  The properties of Kitaev materials are attracting ever increasing attention
owing to their exotic properties. In realistic two-dimensional materials,
Kitaev interaction is often accompanied by the Dzyloshinskii-Moriya
interaction, which poses a challenge of distinguishing their magnitude
separately. In this work, we demonstrate that it can be done by accessing
magnonic transport properties. By studying honeycomb ferromagnets exhibiting
Dzyaloshinskii-Moriya and Kitaev interactions simultaneously, we reveal
non-trivial magnonic topological properties accompanied by intricate magnonic
transport characteristics as given by thermal Hall and magnon Nernst effects.
We also investigate the effect of a magnetic field, showing that it does not
only break the symmetry of the system but also brings drastic modifications to
magnonic topological transport properties, which serve as hallmarks of the
relative strength of anisotropic exchange interactions. Based on our findings,
we suggest strategies to estimate the importance of Kitaev interactions in real
materials.
