  We experimentally implement a system of cavity optomagnonics, where a sphere
of ferromagnetic material supports whispering gallery modes (WGMs) for photons
and the magnetostatic mode for magnons. We observe pronounced nonreciprocity
and asymmetry in the sideband signals generated by the magnon-induced Brillouin
scattering of light. The spin-orbit coupled nature of the WGM photons, their
geometric birefringence and the time-reversal symmetry breaking in the magnon
dynamics impose the angular-momentum selection rules in the scattering process
and account for the observed phenomena. The unique features of the system may
find interesting applications at the crossroad between quantum optics and
spintronics.
