What are spin currents in Heisenberg magnets?

TL;DR

This paper clarifies the proper definition of spin currents in Heisenberg magnets, emphasizing their quantum nature and how they relate to real magnetization transport, especially under inhomogeneous magnetic fields.

Contribution

It introduces a refined definition of spin current operators in Heisenberg magnets and highlights their quantum origin, contrasting with classical or mean field approximations.

Findings

Only the in-plane component of the naive current operator relates to real magnetization transport.

Spin currents vanish in mean field or classical ground states.

Finite spin currents indicate quantum correlations in the system.

Abstract

We discuss the proper definition of the spin current operator in Heisenberg magnets subject to inhomogeneous magnetic fields. We argue that only the component of the naive "current operator" J_ij S_i x S_j in the plane spanned by the local order parameters <S_i> and <S_j> is related to real transport of magnetization. Within a mean field approximation or in the classical ground state the spin current therefore vanishes. Thus, finite spin currents are a direct manifestation of quantum correlations in the system.