Theory of thermomagnonic torques in altermagnets

Abstract

We develop a theory of thermomagnonic torques in insulating altermagnets and predict a spin-splitter magnonic torque arising from the spin Seebeck effect. Additionally, we predict an anisotropic entropic torque. We study the effects of these torques on magnetic-texture dynamics and identify various anisotropic responses to temperature gradients. In particular, we predict spin-current-induced domain-wall precession, which can slow domain-wall motion for certain temperature-gradient directions. We also predict a temperature-gradient-driven anisotropic skyrmion Hall effect that enables fast skyrmion motion in response to thermal gradients. Our findings will be useful for spintronic applications such as magnetic racetrack memories and will serve as a hallmark of altermagnetism in insulating altermagnets with magnetic textures.

Figures (4)

• Figure 1: A minimal model of a two-sublattice altermagnet. The two magnetic sublattices are shown as red and blue dots. The exchange interactions are indicated by double arrows. The unit cell, of area $v=a_0^2$, contains two magnetic sites. The temperature gradient $\boldsymbol\nabla T$ is applied at an angle $\Theta$ with respect to the $x$ axis.
• Figure 2: Entropic and magnonic spin-splitter torques in an altermagnet, calculated using linear-response theory for the model in Eq. \ref{['eq:Halt']}. Here $u_0=\nabla (k_B T)/s$, $J_1=11.1~\mathrm{meV}$, $J_2=-0.28~\mathrm{meV}$, $J_2^\prime=-3.48~\mathrm{meV}$, and $K=0.047~\mathrm{meV}$.
• Figure 3: (a) The domain wall velocity, (b) the angular precession speed $\Omega$, and (c) the domain wall width $\Delta$ as a function of the strength of the entropic torque $\beta u$ for $\Theta=0$. (d) The domain wall velocity for different directions of the temperature gradient with respect to crystallographic axes described by $\Theta$. The magnonic spin transfer torque is chosen to roughly correspond to results in Fig. \ref{['fig:torques']}, i.e., $20\alpha u^\prime=\beta u$. The Gilbert damping is $\alpha=10^{-3}$ for the bold red, $\alpha=2\cdot10^{-3}$ for the dotted blue, and $\alpha=3\cdot10^{-3}$ for the dashed green curves.
• Figure 4: (a) Components of the skyrmion velocity, $v_x$ and $v_y$, for different directions of the temperature gradient $\boldsymbol{\nabla}T$ with respect to the crystallographic axes, parameterized by $\Theta$. The temperature gradient corresponds to $\beta u/c=10^{-5}$. (b) Skyrmion velocity component parallel ($v_{\parallel}$) and perpendicular ($v_{\perp}$) to $\boldsymbol{\nabla}T$ as a function of the strength of the entropic torque $\beta u$. The results are shown for $\Theta=0$ and $\Theta=\pi/4$. Since $v_{\perp}^{\pi/4}=0$, the corresponding curve is not shown. In all plots, the magnonic spin-transfer torque is chosen to roughly match the results in Fig. \ref{['fig:torques']}, i.e., $20\alpha u^\prime=\beta u$. The Gilbert damping is $\alpha=3\times10^{-3}$.