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

TL;DR

This paper demonstrates that a spatially-dependent magnetic field can generate a persistent spin current in a spin-1/2 Heisenberg antiferromagnetic ring, driven by Berry phase effects and influenced by exchange interactions and magnetic field strength.

Contribution

It reveals how spatially varying magnetic fields induce persistent spin currents via Berry phase, with detailed analysis of the current's dependence on exchange ratios and magnetic field.

Findings

Spin current is proportional to the solid angle of the magnetic field.

Maximum spin current occurs at large magnetic fields due to Zeeman energy.

The current's amplitude varies with exchange interaction ratios, showing distinct scaling behaviors.

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 $J_\parallel/J_\perp\ll1$ 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 $\sqrt{J_\parallel/ J_\perp}\exp{(-\sqrt{J_\parallel/J_\perp})}$.