Dzyaloshinskii-Moriya Coupling Research Articles

Simulating Spin Chains Using a Superconducting Circuit: Gauge Invariance, Superadiabatic Transport, and Broken Time‐Reversal Symmetry

AbstractSimulation of materials by using quantum processors is envisioned to be a major direction of development in quantum information science. Here, the mathematical analogies between a triangular spin lattice with Dzyaloshinskii–Moriya coupling on one edge and a three‐level system driven by three fields in a loop configuration are exploited to emulate spin‐transport effects. It is shown that the spin transport efficiency, seen in the three‐level system as population transfer, is enhanced when the conditions for superadiabaticity are satisfied. It is demonstrated experimentally that phenomena characteristic to spin lattices due to gauge invariance, non‐reciprocity, and broken time‐reversal symmetry can be reproduced in the three‐level system.

Skyrmion Crystals and Phase Transitions in Magneto-Ferroelectric Superlattices: Dzyaloshinskii–Moriya Interaction in a Frustrated J1 − J2 Model

The formation of a skyrmion crystal and its phase transition are studied, taking into account the Dzyaloshinskii–Moriya (DM) interaction at the interface between a ferroelectric layer and a magnetic layer in a superlattice. Frustration is introduced in both magnetic and ferroelectric films. The films have a simple cubic lattice structure. The spins inside the magnetic layers are Heisenberg spins interacting with each other via nearest-neighbor (NN) exchange J m and next-nearest-neighbor (NNN) exchange J 2 m . The polarizations in the ferroelectric layers are assumed to be of Ising type with NN and NNN interactions J f and J 2 f . At the magnetoelectric interface, a DM interaction J m f between spins and polarizations is supposed. The spin configuration in the ground state is calculated by the steepest descent method. In an applied magnetic field H perpendicular to the layers, we show that the formation of skyrmions at the magnetoelectric interface is strongly enhanced by the frustration brought about by the NNN antiferromagnetic interactions J 2 m and J 2 f . Various physical quantities at finite temperatures are obtained by Monte Carlo simulations. We show the critical temperature, the order parameters of magnetic and ferroelectric layers as functions of the interface DM coupling, the applied magnetic field, and J 2 m and J 2 f . The phase transition to the disordered phase is studied in detail.

Magnetic phase diagram of a spin S = 1/2 antiferromagnetic two-leg ladder with modulated along legs Dzyaloshinskii-Moriya interaction

We study the ground-state magnetic phase diagram of a spin S=1/2 antiferromagnetic two-leg ladder in the presence of period two lattice units modulated, Dzyaloshinskii-Moriya (DM) interaction along the legs. We consider the case of collinear DM vectors and strong rung exchange and magnetic field. In this limit we map the initial ladder model onto the effective spin $\sigma=1/2$ XXZ chain and study the latter using the continuum-limit bosonization approach. We identified four quantum phase transitions and corresponding critical magnetic fields, which mark transitions from the spin gapped regimes into the gapless quantum spin-liquid regimes. In the gapped phases the magnetization curve of the system shows plateaus at magnetisation M=0 and to its saturation value per rung M=1. We have shown that the very presence of alternating DM interaction leads to opening of a gap in the excitation spectrum at magnetization M=0.5. The width of the magnetization plateau at M=0.5, is determined by the associated with the dynamical generation of a gap in the spectrum is calculated and is shown that its length scales as $(D_{0}D_{1}/J^{2})^{\alpha}$ where $D_{0},D_{1}$ are uniform and staggered components of the DM term, $J$ is the intraleg exchange and $\alpha \leq 3/4$ and weakly depends on the DM couplings.

