Dzyaloshinskii-Moriya coupling in 3d insulators

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, {\it weak ferrimagnetism} in mixed weak ferromagnets with competing signs of the Dzyaloshinskii vectors. We revisit a problem of the DM coupling for a single bond in cuprates specifying the local spin-orbital contributions to 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 the cation-ligand spin density transfer. The intermediate ligand 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 based calculations. Theoretical results are applied to different classes of 3d compounds from conventional weak ferromagnets ($\alpha$-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${}_4$,...).

arXiv comment67 pages, 10 figures

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Cited by in corpus (14)

• Room temperature antiferromagnetic resonance and inverse spin-Hall voltage in canted antiferromagnets
• Dzyaloshinskii interaction and exchange-relativistic effects in orthoferrites
• Multiferroic order parameters in rhombic antiferromagnets. RCrO${}_3$
• Structure-property relationships for weak-ferromagnetic perovskites
• Magnetic phase diagram of HoFeO${}_3$ by neutron diffraction
• One- and two-magnon excitations in antiferromagnet PbFeBO4
• Low temperature Terahertz Spectroscopy of LaFeO${}_3$, PrFeO${}_3$, ErFeO${}_3$, and LuFeO${}_3$: Quasimagnon resonances and ground multiplet transitions
• Charge transfer transitions and circular magnetooptics in ferrites
• Simple Realistic Model of Spin Reorientation in 4f-3d Compounds
• Dzyaloshinskii-Moriya spin density by skew scattering
• Effects of frustration and Dzyaloshinskii-Moriya interaction on the spin-1/2 anisotropic Heisenberg antiferromagnet with the application to La2CuO4
• Spin relaxation in Cs${}_2$CuCl${}_{4-x}$Br${}_x$
• Anisotropic magnetic phase diagrams, tricriticality, and spin-reorientation in high-pressure grown SmCrO${}_3$ single crystals
• Spin-phonon interactions revisited: Far-infrared emission, Raman scattering, and high-resolution x-ray diffraction at the Néel temperature in LaFeO3