  The magnon transport driven by thermal gradient in a perpendicularly
magnetized honeycomb lattice is studied. The system with the nearest-neighbor
pseudodipolar interaction and the next-nearest-neighbor Dzyaloshinskii-Moriya
interaction (DMI) has various topologically nontrivial phases. When an in-plane
thermal gradient is applied, a transverse in-plane magnon current is generated.
This phenomenon is termed as the anomalous magnon Nernst effect that closely
resembles the anomalous Nernst effect for an electronic system. The anomalous
magnon Nernst coefficient and its sign are determined by the magnon Berry
curvatures distribution in the momentum space and magnon populations in the
magnon bands. We predict a temperature-induced sign reversal in anomalous
magnon Nernst effect under certain conditions.
