Persistent spin currents induced by a spatially-dependent magnetic field in a spin-1/2 Heisenberg antiferromagnetic ring

Abstract

We show that a spatially-dependent magnetic field can induce a persistent spin current in a spin-1/2 Heisenberg antiferromagnetic ring, proportional to the solid angle subtended by the magnetic field on a unit sphere. The result is a direct consequence of Berry "parallel transport" in space. The magnitude of the spin current is determined by the ratio of longitudinal and transverse exchange interactions $J_{\parallel }/J_{\perp }$ and by the magnetic field. For large magnetic fields the Zeeman energy strongly renormalizes the Ising term giving rise to a maximum spin current. In the limit of $J_{\parallel }/J_{\perp }\ll 1$ the amplitude of the current behaves like $1-(J_{\parallel }/J_{\perp }{)}^2$. In the opposite limit $\pi J_{\perp }>J_{\parallel }>J_{\perp }$ the amplitude scales as $\sqrt{J_{\parallel }/J_{\perp }}\exp (-\sqrt{J_{\parallel }/J_{\perp }})$.

14 pages plus one figure