Exact solutions for a ferromagnet with Dzyaloshinskii-Moriya interaction

On the two-dimensional non-linear $\Sigma$-model describing a ferromagnet with Dzyaloshinskii-Moriya interaction, we build three families of exact static solutions depending on a single Cartesian variable. One of them describes a clockwise helix configuration, that characterizes the ground state of the system. A second one corresponds to a counterclockwise helix, representing an excited state. These two families of solutions are parameterized by a continuous parameter that depends on the magnetic field and the Dzyaloshinskii-Moriya coupling. Finally, the third family exists only for isolated values of the same parameter, corresponding to a discrete family of Viviani curves on the target sphere. The degeneracy of the resulting spectrum suggests that an approximate symmetry may emerge at specific values of the magnetic field, at which additional solutions could then exist.

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 , ...).

Functional renormalization group for frustrated magnets with nondiagonal spin interactions

In the field of quantum magnetism, the advent of numerous spin-orbit assisted Mott insulating compounds, such as the family of Kitaev materials, has led to a growing interest in studying general spin models with non-diagonal interactions that do not retain the SU(2) invariance of the underlying spin degrees of freedom. However, the exchange frustration arising from these non-diagonal and often bond-directional interactions for two- and three-dimensional lattice geometries poses a serious challenge for numerical many-body simulation techniques. In this paper, we present an extended formulation of the pseudo-fermion functional renormalization group that is capable of capturing the physics of frustrated quantum magnets with generic (diagonal and off-diagonal) two-spin interaction terms. Based on a careful symmetry analysis of the underlying flow equations, we reveal that the computational complexity grows only moderately, as compared to models with only diagonal interaction terms. We apply the formalism to a kagome antiferromagnet which is augmented by general in-plane and out-of-plane Dzyaloshinskii-Moriya (DM) interactions, as argued to be present in the spin liquid candidate material herbertsmithite. We calculate the complete ground state phase diagram in the strength of in-plane and out-of-plane DM couplings, and discuss the extended stability of the spin liquid of the unperturbed kagome antiferromagnet in the presence of these couplings.

Dzyaloshinskii-Moriya interaction in magnetoferroelectric superlattices: Spin waves and skyrmions

We study in this paper effects of Dzyaloshinskii-Moriya (DM) magnetoelectric coupling between ferroelectric and magnetic layers in a superlattice formed by alternate magnetic and ferroelectric films.Magnetic films are films of simple cubic lattice with Heisenberg spins interacting with each other via an exchange $J$ and a DM interaction with the ferroelectric interface. Electrical polarizations of $\pm{1}$ are assigned at simple cubic lattice sites in the ferroelectric films.We determine the ground-state (GS) spin configuration in the magnetic film. In zero field, the GS is periodically non collinear and in an applied field $\mathbf H$ perpendicular to the layers, it shows the existence of skyrmions at the interface. Using the Green's function method we study the spin waves (SW) excited in a monolayer and also in a bilayer sandwiched between ferroelectric films, in zero field. We show that the DM interaction strongly affects the long-wave length SW mode. We calculate also the magnetization at low temperature $T$. We use next Monte Carlo simulations to calculate various physical quantities at finite temperatures such as the critical temperature, the layer magnetization and the layer polarization, as functions of the magnetoelectric DM coupling and the applied magnetic field.Phase transition to the disordered phase is studied in detail.

Unconventional Field-Induced Spin Gap in an S=1/2 Chiral Staggered Chain.

We investigate the low-temperature magnetic properties of the molecule-based chiral spin chain [Cu(pym)(H_{2}O)_{4}]SiF_{6}·H_{2}O (pym=pyrimidine). Electron-spin resonance, magnetometry and heat capacity measurements reveal the presence of staggered g tensors, a rich low-temperature excitation spectrum, a staggered susceptibility, and a spin gap that opens on the application of a magnetic field. These phenomena are reminiscent of those previously observed in nonchiral staggered chains, which are explicable within the sine-Gordon quantum-field theory. In the present case, however, although the sine-Gordon model accounts well for the form of the temperature dependence of the heat capacity, the size of the gap and its measured linear field dependence do not fit with the sine-Gordon theory as it stands. We propose that the differences arise due to additional terms in the Hamiltonian resulting from the chiral structure of [Cu(pym)(H_{2}O)_{4}]SiF_{6}·H_{2}O, particularly a uniform Dzyaloshinskii-Moriya coupling and a fourfold periodic staggered field.

