Dzyaloshinsky-Moriya antisymmetric exchange coupling in cuprates: Oxygen effects

Abstract

We reconsider the conventional Moriya approach to the Dzyaloshinsky-Moriya antisymmetric exchange coupling for a single Cu₁-O-Cu₂ bond in cuprates using a perturbation scheme that provides an optimal way to account for intra-atomic electron correlations, low-symmetry crystal field, and local spin-orbital contributions with a focus on the oxygen term. The Dzyaloshinsky vector and the corresponding weak ferromagnetic moment are shown to be a superposition of comparable and, sometimes, competing local Cu and O contributions. We predict the effect of oxygen staggered spin polarization in the antiferromagnetic edge-shared CuO₂ chains due to the uncompensated oxygen Dzyaloshinsky vectors. The polarization is perpendicular to both the main chain antiferromagnetic vector and the CuO₂ chain normal. The intermediate ¹⁷O NMR is shown to be an effective tool to inspect the effects of Dzyaloshinsky-Moriya coupling in an external magnetic field. In particular, we argue that the puzzling planar ¹⁷O Knight shift anomalies observed in the paramagnetic phase of the generic Dzyaloshinsky-Moriya antiferromagnetic cuprate La₂CuO₄ can be assigned to the effect of the field-induced staggered magnetization. Finally, we revisit the effects of symmetric spin anisotropy, in particular, those directly induced by the Dzyaloshinsky-Moriya coupling. The perturbation scheme generalizes the well-known Moriya approach and presents a basis for reliable quantitative estimates for the symmetric partner of the Dzyaloshinsky-Moriya coupling. In contrast to the conventional standpoint, the parameters of the effective two-ion spin anisotropy are shown to incorporate the contributions of a single-ion anisotropy for two-hole configurations at both Cu and O sites.