Non-linear magnon transport in a bilayer van der Waals antiferromagnets

In this paper, we study the Berry curvature induced linear and nonlinear magnon transport in bilayer van der Waals antiferromagnets, where we deduce forms for the spin and energy currents within the semiclassical Boltzmann formalism under the relaxation time approximation. Even in the absence of the Dzyaloshinskii-Moriya interaction, if we turn on the layer-dependent electrostatic doping (ED) potential and anisotropy in the Heisenberg interactions, the linear response remains zero, whereas, we obtain a nonzero nonlinear thermal Hall response resulting from higher moments of the Berry curvature. We show that, there is a sign reversal of nonlinear thermal Hall conductivity with varying strength of ED potential, which can be potentially useful in spin-based technologies. We also comment on the momentum and temperature dependence of the relaxation time which can influence the transport properties.