  We study magnetic excitations and thermal Hall effect on the
Kitaev-Heisenberg model under magnetic fields. By employing the spin-wave
theory for the magnetic orders realized in this model, we examine the
topological nature of the spin-wave dispersions and calculate the thermal Hall
conductivity. The comprehensive investigations on the field-angle dependence
clarify that the thermal Hall conductivity is sensitive to the spin ordered
pattern and excitation spectra of magnons; this quantity is enhanced by the
noncoplanar spin configurations and small magnon gap in the excitation
spectrum. On the other hand, we also find a common feature in the field-angle
dependence of the thermal Hall conductivity. It vanishes when the magnetic
field is on the planes spanned by the spin axes. We reveal that the behavior is
intrinsic to the Kitaev -Heisenberg model in an applied field and demonstrate
that the introduction of the off-diagonal spin interaction causes the
disappearance of the feature in the thermal Hall conductivity.
