  There have been intensive studies on Kitaev materials for the sake of the
realization of exotic states such as quantum spin liquid and topological
orders. In realistic materials, the Kitaev interaction may coexist with the
Dzyaloshinskii-Moriya interaction (DMI), and it is a challenge to distinguish
their magnitudes separately. Here, we study the topological magnon excitations
and related thermal Hall conductivity of kagome magnet exhibiting Heisenberg,
Kitaev and DM interactions exposed to a magnetic field. In a strong magnetic
field perpendicular to the plane of the lattice ([111] direction) that bring
the system into the fully polarized paramagnetic phase, we find that the magnon
bands carry nontrivial Chern numbers in the full region of the phase diagram.
Furthermore, there are phase transitions relate two topological phases with
opposite Chern numbers, which lead to the sign changes of the thermal Hall
conductivity. In the phase with negative thermal conductivity, the Kitaev
interaction is relatively large and the width of the phase increases with the
strength of DMI. Hence the study here will contribute to the understanding of
related compounds.
