Magnon topology driven by altermagnetism

TL;DR

This work shows that altermagnetism in a two-sublattice checkerboard spin model, when supplemented by a uniform out-of-plane magnetic field and Dzyaloshinskii-Moriya interaction, drives topological magnon bands characterized by nonzero Chern numbers $C^{ u}=m{ pmbox{-}1}$ and chiral edge states. Using linear spin-wave theory and a para-unitary diagonalization, the authors demonstrate that altermagnetic symmetry partially lifts magnon degeneracy and, together with $H$ and $D$, fully gaps the spectrum, enabling Berry curvature and topological transport. The thermal Hall response $oldsymbol{7}_{xy}$ scales as $T^{4}$ at low temperatures and changes sign with the Zeeman field, offering a tunable magnonic transport probe. They also confirm bulk-edge correspondence via topologically protected edge modes in a strip geometry, highlighting the potential for altermagnetism-driven magnonics in spintronic applications.

Abstract

Altermagnets present a class of fully compensated collinear magnetic order, where the two sublattices are not related merely by time-reversal combined with lattice translation or inversion, but require an additional lattice rotation. This distinctive symmetry leads to a characteristic splitting of the magnon bands; however the splitting is only partial -- residual degeneracies persist along certain lines in the Brillouin zone as a consequence of the underlying altermagnetic rotation. We consider a two-dimensional $d$-wave altermagnetic spin model on the checkerboard lattice and introduce additional interactions such as an external magnetic field and Dzyaloshinskii-Moriya interactions, that lift these degeneracies. The resulting magnon bands become fully gapped and acquire non-trivial topology, characterized by nonzero Chern numbers. We demonstrate the crucial role of altermagnetism for the generation of the Berry curvature. As a direct consequence of the topological magnons, we find finite thermal Hall conductivity $κ_{xy}$, which exhibits a characteristic low-temperature scaling, $κ_{xy}\propto T^4$. Moreover, $κ_{xy}$ changes sign under reversal of the magnetic field, exhibiting a sharp jump across zero field at low temperatures. We also demonstrate topologically protected chiral edge modes in a finite strip geometry.

Figures (9)

• Figure 1: Checkerboard lattice spin model in the presence of a Zeeman field and DMI: The lattice consists of two interpenetrating square sublattices-1 and 2 whose site positions are denoted by $\boldsymbol{r}$ and $\boldsymbol{r}'$, respectively, each with lattice constant $a_0$. Spin-$S$ operators reside at every site of the resulting checkerboard lattice. Nearest-neighbor spins across the two sublattices interact via an antiferromagnetic Heisenberg exchange ($J > 0$, black bonds), while next-nearest-neighbor spins within each sublattice along the diagonals of the checkerboard plaquettes interact either ferromagnetically or antiferromagnetically ($J_1$, red bonds). Out-of-plane Dzyaloshinskii-Moriya vectors $\boldsymbol{D}$ are indicated by green arrows on the nearest-neighbor bonds, and $\boldsymbol{H}$ shows the direction of the uniform Zeeman field. The light gray square of side $a_0$ marks the magnetic unit cell of the checkerboard lattice. Arrows at the lattice sites represent the canted classical ground-state configuration of the model.
• Figure 2: Linear spin-wave spectrum [Eq. \ref{['eq:Epm']}] with the Zeeman field $H = H_s/8$ and DMI constant $D = 0.5J$ for a path in the first Brillouin zone ${\rm \Gamma}\,(0,0)\rightarrow {\rm X}\,(\pi/a_0,0)\rightarrow {\rm M}\,(\pi/a_0,\pi/a_0)\rightarrow {\rm \Gamma}\,(0,0)\rightarrow {\rm Y}\,(0,\pi/a_0)$. (a) Spectrum with the AM coupling $J_1 = 0$ shows degeneracy at X and Y, marked by the red circle and (b) with $J_1 = -0.04J$, a gap opens up at X and Y.
• Figure 3: Berry connections ${\cal\boldsymbol{A}}^\pm_{\boldsymbol{q}}$ [Eq. \ref{['eq.Berry-conn']}] of the upper and lower branches for the AM coupling $J_1=-0.04J$, DMI constant $D=0.5J$, and Zeeman field $H=H_s/8$.
• Figure 4: Evolution of the Berry curvature [Eq. \ref{['eq.Berry-curv']}] of the upper (top row) and lower (bottom row) magnon branches as the absolute value of the AM coupling $J_1$ decreases from left to right. The other parameters are fixed at the DMI constant $D=0.5J$ and the Zeeman field $H=H_s/8$.
• Figure 5: (a) The temperature dependence of the thermal Hall conductivity $\kappa_{xy}$ [Eq. \ref{['eq:kappaxy']}] obtained for the DMI constant $D=0.5J$, Zeeman field $H=0.4H_s$, and three different values of the AM coupling $J_1$. The exact value computed from Eq. \ref{['eq:kappaxy']} and the high-temperature estimation Eq. \ref{['eq:kappaxy-approx']} are shown by solid and thick dashed lines, respectively. The thin horizontal dashed lines show the infinite-temperature asymptotic values $\kappa^{\mathrm{lim}}_{xy}$ determined by Eq. \ref{['eq:kxy-lim']}. (b) Dependence of the infinite-temperature asymptotic value $\kappa^{\mathrm{lim}}_{xy}$ on the AM coupling $J_1$. The DMI constant is taken to be $D = 0.5 J$. Solid and dashed lines correspond to the exact values Eq. \ref{['eq:kxy-lim']} and approximation Eq. \ref{['eq:kxy-lim-approx']}, respectively.