Abstract
A fundamental form of magnon-phonon interaction is an intrinsic property of magnetic materials, the “magnetoelastic coupling.” This form of interaction has been the basis for describing magnetostrictive materials and their applications, where strain induces changes of internal magnetic fields. Different from the magnetoelastic coupling, more than 40 years ago, it was proposed that surface acoustic waves may induce surface magnons via rotational motion of the lattice in anisotropic magnets. However, a signature of this magnon-phonon coupling mechanism, termed magneto-rotation coupling, has been elusive. Here, we report the first observation and theoretical framework of the magneto-rotation coupling in a perpendicularly anisotropic film Ta/CoFeB(1.6 nanometers)/MgO, which consequently induces nonreciprocal acoustic wave attenuation with an unprecedented ratio of up to 100% rectification at a theoretically predicted optimized condition. Our work not only experimentally demonstrates a fundamentally new path for investigating magnon-phonon coupling but also justifies the feasibility of the magneto-rotation coupling application.
INTRODUCTION
In a general description, a rectification consists of passing signals in one direction while suppressing those in the opposite direction in a counterpropagation scenario. The best-known example of a rectifier is the electronic diode that converts AC to DC, allowing the development of the huge electronic industry we have today. Despite the great success of the electronic rectifier, challenges remain open, such as efficient rectifiers of small dimensions at high frequencies. Therefore, rectification of other energy entities has been intensively explored, in the form of acoustic rectifiers (1, 2), thermal rectifiers (3), magnon rectifiers (4), and photon rectifiers (5). Here, we demonstrate a giant nonreciprocal behavior of an on-chip acoustomagnetic rectifier at room temperature and gigahertz frequency. Our device exploits the magnon-phonon coupling by which surface acoustic waves (SAWs) interact with ferromagnetic (FM) films and consequently generate spin waves.
At a resonance condition, the coupling of SAWs with magnetic films produces acoustically driven FM resonance (a-FMR) (6, 7). Consequently, the a-FMR generates a spin current that can be converted to charge current by the inverse Edelstein effect (8) or spin Hall effect (9). Evidence of nonreciprocal behaviors in attenuation of amplitudes was reported when SAWs interacted with magnetic films (8, 10, 11). In these works, the origin of the nonreciprocal behaviors was attributed to magnetoelastic coupling that induced attenuation, and the interference between the longitudinal and shear components of the strain tensor in SAWs. However, in the thin-film limit, kd ≪ 1, where k > 0 is the absolute value of the wave number of SAWs and d is the film thickness, the shear strain is strongly diminished, and the remaining longitudinal strain is expected to induce only reciprocal magnetization dynamics, ergo limiting the nonreciprocity (NR) that can be achieved. For Rayleigh-type SAWs, there is an additional dynamical component that survives in the thin-film limit, the rotation tensor of elastic deformation,
Depending on the propagation direction, SAWs rotate the lattice in opposite directions (as indicted by the blue and red oriented cycles in the figure). This rotational motion couples with the magnetization via magnetic anisotropies, giving rise to a circularly polarized effective field, which either suppresses or enhances the magnetization precession (purple cone), and, in turn, induces a nonreciprocal attenuation on the SAWs.
RESULTS
Figure 2A shows the schematics of SAW propagation through a heterostructure, which consists of four layers, Ta(10 nm)/Co20Fe60B20(1.6 nm)/MgO(2 nm)/Al2O3(10 nm), on a piezoelectric substrate, Y-cut LiNbO3. The acoustic waves are excited by applying a radio frequency (rf) voltage on the input port of interdigital transducers (IDTs), which were patterned by electron beam lithography (EBL). Because of the inverse piezoelectric effect, the rf voltage at a frequency of 6.1 GHz induces vibrations of the lattice, launching SAWs propagating parallel to the x axis (see the coordinate system in Fig. 2A). When SAWs propagate through the heterostructure, the oscillation of the lattice points inside the magnet induces an effective rf magnetic field via cubic magnetoelastic coupling and the magneto-rotation coupling. Under a static in-plane external magnetic field H = H(cosϕ, sinϕ, 0), spin waves are excited, which results in SAW attenuation (see Fig. 2B). After passing through the heterostructure, the remaining SAWs are converted back into an rf voltage signal via piezoelectric effect on the output port IDTs. The attenuation was characterized by a vector network analyzer, based on the scattering parameters, S21 and S12. By measuring S21 and S12, we investigated the SAWs propagating along +x and −x direction, respectively, referred to as +k and −k from here on.
