  Brillouin light scattering is an established technique to study magnons, the
elementary excitations of a magnet. Its efficiency can be enhanced by cavities
that concentrate the light intensity. Here, we theoretically study inelastic
scattering of photons by a magnetic sphere that supports optical whispering
gallery modes in a plane normal to the magnetization. Magnons with low angular
momenta scatter the light in the forward direction with a pronounced asymmetry
in the Stokes and the anti-Stokes scattering strength, consistent with earlier
studies. Magnons with large angular momenta constitute Damon Eschbach modes are
shown to inelastically reflect light. The reflection spectrum contains either a
Stokes or anti-Stokes peak, depending on the direction of the magnetization, a
selection rule that can be explained by the chirality of the Damon Eshbach
magnons. The controllable energy transfer can be used to manage the
thermodynamics of the magnet by light.
