Dzyaloshinskii-Moriya Exchange Interaction Research Articles

Strongly canted antiferromagnetic ground state in Cu3(OH)2F4

An unique crystal structure of copper hydroxyl-fluorite, Cu3(OH)2F4, hosts the trimerized chains of both edge-sharing and corner-sharing CuO2F2 plaquettes. The results of the comprehensive study of this compound, including new synthetic route, measurements of specific heat, ac- and dc-susceptibility, pulsed field magnetization, electron spin resonance, muon spin rotation and relaxation and first principles calculations are presented. The data evidence magnetic phase transition at TC = 12.5 K into canted antiferromagnetic state which is due to antisymmetric Dzyaloshinskii-Moriya (DM) exchange interaction. No alteration of DM component stemming from the intrinsic features of the crystal lattice in Cu3(OH)2F4 results in unusually large spontaneous magnetization. At T < TC, the remanence MR constitutes significant portion of saturation magnetization MS which defines the canting angle φ = 4°.

Magnetic skyrmion size and stability in ultrathin nanodots accounting Dzyaloshinskii-Moriya exchange interaction

The stability of the skyrmion magnetization configurations in ultrathin circular magnetic nanodots is calculated analytically and simulated micromagnetically considering realistic magnetic and geometrical dot parameters taken from recent experiments. The chiral Dzyaloshinskii-Moriya exchange interaction (DMI) is taken into account as an interfacial energy term. The diagram of single Néel skyrmion stability/metastability, skyrmion sizes and magnetization profiles are found as a function of the magnetic and geometrical dot parameters. It is shown that most of skyrmions are unstable or metastable and the stability region where the Néel skyrmion is the ground state is small. The Dzyaloshinskii criterion for the instability of ferromagnetic state in bulk ferromagnets with respect to the increasing DMI strength should be essentially modified to describe the stability of magnetic skyrmions in 2D systems like ultrathin ferromagnetic films and nanodots.

Néel skyrmion stability in ultrathin circular magnetic nanodots

The stability of Néel skyrmions in ultrathin circular magnetic nanodots is calculated by considering the Dzyaloshinskii–Moriya exchange interaction (DMI) as an interface term. The areas of the single-Néel skyrmion stability/metastability/instability and skyrmion radius are determined as functions of the uniaxial out-of-plane magnetic anisotropy and DMI strength. It is shown that the well-known criterion of skyrmion stability in infinite film should be changed to describe the stability in nanodots. Néel skyrmions can be the ground state for dots of finite radius, whereas they can only be metastable in infinite films. The skyrmion stability area is extended by decreasing the out-of-plane anisotropy.

Distinct magnetic field dependence of N\xe9el skyrmion sizes in ultrathin nanodots

We investigate the dependence of the Néel skyrmion size and stability on perpendicular magnetic field in ultrathin circular magnetic dots with out-of-plane anisotropy and interfacial Dzyaloshinskii-Moriya exchange interaction. Our results show the existence of two distinct dependencies of the skyrmion radius on the applied field and dot size. In the case of skyrmions stable at zero field, their radius strongly increases with the field applied parallel to the skyrmion core until skyrmion reaches the metastability region and this dependence slows down. More common metastable skyrmions demonstrate a weaker increase of their size as a function of the field until some critical field value at which these skyrmions drastically increase in size showing a hysteretic behavior with coexistence of small and large radius skyrmions and small energy barriers between them. The first case is also characterized by a strong dependence of the skyrmion radius on the dot diameter, while in the second case this dependence is very weak.

Collective magnetic skyrmion gyrotropic modes in a dot chain

We investigate the collective gyrotropic modes in a linear chain of ferromagnetic nanodots in a skyrmion magnetization state. Individual skyrmions in the dots (with thickness about of 1 nm and radius about of 100 nm) are assumed to be stabilized by interplay of isotropic exchange and Dzyaloshinskii-Moriya exchange interactions, magnetic anisotropy and magnetostatic interactions. We consider the dipolar and quadrupolar interactions between moving skyrmions in the dots as prevailing mechanism responsible for dynamic interdot magnetostatic coupling. The frequency dispersion relations of the collective skyrmion gyrotropic excitations are calculated for Bloch and Neel skyrmion configurations and related differences in the frequencies are discussed. The accounting of magnetostatic interactions between the skyrmions removes phase degeneracy of the gyrotropic frequency existing for isolated skyrmions and allows distinguishing the Bloch and Neel skyrmionic configurations by their dynamic response. The interdot magnetostatic coupling and frequency bandwidth are maximal for the large-radius Bloch skyrmions in the relatively thick dots.

