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 (-gμ_B)c/L at zero temperature, provided the staggered correlation length ξ 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 μ_B is the Bohr magneton. For ξ≪L the current is exponentially suppressed.