Topological magnons on the checkerboard lattice

Abstract

Here we investigate topological magnon effects in a ferromagnetic checkerboard lattice, also known as planar pyrochlore, with a Dzyaloshinskii-Moriya interaction (DMI). The DMI breaks the time-reversal symmetry and leads to topological bands with nontrivial Chern numbers, which indicates the existence of edge state modes. We show that the model studied here can be treated as a two-band model, and we calculate the Berry curvature, the spin Hall conductivity, the spin Nernst coefficient, and the thermal Hall conductivity as a function of temperature. Measurements of these quantities can be used to detect finite Berry curvatures. We also analyze the effect of an applied magnetic field and take into account higher-order contributions responsible to anharmonic magnon effects. Our study complements others done in the honeycomb, kagome, Lieb, Shastry-Sutherland, and pyrochlore lattices.