Azimuthal spin-wave excitations in magnetic nanodots over the soliton background: Vortex, Bloch, and Néel-like skyrmions

We study azimuthal spin-wave (SW) excitations in a circular ferromagnetic nanodot in different inhomogeneous, topologically non-trivial magnetization states, specifically, vortex, Bloch-type skyrmion and N\'eel-type skyrmion states. Continuous mapping of the SW spectrum between these states is realized with gradual change of the out-of-plane magnetic anisotropy and Dzyaloshinskii-Moriya exchange interaction (DMI). Our study shows lifting of the SW frequencies degeneracy and change in systematics of the frequency levels. The change is induced by a geometrical Berry phase, that is present for the dot-edge localized SWs in a vortex state and vanishes in skyrmion states. Furthermore, channeling of the azimuthal SWs localized at the skyrmion edge is present and induces large frequency splitting. This is attributed to DMI induced nonreciprocity, while coupling of the breathing and gyrotropic modes is related to soliton motion. Finally, an efficient coupling of the dynamic magnetization in the skyrmion state to uniform magnetic field in nanodots with non-circular symmetry is shown.

Noncollinear Two-Component Quasirelativistic Description of Spin Interactions in Exchange-Coupled Systems. Mapping Generalized Broken-Symmetry States to Effective Spin Hamiltonians.

We provide a consistent mapping of noncollinear two-component quasirelativistic DFT energies with appropriate orientations of localized spinor quantization axes for multinuclear exchange-coupled transition-metal complexes onto an uncoupled anisotropic effective spin Hamiltonian. This provides access to the full exchange interaction tensor between the centers of spin-coupled systems in a consistent way. The proposed methodology may be best viewed as a generalized broken-symmetry density functional theory approach (gBS-DFT). While the calculations provided are limited to trinuclear systems ([M3O(OOCH)6(H2O)3]+, where M = Cr(III), Mn(III), Fe(III)) with C3 symmetry, the method provides a general framework that is extendable to arbitrary systems. It offers an alternative to previous approaches to single-ion zero-field splittings, and it provides access to the less often examined antisymmetric Dzyaloshinskii-Moriya exchange interaction. Spin-orbit coupling is included self-consistently. This will be of particular importance for complexes involving 4d or 5d transition metal centers or possibly also for f-block elements, where a perturbational treatment of spin-orbit coupling may not be valid anymore. While a comparison with experimental data was indirect due to simplifications in the chosen model structures, the agreement obtained indicates the essential soundness of the presented approach.

Research progress on topological properties and micro-magnetic simulation study in dynamics of magnetic skyrmions

