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

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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∥/J⊥ 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∥/J⊥≪1 the amplitude of the current behaves like 1-(J∥/J⊥)². In the opposite limit πJ⊥> J∥>J⊥ the amplitude scales as √J∥/ J⊥(-√J∥/J⊥).