  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.
