Dzyaloshinskii-Moriya Interaction Anisotropy Research Articles

Studying magnon band topology through low-energy magnon excitations: role of anisotropic Dzyaloshinskii-Moriya interaction.

In this work, we study topological properties of magnons via creating spin excitations in both ferromagnets and antiferromagnets in presence of an external magnetic field on a two-dimensional square lattice. It is known that Dzyaloshinskii-Moriya interaction (DMI) plays an important role in coupling between different particle (spin excitation) sectors, here we consider an anisotropic DMI and ascertain the role of the anisotropy parameter in inducing topological phase transitions. While the scenario, for dealing with ferromagnets, albeit with isotropic DMI is established in literature, we have developed the formalism for studying magnon band topology for the antiferromagnetic case. The calculations for the ferromagnetic case are included to facilitate a comparison between the two magnetically ordered systems. Owing to the presence of a two-sublattice structure of an antiferromagnet, a larger number of magnon bands participate in deciding upon the topological properties. However, in both the cases, an extended trivial region is observed even with the DMI to be non-zero, which is surprising since the DMI is the origin of the finite Berry curvature in presence of external magnetic field. The nature of the phases in both the cases and the phase transitions therein are characterized via computing the band structure, ascertaining the presence (or absence) of the chiral edge modes observed in a semi-infinite nano-ribbon geometry, and investigation of the thermal Hall effect. Moreover, the strength of the magnetic field is found to play a decisive role in controlling the critical point that demarcates various topological phases.

Strain mediated transition between skyrmion and antiskyrmion in ferromagnetic thin films

Magnetic topological structures have attracted great attention due to their potential applications in memory and logic devices. Achieving the controllable transition between different magnetic topological structures is crucial for their application. Here, we develop a phase field model with strain-modulated Dzyaloshinskii-Moriya interaction (DMI) and predict the controllable transitions between skyrmion and antiskyrmion states in a ferromagnetic thin film through the application of different strains. It is found that the anisotropic DMI induced by anisotropic strains in the thin film plays an important role in the transitions between various magnetic structures, including skyrmion, antiskyrmion, single domain, and helical domain. Anisotropic DMI also has a significant impact on the chirality and deformation of magnetic topological structures, among which anisotropic DMI can cause anisotropic deformation of skyrmions and antiskyrmions. Furthermore, the formation mechanism of antiskyrmions is elucidated by decomposing the magnetization vectors into Bloch and Néel-type components based on the Lifshitz invariant. This work not only provides an insight into the dynamic behaviors of topological structures but also suggests a new method for controlling magnetic configurations through strain engineering.

Elliptical spin textures in two-dimensional semimetals with spatially anisotropic Dzyaloshinskii-Moriya interaction

Elliptical spin textures in two-dimensional semimetals with spatially anisotropic Dzyaloshinskii-Moriya interaction

Role of isotropic and anisotropic Dzyaloshinskii–Moriya interaction on skyrmions, merons and antiskyrmions in the C nv symmetric system

The lattice Hamiltonian with the presence of a chiral magnetic isotropic Dzyaloshinskii–Moriya interaction (DMI) in a square and hexagonal lattice is numerically solved to give the full phase diagram consisting of skyrmions and merons in different parameter planes. The phase diagram provides the actual regions of analytically unresolved asymmetric skyrmions and merons, and it is found that these regions are substantially larger than those of symmetric skyrmions and merons. With magnetic field, a change from meron or spin spiral (SS) to skyrmion is seen. The complete phase diagram for the C nv symmetric system with anisotropic DMI is drawn and it is shown that this DMI helps to change the SS propagation direction. Finally, the well-defined region of a thermodynamically stable antiskyrmion phase in the C nv symmetric system is shown.

