.5 GHz [Fig. 2(d)]. The simulation results and the SNS-MOKE 2AxM k2 2AxM k2 microscopy measurements shown in Figs. 1(c)–1(e) agree well. From f ¼ xH þ x H þ þ x M F : (2) the datasets, we extract the wave vectors of the propagating spin waves l0 Ms2 l0 Ms2 in the two magnetic domains as a function of frequency. The results In this expression, F ¼ Pk þ sin d2 ½1  Pk ð1 þ cos h2 Þ are plotted in Fig. 2(e), together with calculations based on the k ð1Pk Þ sin h 2 Kalinikos and Slavin model.35 The dispersion curve of the c domain at þ xM xHPþ2Ax 2 ; Pk ¼ 1  1expkdðkdÞ ; xM ¼ cl0 Ms ; and xH M k =l0 Ms 2 a ¼ 45 is shifted up in frequency compared to that of the a domain, ¼ cl0 Hani , where Ms is the saturation magnetization, h is the angle which explains the wavelength up and downconversion when spin between the wave vector k and the magnetization direction, Hani is the waves travel from c to a and from a to c, respectively. For the a magnetic anisotropy field, and d is the Fe film thickness. In Fe/BaTiO3 11 December 2023 10:43:47 domain, we calculate the dispersion relation for different refraction with in-plane magnetization, d ¼ p=2; c=2p ¼ 29 GHz/T, and FIG. 2. (a) Schematic of the c  a  c domain structure used in micromagnetic simulations. Red arrows depict the magnetization direction in the domains. (b)–(d) Simulated spatial maps of spin-wave transport at 9.5 GHz (b), 10.5 GHz (c), and 11.5 GHz (d). The displayed area corresponds to the dashed box shown in (a). Red arrows indicate the direction of spin-wave propagation. (e) Measured (solid symbols), simulated (empty symbols), and calculated (lines) spin-wave dispersion relations for the a and c domains. (f) Phase velocity of DE spin waves in the a and c domains as a function of frequency. Appl. Phys. Lett. 120, 112407 (2022); doi: 10.1063/5.0086430 120, 112407-3 Published under an exclusive license by AIP Publishing Applied Physics Letters ARTICLE scitation.org/journal/apl Hani ¼ 2Kc =Ms for the c domain and Hani ¼ 2Ka =Ms for the a in Figs. 3(b)–3(d)], while a decrease in the a domain width would have domain. In our experiments, the incident angle a is fixed by the orien- the opposite effect. Combined with large and tunable routing angles in tation of the microwave antenna and kin can be calculated using zero magnetic field, this sets the stage for all-electrical signal modula- Eq. (2). Knowing a and kin, the refraction angle b and the wave vector tion in magnonic refractive-index gratings. in the a domain are then derived from Eqs. (1) and (2). Figure 3(a) compares the calculated routing angle (c ¼ a  b) to This project has received funding from the European Union’s the experimental and simulation results for a ¼ 45 . Good agreement Horizon 2020 research and innovation programme under the Marie between the three data sets confirms the validity of Snell’s law. At Skłodowska-Curie grant agreement No. 861145. The work was a ¼ 45 , the routing angle diminishes from about 45 to 20 when the supported by the Academy of Finland (Grant Nos. 317918 and frequency increases from 9.5 to 20 GHz. A smaller difference in phase 325480), JST CREST under Grant No. JPMJCR18J1, and JSPS velocity between the c and a domains at high frequency explains this KAKENHI under Grant No. 21H04614. Lithography was effect [Fig. 2(f)]. Larger routing angles can be attained by increasing performed at the OtaNano—Micronova Nanofabrication Centre of the angle of incidence, as demonstrated for a ¼ 60 in Fig. 3(b). Aalto University. Computational resources were provided by the Together with the data for a ¼ 30 [also shown in Fig. 3(b)], it is clear Aalto Science-IT project. that the routing angle c equals a (i.e., b ¼ 0 ) at the onset of spin- wave transport (f  9:5 GHz) for all incident angles. Tuning of spin- AUTHOR DECLARATIONS wave routing by the angle of incidence at f ¼ 10.5 GHz is depicted in Conflict of Interest Fig. 3(c). Finally, we illustrate how the routing angle changes as a func- The authors have no conflicts to disclose. tion of magnetic anisotropy strength. The data depicted in Fig. 3(d) are calculated at 13.5 GHz for a varying anisotropy strength in the c DATA AVAILABILITY domain, while keeping the anisotropy value of the a domain constant The data that support the findings of this study are available at Ka ¼ 15  103 J/m3. In multiferroic heterostructures, the magnetic from the corresponding author upon reasonable request. anisotropy strength can be tuned by interface strain engineering or the selection of ferromagnetic materials with different magnetostriction REFERENCES constants. 1 A. Khitun, M. Bao, and K. L. Wang, “Magnonic logic circuits,” J. Phys. D. 43, Our results open up perspectives for voltage-controlled routing 11 December 2023 10:43:47 264005 (2010). of spin waves. The Fe/BaTiO3 multiferroic heterostructure enables 2 A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, “Magnon reversible control over the width of the a and c domains by the appli- spintronics,” Nat. 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