  Recently, uncovering the sources of thermal Hall effect in insulators has
become an important issue. In the case of ferromagnetic insulators, it is well
known that Dzyaloshinskii-Moriya (DM) interaction can induce magnon thermal
Hall effect. Specifically, the DM vector parallel to the magnetization
direction induces complex magnon hopping amplitudes, so that magnons act as if
they feel Lorentz force. However, the DM vector which is orthogonal to the
magnetization direction has hitherto been neglected as a possible source of
magnon thermal Hall effect. This is because they play no role in the linear
spin wave theory, an often invoked approximation when computing the magnon
thermal Hall effect. Here, we challenge this expectation by presenting the
self-consistent Schwinger-boson mean field study of two-dimensional magnets
with ferromagnetic Heisenberg interaction and in-plane DM interaction. We find
that the relevant Schwinger-boson mean field Hamiltonian takes the form of
two-dimensional electron gas with Rashba spin-orbit interaction, which is known
to show anomalous Hall effect, spin Hall effect, and Rashba-Edelstein effect,
whose thermal counterparts also appear in our system. Importantly, the thermal
Hall effect can be induced when out-of-plane magnetic field is applied, and
persists even when the magnetic field is large, so that the spins are
significantly polarized, and the linear spin wave theory is expected to be a
reasonable approximation. Since the linear spin wave theory predicts vanishing
thermal Hall effect, our result implies that linear spin wave is not a
sufficient approximation, and that magnon-magnon interaction must be taken into
account to predict the correct thermal Hall conductivity.
