Magnon-Driven Anomalous Hall Effect in Altermagnets

Abstract

We propose a magnon-driven anomalous Hall effect in altermagnets, arising from the coupling between coherently excited chiral magnons and chiral electronic motion. Using density-matrix perturbation theory and symmetry analysis, we show that the resulting Hall conductivity is solely determined by the chiralithy of the Néel-order precession, in sharp contrast to the anomalous Hall effect from the equilibrium Néel order. It then has distinct symmetry requirements from the latter and can exist even when the latter is forbidden by symmetry. The magnon-driven anomalous Hall effect is exemplified in a minimal lattice model with the same symmetry of the altermagnet CrSb, which hosts no static anomalous Hall effect. Our results reveal a direct interplay between chiral magnons and chiral electronic motion, paving the way of probing magnon chirality and to control electronic chirality through magnons.

Figures (2)

• Figure 1: The magnon-driven anomalous Hall effect. (a) Hall-type response driven by Néel vector precession. (b) physical origin of the magnon-driven anomalous Hall effect: two chiral directions are present in altermagnets, the Néel order and its precession direction; the anomalous Hall effect can arise from either chiral direction but only in the later case, the opposite local spin orders contribute constructively.
• Figure 2: Magnon-driven anomalous Hall effect in an altermagnetic minimal model. (a) The lattice structure. (b) Band structure of the minimal model in the absence of spin-orbit coupling. The $k$-path are $-M'=(-0.5,0,0.25)$, $\Gamma'=(0,0,0.25)$, and $M'=(0.5,0,0.25)$. (c), (d) Spin-up and spin-down Fermi surfaces in $k_x-k_y$ plane at $k_z=\pi/2$ (without spin-orbit coupling), together with the Berry curvature $\Omega_z(\boldsymbol{k})$ in (c) and the magnon-driven anomalous Hall response coefficient $\tilde{\chi}_{zz}(\boldsymbol{k})$ in (d) (arbitrary units). (e) Magnon-driven anomalous Hall coefficient $\tilde{\chi}_{zz}$ as a function of Fermi energy with the Néel vector along the $z$ direction. (f) Angular dependence of $\tilde{\chi}_{xz}^{\rm sep}$ and $\tilde{\chi}_{zz}^{\rm sep}$ as the Néel vector rotates from the $z$ to $x$ axis, parameterized by the angle $\theta$. The response coefficient is measured in units of $c_0$S/cm, with $c_0=\tau_0/\hbar$. The inset shows the Néel-vector direction. Model parameters are $t_2/t_1=1.0$, $t_3/t_1=0.5$, $\mu/t_1=0.5$, $\lambda/t_1=0.004$, and $J/t_1=0.45$. The magnon frequency is $\omega/t_1=0.1$. The Fermi energy is fixed at $E_F/t_1=0$ in (f).