Elliptical k[formula omitted] skyrmions in the presence of the anisotropic Dzyaloshinskii–Moriya interaction

In this work, using micromagnetic simulations, we studied the stabilization of kπ skyrmions (k =1, …, 5), in the presence of the anisotropic Dzyaloshinskii–Moriya interaction (DMI), in a ferromagnetic dot. Our results show that the shape and size of the kπ skyrmions depend on the values of Dx and Dy (area unit energy densities along the x and y axes). A rich phase diagram was obtained as a function of Dx and Dy. Also, power spectra and the spatial profile of the spin wave modes of the kπ skyrmions were obtained as a function of Dx and Dy. These results show that the distribution of the maximum amplitudes of oscillation of the spin wave modes are distributed in circular or elliptical ring in the ferromagnetic dot, according to values of Dx and Dy.

Formation and Control of Zero-Field Antiskyrmions in Confining Geometries.

Magnetic skyrmions and antiskyrmions have attracted much interest owing to their topological features and spintronic functionalities. In contrast to skyrmions, the generation of antiskyrmions relies on tunning both the magnitude and direction of the external magnetic field. Here, it is reported that antiskyrmions can be efficiently created via quenching and robustly persist at zero field in the Fe1.9Ni0.9Pd0.2P magnet with the S 4‐symmetry. It is demonstrated that well‐ordered antiskyrmions form in a square lattice in a confining micrometer‐scale square geometry, while the antiskyrmion lattice distorts in triangular, circular, or rotated‐square geometry; the distortion depends on the relative configuration between sample edges and the two q‐vectors arising from the anisotropic Dzyaloshinskii–Moriya interaction, in good agreement with micromagnetic simulations. It is also characterized transformations from antiskyrmions to skyrmions and nontopological bubbles at different directions and values of external field. These results demonstrate a roadmap for generating and controlling antiskyrmions in a confining geometry.

Study of magnetization and specific heat of Heisenberg model on Lieb nanolattice: Anisotropic effects

We study the effects of longitudinal magnetic field and temperature on the thermodynamic properties of two dimensional Heisenberg antiferromagnet on the line-centered square lattice in the presence of anisotropic Dzyaloshinskii–Moriya interaction. We have studied the temperature dependence of specific heat and longitudinal magnetization of Lieb lattice for various physical parameters in the model Hamiltonian. Using a hard core bosonic representation, the behavior of thermodynamic properties has been studied by means of excitation spectrum of mapped bosonic gas. The effect of Dzyaloshinskii–Moriya interaction term on thermodynamic properties has also been studied via the bosonic model by exploiting Green’s function approach. Furthermore we have studied the magnetic field dependence of specific heat and magnetization for various Dzyaloshinskii–Moriya coupling strength. At low temperatures, the specific heat is found to be monotonically increasing with temperature for magnetic fields in the gapped field induced phase region. We have found the magnetic field dependence of specific heat shows a monotonic decreasing behavior for various magnetic fields due to increase of energy gap in the excitation spectrum. Also we have studied the dependence of magnetization on Dzyaloshinskii–Moriya interaction strength for different magnetic field values. • The study of thermodynamic properties of Lieb lattice in the context of Heisenberg model. • The study the temperature dependence of specific heat of Lieb lattice. • The study of magnetization with spin orbit coupling. • The study of specific heat of Lieb lattice.

Anisotropic Dzyaloshinskii-Moriya interaction protected by D2d crystal symmetry in two-dimensional ternary compounds

AbstractMagnetic skyrmions, topologically protected chiral spin swirling quasiparticles, have attracted great attention in fundamental physics and applications. Recently, the discovery of two-dimensional (2D) van der Waals (vdW) magnets have aroused great interest due to their appealing physical properties. Moreover, both experimental and theoretical works have revealed that isotropic Dzyaloshinskii–Moriya interaction (DMI) can be achieved in 2D magnets or ferromagnet-based heterostructures. However, 2D magnets with anisotropic DMI haven’t been reported yet. Here, via using first-principles calculations, we unveil that anisotropic DMI protected by D2d crystal symmetry can exist in 2D ternary compounds MCuX2 (M: 3d transition metal (TM), X: group VIA). Interestingly, by using micromagnetic simulations, we demonstrate that ferromagnetic (FM) antiskyrmions, FM bimerons, antiferromagnetic (AFM) antiskyrmions, and AFM bimerons can be realized in the MCuX2 family. Our discovery opens up an avenue to creating antiskyrmions and bimerons with anisotropic DMI protected by D2d crystal symmetry in 2D magnets.

