We investigate the influence of magnon-magnon interactions on the nonlinear magnon spin Nernst effect in honeycomb antiferromagnets within the framework of semiclassical Boltzmann transport theory under the relaxation time approximation. To incorporate interaction effects, we examine both three-magnon and four-magnon processes using a combination of perturbative many-body Green's function and mean-field approximations. We compute the interactions-induced modification in the magnon band structure and assess its impact on the nonlinear spin transport. In the case of in-plane Dzyaloshinskii-Moriya interaction, three-magnon scattering processes lead to a nonreciprocal splitting of the magnon spectrum, which remains stable and amplifies the spin Nernst effect in the linear regime. Conversely, four-magnon interactions lead to thermal renormalization of the magnon spectrum, which tends to reduce the nonlinear spin Nernst response. Our findings highlight the crucial role of magnon-magnon scattering in shaping the nonlinear spin response magnetic systems.

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• Magnons
• 2-dimensional systems
• Boltzmann theory
• Linear spin wave theory