Weak ferrimagnets with competing Dzyaloshinskii-Moriya coupling are perspective for the exchange-bias effect materials

Here I would like to draw attention to so-called weak ferrimagnets (WFIMs), or mixed compounds with competing Dzyaloshinskii-Moriya (DM) coupling, strictly speaking with different signs of the Dzyaloshinskii vector. Due to theoretical predictions ferrites-chromites RFe1−xCrxO3 (R is rare-earth or Y), Fe1−xCrxBO3, and Fe2−xCrxO3, as well as carbonates Mn1−xNixCO3 with competition of d3-d3, d3-d5, d5-d5, d5-d8, and d8-d8 DM couplings do reveal nontrivial concentration and temperature dependencies of magnetization, in particular, the compensation point(s). The weak ferrimagnets are believed to be perspective compounds for the exchange-bias effect materials.

Generic nearest-neighbor kagome model: XYZ and Dzyaloshinskii-Moriya couplings with comparison to the pyrochlore-lattice case

The kagome lattice is a paragon of geometrical frustration, long-studied for its association with novel ground-states including spin liquids (SLs). Many recently synthesized kagome materials feature rare-earth ions, which may be expected to exhibit highly anisotropic exchange interactions. The consequences of this combination of strong exchange anisotropy and extreme geometrical frustration are yet to be fully understood. Here, we establish a general picture of the interactions and resulting ground-states (GSs) arising from nearest neighbour exchange anisotropy on the kagome lattice. We determine a generic anisotropic exchange Hamiltonian from symmetry arguments. In the high-symmetry case where reflection in the kagome plane is a symmetry of the system, the generic nearest-neighbour Hamiltonian can be locally defined as a XYZ model with out-of-plane Dzyaloshinskii-Moriya interactions. We proceed to study its phase diagram in the classical limit, making use of an exact reformulation of the Hamiltonian in terms of irreducible representations (irreps) of the lattice symmetry group. This reformulation in terms of irreps naturally explains the three-fold mapping between SLs recently studied on kagome by the present authors [Nat Commun 7, 10297 (2016)]. In addition, a number of unusual states are stabilised in the regions where different forms of GS order compete, including a stripy phase with a local Z8 symmetry and a classical analogue of a chiral SL. This generic Hamiltonian also turns out to be a fruitful hunting ground for coexistence of different forms of magnetic order, or of order and disorder, which we find is a particular property of the kagome lattice arising from the odd number of spins per frustrated unit. These results are compared and contrasted with those obtained on the pyrochlore lattice, and connection is made with recent progress in understanding quantum models with S = 1/2

INFLUENCE OF ANISOTROPY AND MAGNETIC FIELD ON THERMAL ENTANGLEMENT IN HEISENBERG MODEL AND THERMODYNAMIC ANALYSIS OF MODEL

The thermal entanglement in a two-qubit anisotropic Heisenberg XXZ system, also XYZ system, with Dzyaloshinskii-Moriya (DM) couplings in an inhomogenous magnetic field, was studied. The effects of these two kinds of anisotropies on the thermal entanglement have been studied in detail in the concept for concurrence, the measure of entanglement. The analytical expressions of concurrence are obtained for this model. It is found that the DM interaction can enhance thermal entanglement and can be efficiently controlled by the DM interaction parameter and ehchange interaction Jx, Jy and Jz. When D is large enough, the entanglement can exist for larger temperatures and strong magnetic field. We also analysed thermodynamic properties of Heisenberg model and the most important results were shown in the paper.

Effects of second neighbor interactions on skyrmion lattices in chiral magnets

In this paper we investigate the influences of the second neighbor interactions on a skyrmion lattice in two-dimensional chiral magnets. Such a system contains the exchange and the Dzyaloshinskii–Moriya for the spin interactions and therefore, we analyse three situations: firstly, the second neighbor interaction is present only in the exchange coupling; secondly, it is present only in the Dzyaloshinskii–Moriya coupling. Finally, the second neighbor interactions are present in both exchange and Dzyaloshinskii–Moriya couplings. We show that such effects cause important modifications to the helical and skyrmion phases when an external magnetic field is applied.

