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, 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 (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 ,...).

Effects of Frustration and Dzyaloshinskii–Moriya Interaction on the Spin‐1/2 Anisotropic Heisenberg Antiferromagnet with the Application to La2CuO4

“…In-plane (dashed curve) and out-of-plane (full curve) zone-center energy gaps ω 1=2k¼0 versus relative temperature T=T N . Full circles denote the experimental data from a study by Keimer et al [33] Solid lines represent the theoretical result based on Equation (11). Figure 11.…”

“…Beside the nearest‐neighbor (NN) and next‐nearest‐neighbor (NNN) exchange interaction, it is often suggested that the description without taking into account the Dzyaloshinskii–Moriya (DM) interactions, [ 1,2 ] arising from spin–orbit coupling, may be considered as incomplete. [ 3–11 ] Namely, in La 2 CuO 4 , due to the spin–orbit couplings arising from the small orthorhombic distortion below the structural tetragonal–orthorhombic transition temperature , CuO 2 planes exhibit a weak ferromagnetic moment, i.e., all spins cant out of the CuO 2 plane by a small angle θ . However, this is not a common feature of the copper oxide layers as in the absence of the orthorhombic distortion DM interaction does not emerge (in , e.g.).…”

NMR Analysis of the Magnetic Structure and Hyperfine Interactions in a FeP Binary Helimagnetic

“…The next 31 P spectrum measurement was started always with decreasing magnetic field. The typical 31 P NMR spectra of the FeP single crys- α0( • ) B loc (T ) B1 -15.5(6) 0.851(9) B2 -14.4(5) 0.848(8) B3 -59.9(5) 0.841(8) B4 -60.0(4) 0.844 (5) talline sample measured at 140 MHz are presented in Fig. 10.…”

“…Such a complex helicoidal magnetic structure is explained as a result of a competition of different isotropic (super)exchange interactions and/or anisotropic antisymmetric Dzyaloshinskii-Moriya coupling 4 (see, e.g., recent review article Ref. 5). It is worth noting that the use of circular polarized x-rays reveals a right-handed chirality in isostructural FeAs 6 that points to the antisymmetric Dzyaloshinskii-Moriya coupling to be main candidate to explain both a small canting for magnetic moments of Fe1, Fe2 (Fe3, Fe4) ions and spiral spin rotation in FeP.…”

Structure–Property Relationships for Weak Ferromagnetic Perovskites

“…[3], the authors of which performed first principles simulations for the structural, elastic, vibrational, electronic, and optical properties of orthorhombic samarium orthoferrite SmFeO 3 within the framework of density functional theory. However, such calculations encounter great difficulties in describing the more "subtle" effects of magnetic, magnetoelastic, and optical anisotropy [4].…”