  A ferromagnetic sphere can support \textit{optical vortices} in forms of
whispering gallery modes and \textit{magnetic quasi-vortices} in forms of
magnetostatic modes with non-trivial spin textures. These vortices can be
characterized by their orbital angular momenta. We experimentally investigate
Brillouin scattering of photons in the whispering gallery modes by magnons in
the magnetostatic modes, zeroing in on the exchange of the orbital angular
momenta between the optical vortices and the magnetic quasi-vortices. We find
that the conservation of the orbital angular momentum results in different
nonreciprocal behaviors in the Brillouin light scattering. New avenues for
chiral optics and opto-spintronics can be opened up by taking the orbital
angular momenta as a new degree of freedom for cavity optomagnonics.