Skyrmions, as a nontrivial topological magnetic structure, have the advantages of topological stability, small size and low driving electrical current, showing potential applications in spintronic memory device. There are several mechanisms for skyrmion formation in magnets. One major mechanism is, in chiral-lattice ferromagnets, the competition between the Dzyaloshinskii-Moriya and ferromagnetic exchange interactions, due to the lack of spatial inversion symmetry. The combination of topology and condensed physics demonstrates various new topological phenomena of skyrmions, which also determine their dynamics. In this review, recent progress on the topological physics foundation of Skyrmions, as well as their dynamics of application in spintronics devices, is reviewed. The topological physics foundations of skyrmions is introduced. Firstly, the structure of skyrmions, which shows a special nontrivial topology in the real space, is presented accompanied with the formation of skyrmions caused by Dzyaloshinskii Moriya interactions in chiral magnets. Secondly, due to the importance of the describable method of the topology of a skyrmion, the topological charge, that characterize the topology, as well as the calculation method are introduced. Also, the arising topological stability is discussed here. Then, the typical topological effects arising from the topology of a skyrmion, including topological Hall effect and the skyrmion Hall effect are reviewed. The next is the introduction of the helical and the spiral spin configuration, the alternatives for Bloch and Nal type skyrmions respectively, which show up under lower external magnetic field with the same interaction. Also the phase transition of the helical/spiral state to skyrmions and the Monte Carlo method to simulate the spin configuration of a chiral magnet are introduced. At last, the spin orbital torque and the spin transfer torque, that describe the driven effect of a skyrmion by an electrical current or a thermal field, are reviewed. The consequence dynamics of skyrmions, the Landau-LifshitzGilbert equation, are also introduced. The recent progress of typical dynamics of skyrmions on several concerned problems in practical applications are reviewed. The applications in spintronics memory require skyrmions have steady transportation driven by electrical current and controllable creation and annihilation process. Firstly, skyrmion can be generated by the spatial nonuniform electric current with a certain geometry constrain. Especially for the Nal type skyrmion, nonuniformity of the spin orbital torque, come from the non-uniform electric current, play an important role in the skyrmion generation process. Secondly, skyrmion moves with a perpendicular velocity under an electrical current, because of the skyrmion Hall effect. So the elimination of skyrmion Hall effect is practically concerned to make the transportation steady. The anti-ferromagnetic skyrmion and antiferromagnetic coupled skyrmion bilayer are found with no skyrmion Hall effect by have two opposite component cancel out. Finally, with topological stability, skyrmions are hard to convert from and to a nontrivial topological spin configuration at low temperature. So the manipulation of skyrmion creation and annihilation are discussed accompanied with their difference of Bloch and Nal type skyrmiom.

EPR-Determined Anisotropy of the g-Factor and Magnetostriction of a Cu2MnBO5 Single Crystal with a Ludwigite Structure

Electron paramagnetic resonance (EPR) and magnetostriction of the Cu2MnBO5 single crystal have been studied. The EPR spectrum consists of a single Lorentzian line due to the exchange-coupled system of spins of Cu2+ and Mn3+ ions. It has been established experimentally that the g-factor in the paramagnetic region is strongly anisotropic and anomalously small, which is not typical of the exchange-coupled system of spins of Cu2+ and Mn3+ ions. At a temperature of 150 K, the g-factors along the crystallographic a, b, and c axes are 2.04, 1.96, and 1.87, respectively. Such small effective g-factor values can be due to the effect of the anisotropic Dzyaloshinskii–Moriya exchange interaction between the spins of Cu2+ and Mn3+ ions directed along the a axis. The presence of two Cu2+ and Mn3+ Jahn–Teller ions occupying four nonequivalent positions in the crystal is responsible for the absence of the inversion center. It is found that the behavior of the magnetostriction of Cu2MnBO5 is not typical of transition-metal crystals but is closer to the behavior of crystals containing rare-earth ions.

Bi‐Stability of Magnetic Skyrmions in Ultrathin Multilayer Nanodots Induced by Magnetostatic Interaction

We report the results of simulations of magnetic skyrmion stability in ultrathin magnetic multilayer nanodots with interfacial Dzyaloshinskii–Moriya exchange interaction (DMI). We found that in presence of the lateral confinement the magnetostatic energy significantly influences the skyrmion stability and leads to stabilization of large‐radius skyrmion even at low values of the DMI strength, in addition to small‐radius skyrmion stabilized by DMI. In particular, stabilization of the skyrmion state with two different radii (bi‐stability) is found in dipolarly‐coupled (Pt/Co/Ir)n circular nanodots with the number of repeats of the unit cell n = 3 and 5. The bi‐stability range is located at the DMI strength of 0.9–1.1 mJ m−2 or at the total Co‐layer thickness of 2.2–2.6 nm.

Magnetic skyrmion low frequency dynamics in thin circular dots

We calculate low-frequency gyrotropic excitation modes of the skyrmion state thin cylindrical magnetic dots. The skyrmion is assumed to be stabilized at room temperature and zero external magnetic field due to an interplay of the isotropic and Dzyaloshinskii-Moriya exchange interactions, perpendicular magnetic anisotropy and magnetostatic interaction. We consider Bloch and Neel-type magnetic skyrmions and assume that the dot magnetization does not depend on the thickness coordinate. The skyrmion gyrotropic frequencies are calculated in GHz range as a function of the skyrmion equilibrium radius, dot radius and the dot magnetic parameters. The magnetostatic interaction is explicitly accounted via appropriate ansatz of the skyrmion magnetization. Recent experiments and calculations of magnetic skyrmion dynamics in infinite thin films and nanodots are discussed.

