Abstract
We present an overview of the microscopic theory of the Dzyaloshinskii–Moriya (DM) coupling in strongly correlated 3d compounds. Most attention in the paper centers around the derivation of the Dzyaloshinskii vector, its value, orientation, and sense (sign) under different types of the (super)exchange interaction and crystal field. We consider both the Moriya mechanism of the antisymmetric interaction and novel contributions, in particular, that of spin–orbital coupling on the intermediate ligand ions. We have predicted a novel magnetic phenomenon, weak ferrimagnetism in mixed weak ferromagnets with competing signs of Dzyaloshinskii vectors. We revisit a problem of the DM coupling for a single bond in cuprates specifying the local spin–orbital contributions to the Dzyaloshinskii vector focusing on the oxygen term. We predict a novel puzzling effect of the on-site staggered spin polarization to be a result of the on-site spin–orbital coupling and the cation-ligand spin density transfer. The intermediate ligand nuclear magnetic resonance (NMR) measurements are shown to be an effective tool to inspect the effects of the DM coupling in an external magnetic field. We predict the effect of a strong oxygen-weak antiferromagnetism in edge-shared CuO 2 chains due to uncompensated oxygen Dzyaloshinskii vectors. We revisit the effects of symmetric spin anisotropy directly induced by the DM coupling. A critical analysis will be given of different approaches to exchange-relativistic coupling based on the cluster and the DFT (density functional theory) based calculations. Theoretical results are applied to different classes of 3d compounds from conventional weak ferromagnets ( α -Fe 2 O 3 , FeBO 3 , FeF 3 , RFeO 3 , RCrO 3 , ...) to unconventional systems such as weak ferrimagnets (e.g., RFe 1 - x Cr x O 3 ), helimagnets (e.g., CsCuCl 3 ), and parent cuprates (La 2 CuO 4 , ...).
Highlights
The history of the Dzyaloshinskii–Moriya interaction is closely related to the history of the discovery and investigation of weak ferromagnetism
Later the phenomenon was observed in many other 3d compounds, such as nickel fluoride NiF2 with rutile structure, orthorhombic orthoferrites RFeO3, rhombohedral carbonates MnCO3, NiCO3, CoCO3, and FeBO3
In 1977 we have shown that the Dzyaloshinskii vectors can be of opposite sign for different pairs of S-type ions [12] that allowed us to uncover a novel magnetic phenomenon, weak ferrimagnetism, and a novel class of magnetic materials, weak ferrimagnets, which are systems such as solid solutions YFe1−xCrxO3 with competing signs of the Dzyaloshinskii vectors and the very unusual concentration and temperature dependence of the magnetization [23,24]
Summary
The history of the Dzyaloshinskii–Moriya interaction is closely related to the history of the discovery and investigation of weak ferromagnetism. Valerii Ozhogin et al [21] in 1968 first raised the issue of the sign of the Dzyaloshinskii vector, the reliable local information on its sign, or to be exact, that of the Dzyaloshinskii parameter d12, was first extracted only in 1990 from the 19F ligand NMR (nuclear magnetic resonance) data in a weak ferromagnet FeF3 [22].
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