Dzyaloshinskii-Moriya Interaction Research Articles

Classical and quantum phases of the pyrochlore S=12 magnet with Heisenberg and Dzyaloshinskii-Moriya interactions

We investigate the ground state and critical temperature phase diagrams of the classical and quantum $S=1/2$ pyrochlore lattice with nearest-neighbor Heisenberg and Dzyaloshinskii-Moriya interactions (DMI). We consider ferromagnetic and antiferromagnetic Heisenberg exchange as well as direct and indirect DMI. Classically, three ground states are found: all-in/all-out, ferromagnetic and a locally ordered $XY$ phase, known as $\Gamma_5$, which displays an accidental classical U(1) degeneracy. Quantum zero-point energy fluctuations are found to lift the classical ground state degeneracy and select the $\psi_3$ state in most parts of the $\Gamma_5$ regime. Likewise, thermal fluctuations treated classically, select the $\psi_3$ state at $T=0^+$. In contrast, classical Monte Carlo finds that the system orders at $T_c$ in the $\psi_2$ state of $\Gamma_5$ for antiferromagnetic Heisenberg exchange and indirect DMI with a transition from $\psi_2$ to $\psi_3$ at a temperature $T_{\Gamma_5} <T_c$. The same method finds that the system orders via a single transition at $T_c$ directly into the $\psi_3$ state for most of the region with ferromagnetic Heisenberg exchange and indirect DMI. Such ordering behavior at $T_c$ for the $S=1/2$ quantum model is corroborated by high-temperature series expansion. To investigate the $T=0$ quantum ground states, we apply the pseudo-fermion functional renormalization group (PFFRG). The quantum paramagnetic phase of the pure antiferromagnetic $S=1/2$ Heisenberg model is found to persist over a finite region in the phase diagram for both direct or indirect DMI. We find that near the boundary of ferromagnetism and $\Gamma_5$ antiferromagnetism the system may potentially realize a quantum ground state lacking conventional magnetic order. Otherwise, for the largest portion of the phase diagram, PFFRG finds the same ordered phases as in the classical model.

Magnetic bubbles with alternating chirality in domain walls

In magnetic multilayers with perpendicular anisotropy, the competition of short-range and long-range interactions gives rise to the stability of cylindrical magnetic domains, also known as magnetic bubbles. The presence of Dzyaloshinsky-Moriya interaction induced by asymmetric interfaces between magnetic and nonmagnetic layers may lead to the formation of cylindrical bubble domains with Neel-type domain walls across the whole thickness of the multilayer. Such domain walls produce no contrast in Lorentz TEM under the normal incidence of the electron beam to the film. The latter is often used as an argument for the presence of Dzyaloshinskii-Moriya interaction in the system. Here we show that in magnetic multilayers, the absence of the Lorentz TEM contrast might also have another origin. In particular, in the absence of interfacial Dzyaloshinskii-Moriya interaction and weak interlayer exchange coupling, the magnetic bubbles might have Bloch-type domain walls of alternate chirality in adjacent layers. Such domain walls also do not produce magnetic contrast in Lorentz TEM at normal incidence of the electron beam. We show that, in the absence of interlayer exchange coupling, the magnetic bubble domains with the domain walls of fixed and alternate chirality have nearly identical energies and can coexist in the same range of magnetic fields. Using the geodesic nudged elastic band method, we prove that these states are separated by finite energy barriers. Furthermore, we demonstrate that magnetic multilayers with only dipolar coupling, besides the magnetic bubbles with nontrivial topology in all layers, can accommodate solutions with trivial topology within the internal layers.

Nucleation and Stability of Toron Chains in Non-Centrosymmetric Magnetic Nanowires.

This work analyzes the magnetic configurations of cylindrical nanowires with a bulk Dzyaloshinskii-Moriya interaction and easy-plane anisotropy. We show that this system allows the nucleation of a metastable toron chain even when no out-of-plane anisotropy exists in the nanowire's top and bottom surfaces, as usually required. The number of nucleated torons depends on the nanowire length and the strength of an external magnetic field applied to the system. The size of each toron depends on the fundamental magnetic interactions and can be controlled by external stimuli, allowing the use of these magnetic textures as information carriers or nano-oscillator elements. Our results evidence that the topology and structure of the torons yield a wide variety of behaviors, revealing the complex nature of these topological textures, which should present an exciting interaction dynamic, depending on the initial conditions.

