  Vortex ring solutions are presented for the Landau-Lifshitz equation, which
models the dynamics of a three-dimensional ferromagnet. The vortex rings
propagate at constant speed along their symmetry axis and are characterized by
the integer-valued Hopf charge. They are stable to axial perturbations, but it
is demonstrated that an easy axis anisotropy results in an instability to
perturbations which break the axial symmetry. The unstable mode corresponds to
a migration of spin flips around the vortex ring that leads to a pinching
instability and ultimately the collapse of the vortex ring. It is found that
this instability does not exist for an isotropic ferromagnet. Similarities
between vortex rings in ferromagnets and vortons in cosmology are noted.
