Micromagnetic Modeling of Surface Acoustic Wave Driven Dynamics: Interplay of Strain, Magnetorotation, and Magnetic Anisotropy

Abstract

We study the coupling mechanism of surface acoustic waves (SAW) with spin waves (SW) using micromagnetic analysis. The SAW magnetoacoustic excitation field is fully implemented, i.e., all strain and lattice-rotation terms are included. A realistic CoFeB film with a weak in-plane uniaxial anisotropy is considered. We investigate the conditions for efficient SAW--SW coupling, with particular emphasis on the case where the SAW propagates parallel to the external magnetic field, a configuration of special interest for magnonic applications. Remarkably, we find that the anisotropy orientation serves as a knob to tune the parallel resonant interaction. Overall, this work provides a unified and practical picture of SAW--SW coupling in thin magnetized films.

Figures (4)

• Figure 1: a) Geometry of the problem and definitions. The slab has dimensions of $\ell_x=\ell_y= \lambda_{\textrm{SAW}}$, $\ell_z=34$ nm and is meshed into $\{N_x,N_y,N_z\}=\{128,128,1\}$. An in-plane static field $\vec{B}_0$ is applied with an angle $\psi$ with respect to $\vec{k}_{\textrm{SAW}} = k_\textrm{SAW}.\hat{\vec{x}}$. A weak uniaxial anisotropy field $\vec{B}_{u}$ with an angle $\varphi_u$ is introduced in the system. EA stands for easy axis. b) Symmetry of the SAW--SW coupling strength $\Delta P(\psi)$ at $f_{\textrm{SAW}}=1.72$ GHz and $B_0=1.5$ mT. The material parameters used in the simulations are as follows. SAW parameters: velocity $v_{\textrm{SAW}}=3870$ m/s, wavevector $|\vec{k}_{\textrm{SAW}}| = 2.8$ rad/$\mu$m, longitudinal strain $\varepsilon_{xx}=0.75 \times10^{-5}$, shear strain $\varepsilon_{xz}=0.05\times10^{-5}$, lattice rotation $\omega_{xz}=1\times10^{-5}$ [lopes_seeger_symmetry_2024]; Magnetics: Saturation magnetization $M_s=1.35$ MA/m, Exchange coupling $A_{\textrm{ex}}= 21$ pJ/m, Gilbert damping $\alpha_G=0.01$, Shape anisotropy $B_{\textrm{shape}}=1$ mT, Magnetoelastic coupling $B_1= B_2=-7.6$ MJ/m$^3$. The vertical dashed line marks $\psi=180^\circ$.
• Figure 2: 2D maps of the SAW--SW coupling strength $\Delta P(B_0,\psi)$ highlighting the interplay of anisotropy with magnetoacoustic excitation. Left column: $\varepsilon_{xx}$ (& $\varepsilon_{xz}$). Right column: full magnetoacoustic drive including strain and rotation ($\varepsilon_{\mu\nu}\,\textrm{and}\,\omega_{\mu\nu}$). (a,b) In the absence of anisotropy $B_u=0$. (c,d) Weak anisotropy $B_u=1.5$ mT oriented at $\varphi_u=105^\circ$. The horizontal dashed line marks $\psi=180^\circ$.
• Figure 3: 2D maps of the SAW--SW coupling strength $\Delta P(\psi,\varphi_u)$, where $\varphi_u$ is varied in increments of $15^\circ$ and $\psi$ in increments of $1^\circ$, at fixed uniaxial anisotropy field $B_u=1.5$ mT, including full magnetoacoustic drive, with strain and rotation ($\varepsilon_{\mu\nu}\,\textrm{and}\,\omega_{\mu\nu}$). Polynomial nth-order interpolation is applied between simulated $\varphi_u$-curves. Left column: $B_0=1.5$ mT. Right column: $B_0=5$ mT. (a,b) $f_{\textrm{SAW}}=1.72$ GHz. (c,d) $f_{\textrm{SAW}}=3.44$ GHz. The horizontal dashed line marks $\psi=180^\circ$.
• Figure 4: 2D maps of the SAW--SW coupling strength $\Delta P(f_{\textrm{SAW}},\psi)$ for $B_u=1.5$ mT and $\varphi_u=120^\circ$. a) field strength $B_0=1.5$ mT. b) $B_0=5$ mT. Parameters used in this simulation are: $|\vec{k}_{\textrm{SAW}}|=v_{\textrm{SAW}}/2\pi f_{\textrm{SAW}}$, full magnetoacoustic drive including strain and rotation ($\varepsilon_{\mu\nu}\,\textrm{and}\,\omega_{\mu\nu}$). The horizontal dashed line marks $\psi=180^\circ$. The arrows show the intersection at which the parallel SAW--SW interaction occurs.