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

We show that the two dimensional (2D) inversion-symmetry broken square lattice antiferromagnet with easy-plane spin anisotropy exhibits a thermal Hall effect and topologically protected edge modes. These phenomena require a finite Berry curvature, and its origin ascribed to the Dzyaloshinskii-Moriya (DM) interactions or the noncoplaner magnetic ordering is established in the kagome, pyrochlore, and decorated honeycomb lattices. There, the square lattice having the edge shared geometry was excluded as a typical no-go example. We show a different mechanism to generate a Berry curvature in a square lattice, where the DM interactions couple to the magnetic moments perpendicular to them by the aid of magnetic field. Such coupling cannot be reduced to the above conventional mechanism that requires a finite magnetic moment parallel to the DM interaction. The thermal Hall conductivity is induced by the magnetic field, and also show a rapid growth in temperature T beyond the power-law, reflecting the almost gapless low energy branch of the antiferromagnet, which is in distict difference with the T^7/2 dependence in the pyrochlore ferromagnets. The topological phase transition occurs by the in-plane rotation of the magnetic field, and the edge modes are protected by the Z2 topological invariant. The present system serves as a standard model for the noncentrosymmetric crystals Ba2MnGe2O7 and Ba2CoGe2O7.