Competitive Orders in Altermagnetic Chiral Magnons

Abstract

The magnons in altermagnets exhibit chiral splitting even in the absence of spin-orbit coupling and external magnetic fields. Typically, this chiral splitting behavior can be well described by alternating isotropic spin exchanges (ISE) near the zero temperature. However, its finite-temperature dynamics, particularly when incorporating spin-orbit coupling effects, remains elusive. In this study, we reveal that, when including magnon-magnon interactions, long-range anisotropic spin exchange (ASE) can also induce chiral splitting of magnons at a finite temperature. Crucially, the chiral splitting induced by ASE competes with that arising from ISE, leading to a pronounced temperature-dependent modulation of the altermagnetic chiral splitting. Moreover, this competition is intimately connected to spin fluctuations, and can reverse the spin current driven by the band splitting as temperature increases. Our work uncovers the intrinsic competition governing collective spin excitations in altermagnets, providing new insights into their finite-temperature dynamical behavior.

Figures (4)

• Figure 1: The illustration of the $d$-wave altermagnet on the square lattice. 2NN spin exchanges exhibit the $d$-wave behavior (${\cal J}^{+}_{2}$$\neq$${\cal J}^{-}_{2}$) due to the breaking ${\cal PT\tau}$ symmetry between opposite-spin sublattices.
• Figure 2: Magnon bands of the monolayer $d$-wave altermagnet at different temperatures. (a)(b) With only ISE : $\Delta_{\cal J}/{\cal J}_{1}$$=$$0.2$. (c)(d) With only ASE : ${\cal J}_{2z}/{\cal J}_{1}$$=$$0.6$. (e)(f) With both ISE : $\Delta_{\cal J}/{\cal J}_{1}$$=$$0.2$ and ASE : ${\cal J}_{2z}/{\cal J}_{1}$$=$$0.6$.
• Figure 3: Altermagnetic splitting of the $d$-wave altermagnet. (a)(c) Linear dependence of the order parameter $\phi$ on (a) ISE ($\Delta_{\cal J}/{\cal J}_{1}$) and (c) ASE (${\cal J}_{2z}/{\cal J}_{1}$) at a given temperature. (b)(d) Dependence of the linear coefficients for (b) ISE ($\Delta_{\cal E}/\Delta_{\cal J}$) and (d) ASE ($\Delta_{\cal E}/{\cal J}_{2z}$) on temperature $T$.
• Figure 4: (a) The dependence of the ISE/ASE ratio (${\cal J}_{2z}/\Delta_{\cal J}$) at which the altermagnetic gap vanishes completely on temperature $T$ and spin number $S$. (b) The dependence of thermal spin conductivity $\sigma$ on ratio ${\cal J}_{2z}/\Delta_{\cal J}$ and temperature $T$.