The stability of 3D skyrmions under mechanical stress studied via Monte Carlo calculations

Using Monte Carlo (MC) simulations, we study the skyrmion stability/instability as a response to uniaxial mechanical stresses. Skyrmions emerge in chiral magnetic materials as a stable spin configuration under external magnetic field B→ with the competition of ferromagnetic interaction and Dzyaloshinskii–Moriya interaction (DMI) at low temperature T. Skyrmion configurations are also known to be stable (unstable) under a compressive stress applied parallel (perpendicular) to B→. To understand the origin of such experimentally confirmed stability/instability, we use the Finsler geometry modeling technique with a new degree of freedom for strains, which plays an essential role in DMI being anisotropic. We find from MC data that the area of the skyrmion state on the B−T phase diagram increases (decreases) depending on the direction of applied stresses, in agreement with reported experimental results. This change in the area of the skyrmion state indicates that skyrmions become more (less) stable if the tensile strain direction is parallel (perpendicular) to B→. From the numerical data in this paper, we find that the so-called magneto-elastic effect is suitably implemented in the effective DMI theory with the strain degree of freedom without complex magneto-elastic coupling terms for chiral magnetic materials. This result confirms that experimentally-observed skyrmion stability and instability are caused by DMI anisotropy.

Spin-wave modes of elliptical skyrmions in magnetic nanodots

Magnetic skyrmions, whose shapes are ellipse due to the presence of anisotropic Dzyaloshinskii–Moriya interaction (DMI), have already been discovered in experiments recently. By using micromagnetic simulations, we discuss the ground state and the spin-wave modes of a single elliptical skyrmion in a confined nanodot. It is found that the shapes of skyrmion are stretched into a horizontal ellipse, vertical ellipse, or stripe shape under different strengths of anisotropic DMI. When elliptical skyrmions are excited by in-plane ac magnetic fields, the spin-wave mode contains a counterclockwise rotation mode at high frequencies and a clockwise (CW) rotation mode at low frequencies, and the CW mode depends on the strength of anisotropic DMI. When elliptical skyrmions are excited by out-of-plane ac magnetic fields, the spin-wave mode is split from a simple breathing mode into two complex breathing modes, including a mixed mode of CW rotation and breathing, and another anisotropic breathing mode. Our results provide an understanding of the rich spin-wave modes for skyrmions, which may contribute to the applications in magnonics.

Doping Control of Magnetic Anisotropy for Stable Antiskyrmion Formation in Schreibersite (Fe,Ni)3 P with S4 symmetry.

Magnetic skyrmions, vortex-like topological spin textures, have attracted much interest in a wide range of research fields from fundamental physics to spintronics applications. Recently, growing attention is also paid to antiskyrmions emerging with opposite topological charge in non-centrosymmetric magnets with D2d or S4 symmetry. In these magnets, complex interplay among anisotropic Dzyaloshinskii-Moriya interaction, uniaxial magnetic anisotropy, and magnetic dipolar interactions generates various magnetic textures. However, the precise role of these magnetic interactions in stabilizing antiskyrmions remains to be elucidated. In this work, the uniaxial magnetic anisotropy of schreibersite (Fe,Ni)3 P with S4 symmetry is controlled by doping and its impact on the stability of antiskyrmions is investigated. The authors' magnetometry study, supported by ferromagnetic resonance spectroscopy, shows that the variation of the Ni content and slight doping with 4d transition metals considerably change the magnetic anisotropy. In particular, doping with Pd induces easy-axis anisotropy, giving rise to formation of antiskyrmions, while a temperature-induced spin reorientation is observed in an Rh-doped compound. In combination with Lorentz transmission electron microscopy and micromagnetic simulations, the stability of antiskyrmion as functions of uniaxial anisotropy and demagnetization energy is quantitatively analyzed, and demonstrated that subtle balance between them is necessary to stabilize the antiskyrmions.