Interfacial Dzyaloshinskii-Moriya Interaction in Pt/CoFeB Films: Effect of the Heavy-Metal Thickness.

We report the observation of a Pt layer thickness dependence on the induced interfacial Dzyaloshinskii-Moriya interaction in ultrathin Pt(d_{Pt})/CoFeB films. Taking advantage of the large spin-orbit coupling of the heavy metal, the interfacial Dzyaloshinskii-Moriya interaction is quantified by Brillouin light scattering measurements of the frequency nonreciprocity of spin waves in the ferromagnet. The magnitude of the induced Dzyaloshinskii-Moriya coupling is found to saturate to a value of 0.45 mJ/m^{2} for Pt thicknesses larger than ∼2 nm. The experimental results are explained by analytical calculations based on the three-site indirect exchange mechanism that predicts a Dzyaloshinskii-Moriya interaction at the interface between a ferromagnetic thin layer and a heavy metal. Our findings open up a way to control and optimize chiral effects in ferromagnetic thin films through the thickness of the heavy-metal layer.

Heisenberg and Dzyaloshinskii-Moriya interactions controlled by molecular packing in trinuclear organometallic clusters

Motivated by recent synthetic and theoretical progress we consider magnetism in crystals of multi-nuclear organometallic complexes. We calculate the Heisenberg symmetric exchange and the Dzyaloshinskii-Moriya antisymmetric exchange. We show how, in the absence of spin-orbit coupling, the interplay of electronic correlations and quantum interference leads to a quasi-one dimensional effective spin model in a typical tri-nuclear complex, Mo$_3$S$_7$(dmit)$_3$, despite its underlying three dimensional band structure. We show that both intra- and inter-molecular spin-orbit coupling can cause an effective Dzyaloshinskii-Moriya interaction. Furthermore, we show that, even for an isolated pair of molecules the relative orientation of the molecules controls the nature of the Dzyaloshinskii-Moriya coupling. We show that interference effects also play a crucial role in determining the Dzyaloshinskii-Moriya interaction. Thus, we argue, that multi-nuclear organometallic complexes represent an ideal platform to investigate the effects of Dzyaloshinskii-Moriya interactions on quantum magnets.

INFLUENCE OF ANISOTROPY AND MAGNETIC FIELD ON THERMAL ENTANGLEMENT IN HEISENBERG MODEL AND THERMODYNAMIC ANALYSIS OF MODEL

The thermal entanglement in a two-qubit anisotropic Heisenberg XXZ system, also XYZ system, with Dzyaloshinskii-Moriya (DM) couplings in an inhomogenous magnetic field, was studied. The effects of these two kinds of anisotropies on the thermal entanglement have been studied in detail in the concept for concurrence, the measure of entanglement. The analytical expressions of concurrence are obtained for this model. It is found that the DM interaction can enhance thermal entanglement and can be efficiently controlled by the DM interaction parameter and ehchange interaction Jx, Jy and Jz. When D is large enough, the entanglement can exist for larger temperatures and strong magnetic field. We also analysed thermodynamic properties of Heisenberg model and the most important results were shown in the paper.

