Magnon spin Nernst effect on the antiferromagnetic checkerboard lattice

In this paper we study topological effects in an anisotropic checkerboard antiferromagnetic lattice in the presence of the Dzyaloshinskii-Moriya interaction (DMI). The time reversal symmetry is broken by anisotropies in the Hamiltonian. However, in contrast to the honeycomb lattice, the DMI does not open a gap here. We calculate the energy spectrum of the magnons and the spin Nernst coefficient in the presence of a longitudinal temperature gradient.