  Chiral magnets support topological skyrmion textures due to the
Dzyaloshinskii-Moriya spin-orbit interaction. In the presence of a sufficiently
large applied magnetic field, such skyrmions are large amplitude excitations of
the field-polarized magnetic state. We investigate analytically the interaction
between such a skyrmion excitation and its small amplitude fluctuations, i.e.,
the magnons in a clean two-dimensional chiral magnet. The magnon spectrum is
found to include two magnon-skyrmion bound states corresponding to a breathing
mode and, for intermediate fields, a quadrupolar mode, which will give rise to
subgap magnetic and electric resonances. Due to the skyrmion topology, the
magnons scatter from a Aharonov-Bohm flux density that leads to skew and
rainbow scattering, characterized by an asymmetric differential cross section
with, in general, multiple peaks. As a consequence of the skew scattering, a
finite density of skyrmions will generate a topological magnon Hall effect.
Using the conservation law for the energy-momentum tensor, we demonstrate that
the magnons also transfer momentum to the skyrmion. As a consequence, a magnon
current leads to magnon pressure reflected in a momentum-transfer force in the
Thiele equation of motion for the skyrmion. This force is reactive and governed
by the scattering cross sections of the skyrmion; it causes not only a finite
skyrmion velocity but also a large skyrmion Hall effect. Our results provide,
in particular, the basis for a theory of skyrmion caloritronics for a dilute
skyrmion gas in clean insulating chiral magnets.
