What are spin currents in Heisenberg magnets?

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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" Jᵢj Sᵢ x Sⱼ in the plane spanned by the local order parameters <Sᵢ> and <Sⱼ> 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.