Crystal chemistry criteria of the existence of spin liquids on the kagome lattice

The structural-magnetic models of 25 antiferromagnetic kagome cuprates similar to herbertsmithite (ZnCu3(OH)6Cl2)—a perspective spin liquid—have been calculated and analyzed. Main correlations between the structure and magnetic properties of these compounds were revealed. It has been demonstrated that, in all AFM kagome cuprates, including herbertsmithite, there exists the competition between the exchange interaction and the antisymmetric anisotropic exchange one (the Dzyaloshinskii–Moriya interaction), as magnetic ions are not linked to the center of inversion in the kagome lattice. This competition is strengthened in all the kagome AFM, except herbertsmithite, by one more type of the anisotropy (duality) of the third in length J3 magnetic couplings (strong J3(J12) next-to-nearest-neighbor couplings in linear chains along the triangle edges and very weak FM or AFM J3(J d) couplings along the hexagon diagonals). The above couplings are crystallographically identical, but are divided to two types of different in strength magnetic interactions. The existence of duality of J3 couplings originated from the structure of the kagome lattice itself. Only combined contributions of dual J3 couplings with anisotropic Dzyaloshinskii–Moriya interactions are capable to suppress frustration of kagome antiferromagnetics. It has been demonstrated that the possibility of elimination of such a duality in herbertsmithite, which made it a spin liquid, constitutes a rare lucky event in the kagome system. Three crystal chemistry criteria of the existence of spin liquids on the kagome lattice have been identified: first, the presence of frustrated kagome lattices with strong dominant antiferromagnetic nearest-neighbor J1 couplings competing only with each other in small triangles; second, magnetic isolation of these frustrated kagome lattices; and third, the absence of duality of the third in length J3 magnetic couplings.

Topological spin textures of antiskyrmionic crystals in two-dimensional magnetic monolayers

The topological textures of a two-dimensional (2D) magnetic monolayer, where ferromagnetic (FM) Heisenberg exchange (HE) and anisotropic Dzyaloshinskii-Moriya (DM) interactions coexist, are investigated with a quantum computational method. We find from our calculated results that when the external magnetic field, exerted perpendicularly to the 2D magnetic monolayer, is gradually increased, FM helical, antiskyrmionic and antivortical lattices (abbreviated as HL, ASL and AVL respectively), spin textures consisting of skyrmions and bimerons, and those of pure bimerons, are induced on the magnetic monolayer successively. The antiskyrmionic lattice states prevail over a broad area in the T-H phase diagram, and the wavelengths of the ASLs and AVLs change discontinuously with the increasing external magnetic field. For comparison, two sets of formulas are used to calculate the topological charge Qav per particle-like spin texture, and the topological charge density, ρi, over the monolayer. Consequently, the calculated ρi contour of every ASL and AVL also forms periodical and symmetric crystals that coincides well with the corresponding spin texture, and divides the ASL or AVL into serval areas with distinct spin structures. For the ASL and spin textures consisting of skyrmions and bimerons, if the formulas of Berg and M. Lüscher (1981) are applied and every bimeron is treated as a skyrmion, the averaged Qav per antiskyrmion and per bimeron are all equal to 1. We also explain why the quantum method is able to work beyond the classical ones.

