What are spin currents in Heisenberg magnets?

Florian Schuetz, Peter Kopietz, Marcus Kollar

Published 2004-05-14, updated 2004-11-16Version 2

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.