Topological magnons in the checkerboard lattice

In analogy with topological insulators in electronic systems, one has the topological magnon insulators which are characterized by the existence of edge states modes in the presence of a gap. In these systems one has a transverse heat current mediated by magnons in response to thermal gradient, or a transverse spin current in response to a magnetic field gradient. Here we study topological magnon effects in a generalized ferromagnetic checkerboard lattice, also known as planar pyrochlore, with Dzyaloshinskii-Moryia interaction (DMI). The DMI breaks the inverse symmetry of the lattice, generates a magnetic flux and leads to non zero Chern numbers. We calculate the Berry curvature, the spin Hall conductivity, the spin Nerst coefficient and the Hall thermal conductivity as a function of temperature. We also analyze the effect of an applied magnetic fiels. Our study complements work done in the honeycomb, kagome, Lieb and pyrochlore lattices.