  Magnetic excitations in ferromagnetic systems with a noncollinear ground
state magnetization experience a fictitious magnetic field due to the
equilibrium magnetic texture. Here, we investigate how such fictitious fields
lead to thermal Hall effects in two-dimensional insulating magnets in which the
magnetic texture is caused by spin-orbit interaction. Besides the well-known
geometric texture contribution to the fictitious magnetic field in such
systems, there exists also an equally important contribution due to the
original spin-orbit term in the free energy. We consider the different possible
ground states in the phase diagram of a two-dimensional ferromagnet with
spin-orbit interaction: the spiral state and the skyrmion lattice, and find
that thermal Hall effects can occur in certain domain walls as well as the
skyrmion lattice.
