  Using a modified spin-wave approach, we show that in the presence of an
inhomogeneous magnetic field or an in plane inhomogeneous electric field a
mesoscopic antiferromagnetic Heisenberg ring with integer spin (i.e., a Haldane
gap system) exhibits a persistent circulating spin current. Due to quantum
fluctuations the current has a finite limit on the order of -g mu_B c/L at zero
temperature, provided the staggered correlation length xi exceeds the
circumference L of the ring, in close analogy to ballistic charge currents in
mesoscopic normal metal rings. Here c is the spin-wave velocity, g is the
gyromagnetic ratio and mu_B is the Bohr magneton. For xi<<L the current is
exponentially suppressed.