(A) Device schematics of SAWs coupling to an FM layer at gigahertz frequencies. (B) Attenuation of acoustic waves, P±k, near a spin-wave resonance condition for SAW numbers +k and −k. arb. units, arbitrary units.
Figure 2B shows attenuation spectra for SAW (+k) and SAW (−k) when an external magnetic field was applied at ϕ = 10∘ in the xy plane. The external magnetic field was initially set to 200 mT to saturate the magnetic film and then swept from 120 to 70 mT in 0.5 mT steps. a-FMR is obtained at an external field value of 96 mT, inducing magnetic field–dependent SAW attenuations. However, in the spectra, the SAW (+k) shows a negligible attenuation P+k, while SAW (−k) shows a relatively large attenuation P−k. The large difference indicates a strong nonreciprocal behavior and, therefore, a strong rectifier effect on acoustic waves. From this, we extract the NR ratio (P+k − P−k)/(P+k + P−k), which depends on the magnetic field direction, and plot it in Fig. 3. The NR shows a strong dependence on the magnetic field direction with respect to the SAW propagation direction
The magnetic field direction is varied with respect to the SAW propagation direction
To understand the origin of the giant NR, we theoretically model the magnetization dynamics driven by propagating SAWs in FM thin films. Treating the film as an isotropic elastic body, SAWs propagating along x axis are fully characterized by the nonvanishing components εxx, εxz, and εzz of the strain tensor
The SAW attenuation P±k is related to the power dissipated by the spin waves excited by the elastic effective field h. It can be readily computed as a function of the magnetization angle ϕ, whose details are given in the Supplementary Materials. The formula taking into account of exchange interaction, the uniaxial and cubic magnetic anisotropy, dipole-dipole interaction, and the Dzyaloshinskii-Moriya interaction (DMI) induced by the inversion symmetry breaking at the interface has been used to fit the data in Fig. 3. The agreement is quantitative, suggesting that the magneto-rotation coupling is responsible for the giant NR.
So far, we focused on the nonreciprocal behavior of SAW attenuation P±k. In addition, we observed a nonreciprocal behavior in the resonance field
With the a-FMR, we observe a clear difference under the resonance condition of the acoustic waves with the spin waves in the 1.6-nm-thick CoFeB layer (see Fig. 4A). After obtaining the resonance field
(A) Resonance field difference ΔHres between acoustomagnetic waves was induced by SAWs propagating in +k and −k. (B) Angle dependence of the resonance field difference between acoustomagnetic waves induced by SAWs with wave numbers +k and −k fitted according to Eq. 2.
DISCUSSION
In conclusion, we demonstrated strongly nonreciprocal acoustic attenuation in power (Fig. 2B) and resonance field (Fig. 4A) separately. These intriguing nonreciprocal features of the presented acoustic devices suggest an extraordinary versatility of acoustomagnetic applications. The marked angular dependence of the nonreciprocal ratio (Fig. 3) indicates an efficient and adjustable acoustic rectifier, and the systematic change of NR in resonance field (Fig. 4B) presents its capability as a new route for characterization of DMI. Besides, since the NR introduced here stems from the magnetic anisotropy, it can be further modulated by external electric field, as has been reported for the CoFeB/MgO interface (18). Considering the wide application of the general acoustic device in sensing, filtering, and information transportation, utilization of acoustic-magneto rectifier would not only provide highly accurate methods for sensing magnetic properties but also further advance the present acoustic technology and eventually push the development of acoustomagnetic logic devices as an attractive alternative to their magnonic counterparts (19, 20).
MATERIALS AND METHODS
Device fabrication
Figure 2A shows the schematics of SAWs propagation through a heterostructure, which consists of four layers, Ta(10 nm)/Co20Fe60B20(1.6 nm)/MgO(2 nm)/Al2O3(10 nm), grown by rf sputtering on a piezoelectric substrate, Y-cut LiNbO3.
SUPPLEMENTARY MATERIALS
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/32/eabb1724/DC1
This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.
REFERENCES AND NOTES
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