Quantum phase transitions of a generalized compass chain with staggered Dzyaloshinskii–Moriya interaction

We consider a class of one-dimensional compass models with staggered Dzyaloshinskii–Moriya exchange interactions in an external transverse magnetic field. Based on the exact solution derived from Jordan–Wigner approach, we study the excitation gap, energy spectra, spin correlations and critical properties at phase transitions. We explore mutual effects of the staggered Dzyaloshinskii–Moriya interaction and the magnetic field on the energy spectra and the ground-state phase diagram. Thermodynamic quantities including the entropy and the specific heat are discussed, and their universal scalings at low temperature are demonstrated.

Spin excitation spectrum in a magnetic nanodot with continuous transitions between the vortex, Bloch-type skyrmion, and Néel-type skyrmion states

We study spin-wave excitations in a circular ferromagnetic nanodot in different inhomogeneous, topologically non-trivial magnetization states, specifically, vortex and skyrmion states. Gradual change in the strength of the out-of-plane magnetic anisotropy and the Dzyaloshinskii-Moriya exchange interaction leads to continuous phase transitions between different stable magnetic configurations and allows for mapping of dynamic spin modes in and between the vortex, Bloch-type skyrmion and N\'eel-type skyrmion states. Our study elucidates the connections between gyrotropic modes, azimuthal spin waves and breathing modes in various stable magnetization states and helps to understand the rich spin excitation spectrum on the skyrmion background.

Magnetic ordering induced ferroelectricity in α-Cu2V2O7 studied through non-magnetic Zn doping

We have studied the magnetic and electronic properties of Cu2-xZnxV2O7 by magnetization, specific heat, and dielectric measurements. X-ray structural analysis shows a Zn-mediated phase transition from the α- to the β-phase beyond a critical Zn concentration of xc = 0.15. While Cu2V2O7 exhibits a canted antiferromagnetism with an associated weak ferromagnetism in the α-phase, the β-phase is purely antiferromagnetic. The spin canting arises due to the Dzyaloshinskii-Moriya exchange interaction in the anti-symmetric α-phase. The temperature dependence of the heat capacity for the sample in the α-phase shows a clear lambda like transition at a temperature where the magnetic susceptibility also displays an anomaly and indicates an onset of long range magnetic ordering. Dielectric properties display a clear anomaly around the magnetic transition temperature in α-Cu2V2O7. The anomaly weakens with the increase in the Zn concentration and disappears at the doping level where α to β phase transition occurs. This confirms the existence of magneto-electric coupling in α-Cu2V2O7 but not in its β-phase. Analysis of the experimental data shows that magneto-electric coupling is non-linear in nature, which is in agreement with the Landau theory of continuous phase transition. So, α-Cu2V2O7 establishes itself as a promising candidate for magnetic multiferroics.

Gyrotropic Skyrmion Modes in Ultrathin Magnetic Circular Dots

We calculate gyrotropic excitation modes of the skyrmion ground state in ultrathin cylindrical magnetic dots. The skyrmion is assumed to be stabilized at room temperature and zero external magnetic field due to an interplay of the isotropic and Dzyaloshinskii-Moriya exchange interactions, perpendicular magnetic anisotropy, and magnetostatic interaction. The gyrotropic frequencies of the Bloch- and Neel-type magnetic skyrmions are calculated in the gigahertz range as a function of the skyrmion equilibrium radius, dot radius, and the dot magnetic parameters. Recent experiments and simulations of magnetic skyrmion gyrotropic dynamics in nanodots are discussed.