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The topological textures of a two-dimensional (2D) magnetic monolayer, where ferromagnetic (FM) Heisenberg exchange (HE) and anisotropic Dzyaloshinskii-Moriya (DM) interactions coexist, are investigated with a quantum computational method. We find from our calculated results that when the external magnetic field, exerted perpendicularly to the 2D magnetic monolayer, is gradually increased, FM helical, antiskyrmionic and antivortical lattices (abbreviated as HL, ASL and AVL respectively), spin textures consisting of skyrmions and bimerons, and those of pure bimerons, are induced on the magnetic monolayer successively. The antiskyrmionic lattice states prevail over a broad area in the T-H phase diagram, and the wavelengths of the ASLs and AVLs change discontinuously with the increasing external magnetic field. For comparison, two sets of formulas are used to calculate the topological charge Qav per particle-like spin texture, and the topological charge density, ρi, over the monolayer. Consequently, the calculated ρi contour of every ASL and AVL also forms periodical and symmetric crystals that coincides well with the corresponding spin texture, and divides the ASL or AVL into serval areas with distinct spin structures. For the ASL and spin textures consisting of skyrmions and bimerons, if the formulas of Berg and M. Lüscher (1981) are applied and every bimeron is treated as a skyrmion, the averaged Qav per antiskyrmion and per bimeron are all equal to 1. We also explain why the quantum method is able to work beyond the classical ones.

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The topological textures of a two-dimensional (2D) magnetic monolayer, where ferromagnetic (FM) Heisenberg exchange (HE) and anisotropic Dzyaloshinskii-Moriya (DM) interactions coexist, are investigated with a quantum computational method. We find from our calculated results that when the external magnetic field, exerted perpendicularly to the 2D magnetic monolayer, is gradually increased, FM helical, antiskyrmionic and antivortical lattices (abbreviated as HL, ASL and AVL respectively), spin textures consisting of skyrmions and bimerons, and those of pure bimerons, are induced on the magnetic monolayer successively. The antiskyrmionic lattice states prevail over a broad area in the T-H phase diagram, and the wavelengths of the ASLs and AVLs change discontinuously with the increasing external magnetic field. For comparison, two sets of formulas are used to calculate the topological charge Qav per particle-like spin texture, and the topological charge density, ρi, over the monolayer. Consequently, the calculated ρi contour of every ASL and AVL also forms periodical and symmetric crystals that coincides well with the corresponding spin texture, and divides the ASL or AVL into serval areas with distinct spin structures. For the ASL and spin textures consisting of skyrmions and bimerons, if the formulas of Berg and M. Lüscher (1981) are applied and every bimeron is treated as a skyrmion, the averaged Qav per antiskyrmion and per bimeron are all equal to 1. We also explain why the quantum method is able to work beyond the classical ones.

Magnetoentropic mapping and computational modeling of cycloids and skyrmions in the lacunar spinels GaV4S8 and GaV4Se8

We report the feasibility of using magnetoentropic mapping for the rapid identification of magnetic cycloid and skyrmion phases in uniaxial systems, based on the GaV4S8 and GaV4Se8 model skyrmion hosts with easy-axis and easy-plane anisotropies respectively. We show that these measurements can be interpreted with the help of a simple numerical model for the spin Hamiltonian to yield unambiguous assignments for both single phase regions and phase boundaries. In the two lacunar spinel chemistries, we obtain excellent agreement between the measured magnetoentropic features and a minimal spin Hamiltonian built on Heisenberg exchange, single-ion anisotropy, and anisotropic Dzyaloshinskii-Moriya interactions. In particular, we identify characteristic high-entropy behavior in the cycloid phase that serves as a precursor to the formation of skyrmions at elevated temperatures and is a readily-measurable signature of this phase transition. Our results demonstrate that rapid magnetoentropic mapping guided by numerical modeling is an effective means of understanding the complex magnetic phase diagrams innate to skyrmion hosts. One notable exception is the observation of an anomalous, low-temperature high-entropy state in the easy-plane system GaV$_4$Se$_8$, which is not captured in the numerical model. Possible origins of this state are discussed.

Room-temperature antiskyrmions and sawtooth surface textures in a non-centrosymmetric magnet with S4 symmetry.