Surface properties of ferromagnetic films and spin wave modes

Ferromagnetic films are a fundamental platform in Magnonics, the area that studies spin wave propagation and its possible applications. These films have been studied for a long time experimentally and theoretically, either individually or as parts of multifilms structures. The present study delves into an issue of interest that remains to be studied in detail, which is the relation between the surface properties of these films and the spin wave propagation in them. The main idea of this work is that the frequencies of spin waves may be determined experimentally with precision and through their relation with surface properties one may theoretically validate and derive the main parameters of models that describe the behavior of the surfaces. Several parameters may be changed in the process of testing the relation between surface properties and spin waves, like an applied magnetic field orientation and strength, the angle of in-plane spin wave propagation, etc. This study uses a continuum micromagnetic model for the description of the magnetization dynamics, in this case, the surface properties enter through effective boundary conditions. Three models of surface properties are studied: uniaxial surface anisotropy, the latter combined with bulk uniaxial anisotropy, and surfaces with Dzyaloshinskii-Moriya interactions (DMI). In general, the boundary conditions affect the equilibrium magnetization in boundary layer regions close to the surfaces: an asymptotic analysis predicts their penetration lengths for reasonable surface anisotropies. For very thin films, this is quite relevant since the boundary layers are of the order of the film thickness, we propose this as a practical way to define what may be considered a very thin film. Effective physical parameters of thin films and very thin films clearly depend on the surface properties. The main effects of the surfaces on spin waves occur for angles of inclination of the applied magnetic field close to perpendicular to the plane, and they may be of significant magnitude. Several different numerical methods were used to solve for the spin waves, in the context of an orthogonality equation method.

EPR and SQUID interrogations of Cr(III) trimer complexes in the MIL-101(Cr) and bimetallic MIL-100(Al/Cr) MOFs

Herein, electron paramagnetic resonance (EPR) spectroscopy at X- (9.4 GHz), Q- (34 GHz) and W-band (95 GHz), and superconducting quantum interference device (SQUID) measurements on antiferromagnetically coupled metal trimers in MIL-101(Cr) and MIL-100(Al_{0.8}0.8Cr_{0.2}0.2) MOFs were investigated. At low temperatures, the Cr(III) trimers exhibit a Dzyaloshinsky-Moriya (D-M) interaction, and have a total spin state S_T = 1/2T=1/2.

The efficiency of fractional channels in the Heisenberg XYZ model

A fractional quantum state has created between two-qubit system by a Heisenberg XYZ model in the presence of the Dzyaloshinskii–Moriya (DM) interaction. The impact of the initial state settings and the interaction parameters on the amount of the quantum correlation is discussed. We used the concurrence and local quantum uncertainty to quantify these correlations. It is shown that, both quantifiers increase suddenly/gradually depending on the order of the fractional state, and whether the system is ferromagnetic or anti-ferromagnetic. The fractional parameter may increase/ stabilized the memory of the generated fractional state. Small values of the DM interaction can maximize the initial quantum correlation of a partial entangled state. The possibility of using these fractional time-dependent states as quantum channels to perform quantum teleportation has examined. It is shown that, preparing the system in anti-ferromagnetic regime improves the fidelity of the teleported state. The strength of the DM interaction and the fractional’s order has a clear effect on the fidelity’s behavior, where they may be used as control parameters to increase the efficiency of the fractional quantum channel in the context of quantum communication.

Two-dimensional GdI2/GeC van der Waals heterostructure: Bipolar magnetic semiconductor, high critical temperature and large magnetic anisotropy

The band alignment, intrinsic ferromagnetism, Dzyaloshinskii-Moriya interaction, magnetic anisotropy and critical temperature (TC) of a GdI2/GeC van der Waals (vdW) heterostructure were systematically investigated by first-principles calculations and Monte Carlo simulations. The proposed GdI2/GeC vdW heterostructure is a bipolar magnetic semiconductor with Type-I band alignment, large in-plane magnetic anisotropy energy (MAE) of − 0.912 mJ/m2 and high critical temperature of 466 K. In addition, under biaxial strains, the heterostructure transformed from semiconductor into metal, while the easy magnetization axis maintained in-plane and TC increased. The results indicated that the GdI2/GeC vdW heterostructure presented large MAE and high TC, having potential applications in spintronic devices.

