Theory of Dzyaloshinski-Moriya antiferromagnetism in distorted CuO2 and NiO2 planes

Direct Observation and Analysis of Low-Energy Magnons with Raman Spectroscopy in Atomically Thin NiPS3

van der Waals (vdW) magnets have rapidly emerged as a fertile playground for fundamental physics and exciting applications. Despite the impressive developments over the past few years, technical limitations pose a severe challenge to many other potential breakthroughs. High on the list is the lack of suitable experimental tools for studying spin dynamics on atomically thin samples. Here, Raman scattering techniques are employed to directly observe the low-lying magnon (∼1 meV) even in bilayer NiPS3. The advantage is that it offers excellent energy resolutions far better on low-energy sides than most inelastic neutron spectrometers can offer. More importantly, with appropriate theoretical analysis, the polarization dependence of the Raman scattering by those low-lying magnons also provides otherwise hidden information on the dominant spin-exchange scattering paths for different magnons. By comparing with high-resolution inelastic neutron scattering data, these low-energy Raman modes are confirmed to be indeed of magnon origin. Because of the different scattering mechanisms involved in inelastic neutron and Raman scattering, this information is fundamental in pinning down the final spin Hamiltonian. This work demonstrates the capability of Raman spectroscopy to probe the genuine two-dimensional spin dynamics in atomically thin vdW magnets, which can provide insights that are obscured in bulk spin dynamics.

Long-Lived Higgs Modes in Strongly Correlated Condensates

We investigate order parameter fluctuations in the Hubbard model within a time-dependent Gutzwiller approach. While in the weak coupling limit we find that the amplitude fluctuations are short-lived due to a degeneracy with the energy of the edge of the quasiparticle continua (and in agreement with Hartree-Fock+RPA theory), these are shifted below the edge upon increasing the interaction. Our calculations therefore predict undamped amplitude (Higgs) oscillations of the order parameter in strongly coupled superconductors, cold atomic fermion condensates, and strongly interacting charge- and spin-density wave systems. We propose an experimental realization for the detection of the spin-type Higgs mode in undoped cuprates and related materials where, due to the Dzyaloshinsky-Moriya interaction, it can couple to an out-of-plane ferromagnetic excitation that is visible via the Faraday effect.

Dzyaloshinskii–Moriya Coupling in 3d Insulators

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 , ...).

Isotropic and Antisymmetric Double-Exchange, Zero-Field, Zeeman, and Hyperfine Splittings in Trinuclear Valence-Delocalized [Cu37+] Clusters

Valence delocalization in the [Cu3(7+)] trimer is considered in the model of the double-exchange coupling, in which full delocalization corresponds to the migration of the single d(x2-y2) hole and relatively strong isotropic double-exchange coupling. Strong double exchange results in the pairing of the individual spins in the delocalized trimer even at room temperature. The model explains the delocalized singlet 1A1 ground state in the planar Cu3(mu3-O) core by strong double exchange with positive double-exchange parameter t(0), whereas the delocalized triplet ground state of the [Cu3(7+)] trimer, which was observed in the Cu3(mu3-S)2 cluster, may be explained by the double exchange with relatively weak positive t(0): 0 < t(0) < 2J (degenerate 3E ground state) or negative t(0) (triplet 3A2 ground state). An analysis of the splitting of the delocalized degenerate 3E term requires inclusion of the antisymmetric double-exchange interaction, which takes into account the spin-orbit coupling in the double-exchange model. The cluster parameter KZ of the antisymmetric double-exchange coupling is proportional to t(0) and anisotropy of the g factor Deltag(parallel)[Cu(II)], KZ << t(0). Antisymmetric double exchange is relatively large in the [Cu3(7+)] cluster with the d(x2-y2) magnetic orbitals lying in the Cu3 plane [Cu3(mu3-O) core], whereas for the d(x2-y2) magnetic orbitals lying in the plane perpendicular to Cu3, antisymmetric double-exchange coupling is weak [Cu3(mu3-S)2 cluster]. The antisymmetric double-exchange coupling results in the linear zero-field splitting DeltaK = 2[equation: see text]KZ (approximately t(0)) of the delocalized degenerate 3E term that leads to strong anisotropy of the Zeeman splittings in the external magnetic field and a complex electron paramagnetic resonance (EPR) spectrum. The delocalized model of hyperfine interaction explains the hyperfine structure [10 hyperfine lines with the relative intensities 1:3:6:10:12:12:10:6:3:1 and the interval a/3] of the EPR transitions in the triplet states that was observed in the EPR spectra of the Cu3(mu3-S)2 cluster.

Spin-orbit coupling-induced magnetic phase in the d-density-wave phase of La(2-x)Ba(x)CuO4 superconductors

We study the effects of spin-orbit coupling in the d-density wave (DDW) phase. In the low-temperature orthorhombic phase of La(2-x)Ba(x)CuO4, we find that spin-orbit coupling induces ferromagnetic moments in the DDW phase, which are polarized along the [110] direction with a considerable magnitude. This effect does not exist in the superconducting phase. On the other hand, if the d-density wave order does not exist at zero field, a magnetic field along the [110] direction always induces such a staggered orbital current. We discuss experimental constraints on the DDW states in light of our theoretical predictions.

Chiral fluctuations in MnSi above the Curie temperature

Polarized neutrons are used to determine the antisymmetric part of the magnetic susceptibility in noncentrosymmetric MnSi. The paramagnetic fluctuations are found to be incommensurate with the chemical lattice and to have a chiral character. We argue that antisymmetric interactions must be taken into account to properly describe the critical dynamics in MnSi above T(C). The possibility of directly measuring the polarization dependent part of the dynamical susceptibility in a large class of compounds by polarized inelastic neutron scattering is outlined as it can yield evidence for antisymmetric interactions such as spin-orbit coupling in metals as well as in insulators.