Topological spin textures have attracted much attention both for fundamental physics and spintronics applications. Among them, antiskyrmions possess a unique spin configuration with Bloch-type and Néel-type domain walls owing to anisotropic Dzyaloshinskii-Moriya interaction in the non-centrosymmetric crystal structure. However, antiskyrmions have thus far only been observed in a few Heusler compounds with D2d symmetry. Here we report a new material, Fe1.9Ni0.9Pd0.2P, in a different symmetry class (S4), in which antiskyrmions exist over a wide temperature range that includes room temperature, and transform into skyrmions on changing magnetic field and lamella thickness. The periodicity of magnetic textures greatly depends on the crystal thickness, and domains with anisotropic sawtooth fractals were observed at the surface of thick crystals and attributed to the interplay between the dipolar interaction and the Dzyaloshinskii-Moriya interaction as governed by crystal symmetry. Our findings provide an arena in which to study antiskyrmions, and should stimulate further research on topological spin textures and their applications.

Stability of long-lived antiskyrmions in the Mn-Pt-Sn tetragonal Heusler material

The lifetime of antiskyrmions at room temperature in an Mn--Pt--Sn tetragonal Heusler material has been calculated using an atomic scale representation including nearly a million spins. The evaluation of the pre-exponential factor in the Arrhenius rate expression for this large system is made possible by implementation of harmonic transition state theory that avoids evaluation of the eigenvalues of the Hessian matrix. The parameter values in the extended Heisenberg Hamiltonian, including anisotropic Dzyaloshinskii-Moriya interaction, are chosen to reproduce experimental observations [Nayak et al., Nature (London) 548, 561 (2017)], in particular, the 150-nm diameter. The calculated results are consistent with the long lifetime observed in the laboratory and this exceptional stability of the antiskyrmions is found to result from large activation energy for collapse due to strong exchange coupling while the pre-exponential factor in the Arrhenius expression for the lifetime is found to have a typical magnitude of ${10}^{\ensuremath{-}12}$ s, despite the large number of spins. The long lifetime is, therefore, found to result from energetic effects rather than entropic effects in this system.

Orientation and internal structure of domain walls in ferromagnetic films with anisotropic Dzyaloshinskii-Moriya interaction

We present an analytical study of domain-wall internal structure and orientation in a ferromagnetic film with out-of-plane anisotropy and the anisotropic interfacial Dzyaloshinskii-Moriya interaction (iDMI). The term “anisotropic” means that the iDMI constant is different for different in-plane directions. The interplay between the magnetostatic interaction and the iDMI in a domain wall defines both its structure and orientation. In the case of the isotropic iDMI there is no preferable orientation of the DW in the film plane leading to formation of labyrinth domain structure with random shapes of the domains. In the case of the anisotropic iDMI an oriented domain stripe structure and zigzag domains appear. Depending on system parameters, either the Bloch domain walls, or the Néel ones or the hybrid canted walls realize in the magnetic film. The spatial orientation of the DW and the orientation of the magnetization rotation plane in the DW are intimately related by a simple linear ratio. The analytical results are corroborated by micromagnetic simulations.

Enhanced Stability of Antiferromagnetic Skyrmion during Its Motion by Anisotropic Dzyaloshinskii–Moriya Interaction

Searching for new methods to enhance the stability of antiferromagnetic (AFM) skyrmion during its motion is an important issue for AFM spintronic devices. Herein, the spin‐polarized current‐induced dynamics of a distorted AFM skyrmion is numerically studied, based on the Landau–Lifshitz–Gilbert simulations of the model with an anisotropic Dzyaloshinskii–Moriya (DM) interaction. It is demonstrated that the DM interaction anisotropy induces the skyrmion deformation, which suppresses the distortion during the motion and enhances the stability of the skyrmion. Moreover, the effect of the DM interaction anisotropy on the skyrmion velocity is investigated in detail, and the simulated results are further explained by Thiele's theory. This work unveils a promising strategy to enhance the stability and the maximum velocity of AFM skyrmion, benefiting future spintronic applications.