Magnon topology driven by altermagnetism

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.

💡 Research Summary

This theoretical study investigates the emergence of topological magnons (quantized spin waves) in altermagnets, a newly identified class of fully compensated collinear magnets. Unlike conventional antiferromagnets, the two spin sublattices in an altermagnet are related by a combination of time-reversal and a lattice rotation, not just translation or inversion. This unique symmetry leads to a characteristic partial splitting of magnon bands, but residual degeneracies persist along specific high-symmetry lines in the Brillouin Zone (BZ), preventing the definition of topological invariants.

The authors propose a minimal model to lift these degeneracies and engineer fully gapped topological magnon bands. The model is based on a two-dimensional d-wave altermagnetic spin system on a checkerboard lattice. The Hamiltonian includes an antiferromagnetic Heisenberg coupling (J) between nearest-neighbor spins on different sublattices and a crucial “altermagnetic coupling” (J1) between next-nearest-neighbor spins along the diagonals within the same sublattice. This J1 term is responsible for the altermagnetic character. To this base model, two additional interactions are introduced: (1) a uniform out-of-plane Zeeman magnetic field (H), and (2) a specific pattern of out-of-plane Dzyaloshinskii-Moriya interaction (DMI, D) allowed by the symmetry of the checkerboard lattice.

Classical ground state analysis reveals that the Zeeman field induces a canted “spin-flop” state where spins tilt out of the lattice plane, while the DMI does not affect the ground state energy but influences spin-wave dynamics. Using linear spin-wave theory (Holstein-Primakoff transformation), the magnon spectrum is derived analytically. The key finding is that when all three ingredients—altermagnetic coupling (J1), Zeeman field (H), and DMI (D)—are present, the residual degeneracies are completely lifted, resulting in two fully gapped magnon bands. Notably, the gap size at the X and Y points of the BZ is determined solely by the altermagnetic coupling J1.

The topological nature of the resulting bands is characterized by calculating the Berry curvature and the Chern number. The lower and upper magnon bands acquire Chern numbers of +1 and -1, respectively, signaling non-trivial topology. The analysis highlights the essential role of altermagnetism: in the limit of vanishing J1 (a standard antiferromagnet), the Berry curvature becomes highly localized near the midpoints of the BZ edges. A finite J1 redistributes this curvature across the BZ, solidifying the topological character. Furthermore, the sign of the Chern number (and Berry curvature) reverses if the sign of any one of the three couplings (H, D, or J1) is flipped, demonstrating external tunability.

As a direct physical consequence of the topological magnons, the thermal Hall conductivity κ_xy is computed. It exhibits a characteristic low-temperature scaling behavior, κ_xy ∝ T^4, which serves as a signature of the topological bands. Moreover, κ_xy is sensitive to the direction of the external magnetic field, changing sign upon field reversal and displaying a sharp jump across zero field at low temperatures—a hallmark of topological response.

Finally, to confirm the bulk-boundary correspondence principle, the magnon spectrum is calculated for a finite-width strip (ribbon geometry). The results clearly show the existence of chiral edge states within the bulk band gap. These states are topologically protected and propagate unidirectionally along the edges, providing further evidence for the non-trivial topology of the magnon bands.

In summary, this work establishes altermagnets as a promising platform for topological magnonics. The intrinsic partial band splitting in altermagnets provides a natural starting point, requiring only relatively weak additional perturbations (Zeeman field and DMI) to achieve fully gapped topological bands. This framework opens new avenues for designing topological magnetic materials and devices with potentially enhanced functionalities for spintronics and magnon-based information processing.