Persistent spin currents in mesoscopic Haldane gap spin rings

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.