The Dzyaloshinskii-Moriya interaction, which arises from a mixture of superexchange and spin-orbit coupling NN Cu²⁺ spin with a term of the Dᵢⱼ{·}(Sᵢ×{}Sⱼ). The coupling constants Dᵢⱼ are estimated for several cuprate crystal structures. The pattern of the Dᵢⱼ varies considerably between these structures and only in some cases causes a weak ferromagnetic component in an ordered antiferromagnetic of the Cu spins. In no case, however, does this interaction stabilize a flux phase.
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Coffey et al. (1991) studied this question.
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