Chirality and polarization of inertial antiferromagnetic resonances driven by spin-orbit torques

TL;DR

This work demonstrates that inertial spin dynamics in antiferromagnets can be actively controlled by two orthogonal spin-orbit torques, enabling continuous tuning of resonance polarization from elliptic to circular to linear and enabling handedness switching at inertia-dependent critical ratios $r_n$ and $r_p$. Using a minimal inertial LLG framework for a bilayer AFM/HM system, the authors derive analytic expressions for resonant frequencies $\omega_{n,p}$ and peak amplitudes, highlighting how inertia shifts and enhances polarization ellipticity. Crucially, the critical ratios $r_n(\eta)$ and $r_p(\eta)$ depend on the inertial relaxation time, yielding region-like phase diagrams where sublattices can exhibit different polarization states and opposite handedness for the same resonance. The findings provide a practical route to measure the inertial time $\eta$ via polarization switching and establish a richer polarization/handedness landscape for AFMs than for ferromagnets, with potential uses in spin-wave-based information processing.

Abstract

It is widely accepted that the handedness of a resonant mode is an intrinsic property. We show that, by tailoring the polarization and handedness of alternating spin-orbit torques used as the driving force, the polarization state and handedness of inertial resonant modes in an antiferromagnet (AFM) can be actively controlled. In contrast with ferromagnets, whose resonant-mode polarization is essentially fixed, AFM inertial modes can continuously evolve from elliptic through circular to linear polarization as the driving polarization is varied. We further identify an inertia-dependent critical degree of driving polarization at which the mode becomes linearly polarized while its handedness reverses.

Figures (8)

• Figure 1: (color online). Schematic diagram of model.
• Figure 2: (color online). AFM spectra without spin inertia exhibit the single precessional resonance (dashed lines, $\eta=0$). Finite spin inertia $\eta>0$ shifts the precessional AFM resonance and induces the additional nutational resonances (solid lines). Peaks labeled with red (purple) points correspond to precessional (nutational) resonances. Both axes are shown on a logarithmic scale; low-frequency parts are omitted for clarity. Curves are evaluated from Eq. (\ref{['amplitude']}) using $\omega_{E}=9.25$ THz, $\omega_{K}=0.14$ THz, $\alpha=0.01$, $\beta=0.02$, $J_{x}=1$ GA$/$m$^{2}$, $J_{y}=2$ GA$/$m$^{2}$, and $\rho\approx0.13$ Hz$/$(A$/$m$^{2}$). The values of $\omega_{E}$, $\omega_{K}$, and $\rho$ are derived from the magnetic parameters of MnF$_{2}$PVaidya for a film thickness $d=3$nm and SOT efficiency $\xi=0.32$.
• Figure 3: (color online). (a) Resonant frequencies as a function of $\eta$. Curves are computed from Eq. (\ref{['resonant frequency']}). A logarithmic scale is used on the frequency axis, and low-frequency regions are omitted for clarity. (b) and (c) show the dependence of peak heights on $\eta$ for precession and nutation, respectively. Curves are computed from Eqs. (\ref{['peak heights of precession']}) and (\ref{['peak heights of nutation']}). The parameters used are the same as in Fig. \ref{['spectrum_all']}.
• Figure 4: (color online). Ellipticity (upper row) and inter-component phase difference (lower row) as functions of the current ratio $J_{y}/J_{x}$ at positive frequencies for several values of $\eta$. Panels (a)-(d) present the nutational modes of sublattices 1 and 2, while (e)-(h) display the corresponding precessional modes. The curves are calculated with Eqs. (\ref{['en']}), (\ref{['ep']}), and (\ref{['phase dfferences at resonance']}). Parameters are identical to those in Fig. \ref{['spectrum_all']}.
• Figure 5: (color online). Polarization and handedness of resonant modes for four branches ($\pm\omega_{p}$, $\pm\omega_{n}$) at various values of $J_{y}/J_{x}$. The inertial relaxation time is set to $\eta=100$ fs, yielding $r_{n}=1.6855$ and $r_{p}=19.4488$ from Eq. (\ref{['rnp']}). In each panel, the horizontal and vertical axes correspond to $m_{x}$ and $m_{y}$ components, respectively. Curves represent the magnetization orbits, and arrows indicate the sense of rotation. In the panels in columns 1-5, $J_{x}=1$GA$/$m$^{2}$ and $J_{y}$ is calculated by the ratio $J_{y}/J_{x}$. In the panels in columns 6-9, $J_{y}=1$GA$/$m$^{2}$ and $J_{x}$ is calculated by the ratio.