Helicity-Selective Phonon Absorption and Phonon-Induced Spin Torque from Interfacial Spin-Lattice Coupling

Abstract

In magnetic heterostructures with broken inversion symmetry, the Rashba effect gives rise to a gradient-free interaction between magnons and phonons, which we term interfacial spin-lattice coupling. Here, we investigate the dynamic consequences of this interfacial coupling in ferromagnetic heterostructures. By expressing the interaction in terms of circular variables for magnetization and lattice displacement, we reveal a direct interface-induced helicity-helicity coupling hat does not rely on lattice deformation gradients. Consequently, it leads to helicity-dependent phonon absorption, enabling in-plane acoustic waves to exert a spin torque on the magnetization, which becomes dominant in thin magnetic films. Our findings highlight the crucial, yet overlooked, role of inversion-asymmetric interfaces in angular-momentum conversion between spin and lattice, opening up possibilities for efficient phonon-driven magnetic devices that are enabled by interface engineering.

Figures (8)

• Figure 1: Schematic illustration of helicity-dependent phonon absorption and phonon-induced spin torque. A linearly polarized acoustic wave propagating on a substrate can be decomposed into CCW (blue) and CW (red) circular components. Upon interacting with the normal metal/ferromagnet (NM/FM) bilayer, the CCW phonon resonantly couples to the magnetization precession and is absorbed, thereby exerting a spin torque. In stark contrast, the off-resonant CW phonon propagates freely through the heterostructure without absorption, realizing a magnetization-controlled helicity filter for phonons.
• Figure 2: Magnon–phonon hybrid dispersion. (a) Dispersion relations of magnons and phonons along $k_x$ ($k_y = 0$) in the absence of interfacial spin-lattice coupling ($\lambda_{SL}=0$). The dashed line represents the magnon mode, while the solid lines denote the linear dispersions of the longitudinal and transverse phonon modes. (b) Hybridized dispersions in the presence of interfacial spin-lattice coupling. The color scale illustrates the phonon helicity weighted by the phonon energy ratio: $h = \frac{|u_+|^2 - |u_-|^2}{|u_+|^2 + |u_-|^2} \frac{E_\text{ph}}{E_\text{ph} + E_\text{mag}}$ , where $E_\text{ph}$ ($E_\text{mag}$) denotes the bare phonon (magnon) energy. The results are obtained for an effective magnetic field of $B_{\text{eff}}=0.056$ T.
• Figure 3: Helicity-dependent phonon absorption and propagation length. (a,b) Phonon absorption rates, $\Gamma_\text{SL}=\Delta P/\langle \mathcal{E}_\text{ph}\rangle$, for (a) CCW and (b) CW helicities, with the transferred power from phonons to magnons $\Delta P$ [Eq. \ref{['DeltaP']}]. (c,d) Corresponding phonon propagation lengths, $l_{\text{ph}}\approx v_g/(\Gamma_0+\Gamma_\text{SL})$, with $v_g$ the group velocity, $\Gamma_0=\omega/Q$ the intrinsic phonon damping rate and $Q$ the phonon quality factor. The parameters used are $B_{\text{eff}}=0.056$ T, $\alpha=0.1$, and $Q=1000$.
• Figure 4: Phonon-driven magnetization precession and ensuing spin pumping. (a, c) Amplitudes of magnetization precession [Eq. \ref{['Lmeq']}] and (b, d) the corresponding spin current profiles [Eq. \ref{['Jpump']}]. The results are obtained for effective magnetic fields of $B_{\text{eff}} = 0.056$ T [top panels: (a, b)] and $B_{\text{eff}} = 0.1$ T [bottom panels: (c, d)]. The color map shows the pumped spin current density, expressed in electrical units as $J_s = \frac{2e}{\hbar} j_s^\text{pump}$. The parameters used are $\alpha=0.1$ and $u_0 = 3.5$ pm.
• Figure S1: Magnon-phonon hybrid band structures. Hybridized dispersions in the presence of interfacial spin-lattice coupling for (a) $\theta = 0$, (b) $\theta = \pi/4$, and (c) $\theta = \pi/2$. The color scale illustrates the phonon helicity weighted by the phonon energy ratio: $h = \frac{|u_+|^2 - |u_-|^2}{|u_+|^2 + |u_-|^2} \frac{E_\text{ph}}{E_\text{ph} + E_\text{mag}}$ , where $E_\text{ph}$ ($E_\text{mag}$) denotes the bare phonon (magnon) energy.