Topological magnons in the antiferromagnetic checkerboard lattice

Topological magnon excitations have attracted much attention in the latter years, and have become a very active area of research. Motivated by this, we investigate here spin Hall and thermal spin Hall conductivities in the antiferromagnetic checkerboard lattice. We include the Dzyaloshinskii-Morya interaction, and for spin S > 1/2 a single ion anisotropy term. We use the standard spin wave approach and study the effect of magnon-magnon interactions using a self consistent mean-field spin wave theory.