  We show that at low temperatures T an inhomogeneous radial magnetic field
with magnitude B gives rise to a persistent magnetization current around a
mesoscopic ferromagnetic Heisenberg ring. Under optimal conditions this spin
current can be as large as g mu_B (T / hbar) exp [ - 2 pi (g mu_B B / Delta
)^1/2 ], as obtained from leading-order spin-wave theory. Here g is the
gyromagnetic factor, mu_B is the Bohr magneton, and Delta is the energy gap
between the ground state and the first spin-wave excitation. The magnetization
current endows the ring with an electric dipole moment.
