Thermal Hall effect and topological edge states in a square-lattice antiferromagnet

We show that the two-dimensional spatial-inversion-symmetry (SIS) broken square-lattice antiferromagnet with easy-plane spin anisotropy exhibits a thermal Hall effect and the edge modes characterized by the ${\mathbb{Z}}₂$ topological invariant. These topological properties require a nonzero Berry curvature, and its origin is ascribed to the Dzyaloshinskii-Moriya (DM) interactions or the noncoplanar magnetic ordering generating a U(1) gauge field that couples to the kinetic motion of magnons. Although this picture is established in ferromagnets on the kagome and pyrochlore lattices, it does not apply to our square-lattice model since such gauge field cancels out in an edge-shared geometry. Instead, our case has an analogy with the anomalous Hall effect of Rashba electronic system where the spin-orbit coupling generates an SU(2) gauge field. The two species of magnons defined on antiferromagnetic sublattices can be regarded as the pseudospin degrees of freedom of magnons. The DM interactions that emerge due to the SIS breaking serve as a pseudo-spin-orbit coupling of magnons and generate a Berry curvature, when the direction of the magnetic moments is properly controlled by the magnetic field. The thermal Hall conductivity of our antiferromagnet shows rapid growth in temperature $T$ beyond the power law, reflecting the almost gapless low-energy branch of the antiferromagnet, which distinctively differs from the ${T}^7/2$ dependence in the pyrochlore ferromagnets. The present system serves as a standard model for the noncentrosymmetric crystals ${\mathrm{Ba}}₂{\mathrm{MnGe}}₂{\mathrm{O}}₇$ and ${\mathrm{Ba}}₂{\mathrm{CoGe}}₂{\mathrm{O}}₇$.