Densely packed skyrmions stabilized at zero magnetic field by indirect exchange coupling in multilayers

Room-temperature stabilization of skyrmions in magnetic multilayered systems results from a fine balance between several magnetic interactions, namely, symmetric and antisymmetric exchange, dipolar interaction and perpendicular magnetic anisotropy as well as, in most cases, Zeeman through an applied external field. Such field-driven stabilization approach is, however, not compatible with most of the anticipated skyrmion based applications, e.g., skyrmion memories and logic or neuromorphic computing, which motivates a reduction or a cancellation of field requirements. Here, we present a method to stabilize at room-temperature and zero-field, a densely packed skyrmion phase in ferromagnetic multilayers with moderate number of repetitions. To this aim, we finely tune the multilayer parameters to stabilize a dense skyrmion phase. Then, relying on the interlayer electronic coupling to an adjacent bias magnetic layer with strong perpendicular magnetic anisotropy and uniform magnetization, we demonstrate the stabilization of sub-60 nm diameter skyrmions at zero-field with adjustable skyrmion density.

Quantum correlations in spin-1/2 XXZ chains with modulated magnetic fields and modulated Dzyaloshinskii–Moriya interaction

Quantum correlations in spin-1/2 XXZ chains with modulated magnetic fields and modulated Dzyaloshinskii–Moriya interaction

Static and dynamical signatures of Dzyaloshinskii-Moriya interactions in the Heisenberg model on the kagome lattice

Motivated by recent experiments on Cs_22Cu_33SnF_{12}12 and YCu_{3}3(OH)_{6}6Cl_{3}3, we consider the {S=1/2}S=1/2 Heisenberg model on the kagome lattice with nearest-neighbor super-exchange JJ and (out-of-plane) Dzyaloshinskii-Moriya interaction J_DJD, which favors (in-plane) {Q=(0,0)}Q=(0,0) magnetic order. By using both variational Monte Carlo and tensor-network approaches, we show that the ground state develops a finite magnetization for J_D/J \gtrsim 0.03 \mathrm{-} 0.04JD/J≳0.03−0.04; instead, for smaller values of the Dzyaloshinskii-Moriya interaction, the ground state has no magnetic order and, according to the fermionic wave function, develops a gap in the spinon spectrum, which vanishes for J_D \to 0JD→0. The small value of J_D/JJD/J for the onset of magnetic order is particularly relevant for the interpretation of low-temperature behaviors of kagome antiferromagnets, including ZnCu_{3}3(OH)_{6}6Cl_{2}2. For this reason, we assess the spin dynamical structure factor and the corresponding low-energy spectrum, by using the variational Monte Carlo technique. The existence of a continuum of excitations above the magnon modes is observed within the magnetically ordered phase, with a broad peak above the lowest-energy magnons, similarly to what has been detected by inelastic neutron scattering on Cs_{2}2Cu_{3}3SnF_{12}12.

Layer-dependent Dzyaloshinskii–Moriya interaction and field-free topological magnetism in two-dimensional Janus MnSTe

Magnetic skyrmions, as topologically protected whirl-like solitons, have been the subject of growing interest in non-volatile spintronic memories and logic devices. Recently, much effort has been devoted to searching for skyrmion host materials in two-dimensional (2D) systems, where intrinsic inversion symmetry breaking and a large Dzyaloshinskii–Moriya interaction (DMI) are desirable to realize a field-free skyrmion state. Among these systems, 2D magnetic Janus materials have become important candidates for inducing a sizable DMI and chiral spin textures. Herein, we demonstrate that layer-dependent DMI and field-free magnetic skyrmions can exist in multilayer MnSTe. Moreover, strong interlayer exchange coupling and Bethe–Slater curve-like behaviors arising from the Mn–Mn double exchange mechanism are found in bilayer MnSTe. We also uncover that the distribution of DMIs in multilayer MnSTe can be understood as making a significant contribution to the intermediate DMI using the three-site Fert–Lévy model. Our results unveil great potential for designing skyrmion-based spintronic devices in multilayer 2D materials.

