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The properties of Kitaev materials are attracting ever increasing attentionowing to their exotic properties. In realistic two-dimensional materials,Kitaev interaction is often accompanied by the Dzyloshinskii-Moriyainteraction, which poses a challenge of distinguishing their magnitudeseparately. In this work, we demonstrate that it can be done by accessingmagnonic transport properties. By studying honeycomb ferromagnets exhibitingDzyaloshinskii-Moriya and Kitaev interactions simultaneously, we revealnon-trivial magnonic topological properties accompanied by intricate magnonictransport characteristics as given by thermal Hall and magnon Nernst effects.We also investigate the effect of a magnetic field, showing that it does notonly break the symmetry of the system but also brings drastic modifications tomagnonic topological transport properties, which serve as hallmarks of therelative strength of anisotropic exchange interactions. Based on our findings,we suggest strategies to estimate the importance of Kitaev interactions in realmaterials.

The interplay of Dzyaloshinskii-Moriya and Kitaev interactions for magnonic properties of Heisenberg-Kitaev honeycomb ferromagnets