  The discovery of spontaneous magnetism in van der Waal (vdW) magnetic
monolayers has opened up an unprecedented platform for investigating magnetism
in purely two-dimensional systems. Recently, it has been shown that the
magnetic properties of vdW magnets can be easily tuned by adjusting the
relative composition of halides. Motivated by these experimental advances, here
we derive a model for a trihalide CrClBrI monolayer from symmetry principles
and we find that, in contrast to its single-halide counterparts, it can display
highly anisotropic nearest- and next-to-nearest neighbor Dzyaloshinskii-Moriya
and Heisenberg interactions. Depending on the parameters, the DM interactions
are responsible for the formation of exotic chiral spin states, such as
skyrmions and spin cycloids, as shown by our Monte Carlo simulations. Focusing
on a ground state with a two-sublattice unit cell, we find spin-wave bands with
nonvanishing Chern numbers. The resulting magnon edge states yield a magnon
thermal Hall conductivity that changes sign as function of temperature and
magnetic field, suggesting chromium trihalides as a candidate for testing
topological magnon transport in two-dimensional noncollinear spin systems.