The in-plane Dzyaloshinsky-Moriya interaction in monolayer 2H-FeTe2

Based on density functional theory calculations, we study the electronic structure and magnetism of monolayer 2H-FeTe2. The dispersion relation between energy and wave vector q of the in-plane spin spiral at opposite direction E(q) and E(−q) is obtained with the generalized Bloch theorem. Additionally, the Heisenberg interaction (HBI) and Dzyaloshinsky-Moriya interaction (DMI) parameters (Ji and di) under multiple neighbors are extracted from the energy values by applying HBI with DMI model. We find that collinear ferromagnetic and antiferromagnetic states coexist in monolayer 2H-FeTe2. Moreover, the positive value of J3 plays a key role in the generation of ferromagnetism. The DMI parameters d1=−4.59 meV and d5=1.51 meV indicate that the appearance of intrinsic in-plane DMI is due to the broken inversion symmetry within the monolayer. Our work will facilitate understanding the generation of chiral spin textures in 2D magnets and the design of orbital spintronic electronic devices.

Field direction dependent skyrmion crystals in noncentrosymmetric cubic magnets: A comparison between the point groups (O,T) and Td

We investigate the instability toward a skyrmion crystal (SkX) in noncentrosymmetric cubic magnets with an emphasis on a comparison between point groups $(O,T)$ and ${T}_{\mathrm{d}}$. By constructing low-temperature magnetic phase diagrams under an external magnetic field for three directions based on numerically simulated annealing, we find that the system under the point groups $(O,T)$ exhibits different two types of SkXs depending on the field direction, while that under ${T}_{\mathrm{d}}$ does not show such an instability. The difference between them is understood from the difference in the momentum-dependent Dzyaloshinskii-Moriya interaction under each point group. Meanwhile, we show that the system under ${T}_{\mathrm{d}}$ leads to the SkX instability by considering an additional effect of the uniaxial strain, which lowers the symmetry to ${D}_{2\mathrm{d}}$. We obtain two different SkXs: N\'eel-type SkX and anti-type SkX, the former of which is stabilized in the presence of the interactions at the three-dimensional ordering wave vectors. The present results provide rich topological spin textures in the three-dimensional systems, which are sensitive to the magnetic-field direction and point-group symmetry.

Control of Quantum‐Memory Induced by Generated Thermal XYZ‐Heisenberg Entanglement: y‐Component DM Interaction

AbstractThis study explores the thermal quantum‐memory‐assisted entropic uncertainty relation (QM‐EUR) and entanglement in a general two‐qubit XYZ‐Heisenberg spin chain model in the presence of the Dzyaloshinskii–Moriya (DM) interaction. The characterization of y‐component DM and spin–spin interactions are particularly focused. It is found that the DM and spin–spin interaction strengths highly regulate the flow behavior and the initial final levels of QM‐EUR and entanglement. In comparison, the spin–spin interaction strength in the z‐direction remains useful in both ferromagnetic and anti‐ferromagnetic regimes for entropic uncertainty suppression and entanglement generation. Additionally, the negative and the positive directed DM values can usefully turn classical states into resourceful quantum states. The dynamics of thermal QM‐EUR and entanglement‐of‐formation have symmetric behaviors only with respect to y‐component DM and z‐component spin–spin interaction. Finally, different critical points of temperature, component DM as well as spin–spin interaction are encountered, which should be opted to preserve quantum correlations and degrade uncertainty.

Exchange and Dzyaloshinskii-Moriya interaction in Rh/Co/Fe/Ir multilayers: Towards skyrmions in exchange-frustrated multilayers

We study the magnetic interactions in transition-metal multilayers composed of Co layers and Co/Fe bilayers sandwiched between Ir and Rh layers based on density functional theory (DFT). By mapping our total energy DFT calculations of collinear and noncollinear spin states including spin-orbit coupling to an atomistic spin model we extract the intra- and interlayer exchange constants, the intra- and interlayer Dzyaloshinskii-Moriya interaction constants and the magnetocrystalline anisotropy energies of several multilayers. We demonstrate that the exchange frustration, which stabilizes zero-field sub-10 nm magnetic skyrmions in Rh/Co films on the Ir(111) surface [S. Meyer et al., Nat. Commun. 10, 3823 (2019)], can be transferred to multilayers formed by a repetition of Rh/Co/Ir trilayers. Increasing the number of Co layers reduces the exchange frustration whereas with adding Fe, a sufficient exchange frustration and strength of the Dzyaloshinskii-Moriya interaction can be obtained to stabilize topological spin structures such as skyrmions in Rh/Co/Fe/Ir multilayers. We show that the exchange interaction in Rh/Co/Fe/Ir multilayers results from the interplay of strong frustration of intralayer exchange in the Fe layer, weak ferromagnetic intralayer exchange in the Co layer, and ferromagnetic interlayer Fe-Co exchange. We analyze the Dzyaloshinskii-Moriya interaction in terms of inter- and intralayer contributions as well as its sign based on the electronic structure of Co/Fe based multilayers with different stacking sequences.