Magnetic phases and unusual topological electronic structures of Weyl semimetals in strong interaction limit

The interplay of electronic band structures and electron-electron interactions is known to brew new phases in condensed matter. In this paper, we investigate thermodynamic phases and corresponding electronic structures of the Weyl semimetal in the strong onsite Coulomb interaction limit. Based on a minimum model of the Weyl semimetal with two linear Weyl nodes, it is shown that generically the Weyl semimetal becomes magnetic in the presence of interactions. In particular, it is shown that the Dzyaloshinskii-Moriya exchange interaction is generally induced so that the A-type antiferromagnetic (A-AFM) phase and the spiral spin density wave (SSDW) states are two generic phases. Furthermore, we find that Weyl nodes proliferate and it is possible to doubly enhance the unusual properties of non-interacting Weyl semimetals through the realization of double-Weyl nodes in strong correlation limit. Specifically, it is shown that in the SSDW phase, linear Weyl nodes are tuned into double-Weyl nodes with the corresponding charges being $\pm 2$. As the spin-orbit coupling increases, a quantum phase transition occurs with the SSDW phase being turned into an A-AFM phase and at the same time, double-Weyl nodes are disintegrated into two pairs of linear Weyl nodes. Our results reveal the unusual interplay between the topology of electronic structures and magnetism in strongly correlated phases of Weyl semimetals.

Spin-wave and electromagnon dispersions in multiferroicMnWO4as observed by neutron spectroscopy: Isotropic Heisenberg exchange versus anisotropic Dzyaloshinskii-Moriya interaction

High resolution inelastic neutron scattering reveals that the elementary magnetic excitations in multiferroic MnWO4 consist of low energy dispersive electromagnons in addition to the well-known spin-wave excitations. The latter can well be modeled by a Heisenberg Hamiltonian with magnetic exchange coupling extending to the 12th nearest neighbor. They exhibit a spin-wave gap of 0.61(1) meV. Two electromagnon branches appear at lower energies of 0.07(1) meV and 0.45(1) meV at the zone center. They reflect the dynamic magnetoelectric coupling and persist in both, the collinear magnetic and paraelectric AF1 phase, and the spin spiral ferroelectric AF2 phase. These excitations are associated with the Dzyaloshinskii-Moriya exchange interaction, which is significant due to the rather large spin-orbit coupling.

Skyrmion State Stability in Magnetic Nanodots With Perpendicular Anisotropy

Stability of skyrmion magnetization configuration in a circular magnetic nanodot with an uniaxial anisotropy perpendicular to the dot plane is calculated. It is shown that the skyrmion state can have magnetic energy lower than the vortex and perpendicular single domain state in a finite range of magnetic anisotropy fields at room temperature even in the case of absence of the Dzyaloshinskii-Moriya exchange interaction and external magnetic field.

Effects of the Dzyaloshinskii-Moriya interaction in Cr3 triangular spin clusters detected by specific heat and multi-frequency electron spin resonance.

An oxo-centered [Cr3O(O2C(t)Bu)6(H2O)3](O2C(t)Bu) HO2C(t)Bu·2EtOH triangular cluster has been synthesized and its magnetic properties have been studied by means of complementary techniques, namely magnetometry, specific heat and multi-frequency Electron Paramagnetic Resonance (EPR). Measurements on oriented single-crystals evidenced the presence of anisotropy that we attributed to the combined effect of Dzyaloshinskii-Moriya exchange interaction and distortion. By means of a minimal set of parameters, we show that a simple analytical model well describes the main features of the full set of experimental data.

Exact treatment of magnetism-driven ferroelectricity in the one-dimensional compass model

We consider a class of one-dimensional compass models with antisymmetric Dzyaloshinskii-Moriya exchange interaction in an external magnetic field. Based on the exact solution derived by means of Jordan-Wigner transformation, we study the excitation gap, spin correlations, ground-state degeneracy, and critical properties at phase transitions. The phase diagram at finite electric and magnetic field consists of three phases: ferromagnetic, canted antiferromagnetic, and chiral. Dzyaloshinskii-Moriya interaction induces an electrical polarization in the ground state of the chiral phase, where the nonlocal string order and special features of entanglement spectra arise, while strong chiral correlations emerge at finite temperature in the other phases and are controlled by a gap between the nonchiral ground state and the chiral excitations. We further show that the magnetoelectric effects in all phases disappear above a typical temperature corresponding to the total bandwidth of the effective fermionic model. To this end we explore the entropy, specific heat, magnetization, electric polarization, and the magnetoelectric tensor at finite temperature. We identify rather peculiar specific-heat and polarization behavior of the compass model which follows from highly frustrated interactions.