Investigations of the Quantum Correlation in Two-Qubit Heisenberg XYZ Model with Decoherence

Quantum correlation dynamics in an anisotropic Heisenberg XYZ model under decoherence is investigated with the use of concurrence C and quantum discord (QD). With the Werner state as the initial state, we discuss the influence of mixture degree r on the dynamics. There are some difference between the time evolution behaviors of these two correlation measures with different value of r. For 0 ≤ r ≤ 1/3, there exists quantum discord but no entanglement; For 1/3<r<1, there is a ”entanglement sudden death and birth” phenomenon in the concurrence but not in the QD; For r=1, there is one interesting thing that the concurrence decays from 1 to a minimum value close to 0 but the QD vanish. In addition, we have investigated the influence of different parameters on the two correlation measures. It has been found that, the concurrence and QD both exhibit osillatory behaviors with the time evolution, which is independent on the magnetic field B and the coupling coefficient J z . However, the Dzyaloshinskii-Moriya interaction (D) and coupling coefficient J have strong influence on concurrence and QD. With the increasing of the D or J, the frequency of the oscillation getting larger. When time is fixed, with the increasing of D or J, the concurrence and QD change periodically.

Barlowite as a canted antiferromagnet: Theory and experiment

We investigate the structural, electronic and magnetic properties of the newly synthesized mineral barlowite Cu4(OH)6FBr which contains Cu2+ ions in a perfect kagome arrangement. In contrast to the spin-liquid candidate herbertsmithite ZnCu3(OH)6Cl2, kagome layers in barlowite are perfectly aligned due to the different bonding environments adopted by F- and Br- compared to Cl-. We perform density functional theory calculations to obtain the Heisenberg Hamiltonian parameters of Cu4(OH)6FBr which has a Cu2+ site coupling the kagome layers. The 3D network of exchange couplings together with a substantial Dzyaloshinskii-Moriya coupling lead to canted antiferromagnetic ordering of this compound at TN=15 K as observed by magnetic susceptibility measurements on single crystals.

Anisotropic magnetic couplings and structure-driven canted to collinear transitions inSr2IrO4by magnetically constrained noncollinear DFT

We put forward a scheme to study the anisotropic magnetic couplings in Sr2IrO4 by mapping fully relativistic constrained noncollinear density functional theory including an on-site Hubbard U correction onto a general spin model Hamiltonian. This procedure allows for the simultaneous account and direct control of the lattice, spin and orbital interactions within a fully ab initio scheme. We compute the isotropic, single site anisotropy and Dzyaloshinskii-Moriya (DM) coupling parameters, and clarify that the origin of the canted magnetic state in Sr2IrO4 arises from the interplay between structural distortions and the competition between isotropic exchange and DM interactions. A complete magnetic phase diagram with respect to the tetragonal distortion and the rotation of IrO6 octahedra is constructed, revealing the presence of two types of canted to collinear magnetic transitions: a spin-flop transition with increasing tetragonal distortion and a complete quenching of the basal weak ferromagnetic moment below a critical octahedral rotation.

Microscopic theory of Dzyaloshinskii–Moriya coupling and related exchange-relativistic effects

I present a short overview of the results of the microscopic theory of the Dzyaloshinskii–Moriya coupling and other related exchange-relativistic effects such as exchange anisotropy, antisymmetric magnetoelectric coupling, antisymmetric magnetogyrotropic effects, and electron-nuclear antisymmetric supertransferred hyperfine interactions in strongly correlated 3d compounds.

Quantum theory of spin waves in finite chiral spin chains

We calculate the effect of spin waves on the properties of finite size spin chains with a chiral spin ground state observed on bi-atomic Fe chains deposited on Iridium(001). The system is described with a Heisenberg model supplemented with a Dzyaloshinskii-Moriya (DM) coupling and a uniaxial single ion anisotropy that presents a chiral spin ground state. Spin waves are studied using the Holstein-Primakoff (HP) boson representation of spin operators. Both the renormalized ground state and the elementary excitations are found by means of Bogoliubov transformation, as a function of the two variables that can be controlled experimentally, the applied magnetic field and the chain length. Three main results are found. First, because of the non-collinear nature of the classical ground state, there is a significant zero point reduction of the ground state magnetization of the spin spiral. Second, the two lowest energy spin waves are edge modes in the spin spiral state that, above a critical field the results into a collinear ferromagnetic ground state, become confined bulk modes. Third, in the spin spiral state, the spin wave spectrum exhibits oscillatory behavior as function of the chain length with the same period of the spin helix.