Thermal Fisher and Wigner–Yanase information correlations in two-qubit Heisenberg XYZ chain

Using Wigner–Yanase and Fisher information [including local quantum uncertainty (LQU) and local quantum Fisher information (LQFI)] as well as log-negativity, we investigate the thermal non-local correlations of two-qubit Heisenberg XYZ non-X states produced in the presence of the Dzyaloshinskii–Moriya (DM) interaction. The two-spin XYZ-Heisenberg non-local correlation decay can be weakened by increasing the DM interaction as well as the spin–spin XYZ-Heisenberg interactions. The LQFI correlation has greater resistance to thermal degradation. The spin–spin y-component antiferromagnetic coupling has a higher ability to protect the generated spin–spin nonlocal correlations against high temperatures. The emergence of the phenomena of the sudden death of log-negativity and the sudden change of the LQFI and LQU depend on the spin–spin XYZ-Heisenberg and DM interactions as well as on the bath temperature. The generated asymmetric correlations resulting due to the x,y-component spin interactions confirm that the antiferromagnetic coupling has a high ability to generate a maximally correlated two-qubit state. While the generated correlations, due to two-spin z-component interaction, present symmetric dynamics, and its amount depends on the x-component spin interaction.

An influence of the Dzyaloshinskii-Moriya interaction on the magnetization reversal process of the finite-size Co chains on Pt(664) surface

Energy barriers for magnetization reversal of the finite-size Co chains on Pt(664) surface are calculated with taking the Dzyaloshinskii-Moriya interaction into account. For the numerical calculations the geodesic nudged elastic band method is employed. It has been found that the ground states of such atomic chains are noncollinear. The magnetization reversal of short atomic chains occurs without the formation of domain walls. At the same time, there are two nonequivalent ways for the magnetization reversal of longer atomic chains. The first way is the formation of clockwise domain wall (CDW) and the second way is the formation of anticlockwise domain wall (ACDW). The second way is energetically preferable. It is shown that a metastable state corresponding to the location of ACDW in the middle of the atomic chain can appear. The variation of the parameters of the Hamiltonian shows that the magnetization reversal via the CDW formation can occur only in a certain region of the parameters. The influence of the long-range dipole–dipole interaction on the energy barriers for the magnetization reversal is also investigated. It is shown that the most of the presented results can be satisfactory explained in the framework of the XY-model. The magnetic configurations of the atomic chain near the local minima and the saddle points can be approximated with simple analytical functions.

Correlation of Interface Interdiffusion and Skyrmionic Phases.

Magnetic skyrmions are prime candidates for the next generation of spintronic devices. Skyrmions and other topological magnetic structures are known to be stabilized by the Dzyaloshinskii-Moriya interaction (DMI) that occurs when the inversion symmetry is broken in thin films. Here, we show by first-principles calculations and atomistic spin dynamics simulations that metastable skyrmionic states can also be found in nominally symmetric multilayered systems. We demonstrate that this is correlated with the large enhancement of the DMI strength due to the presence of local defects. In particular, we find that metastable skyrmions can occur in Pd/Co/Pd multilayers without external magnetic fields and can be stable even near room temperature conditions. Our theoretical findings corroborate with magnetic force microscopy images and X-ray magnetic circular dichroism measurements and highlight the possibility of tuning the intensity of DMI by using interdiffusion at thin film interfaces.

Study of skyrmions stability in strained VTe2 monolayer using DFT calculations and Monte-Carlo simulations

The structural, electronic, and magnetic properties of the H-VTe2 monolayer under external strain have been studied by first-principles approaches with Hubbard U corrections combined with Monte Carlo (MC) simulation. We investigated the magnetic spin textures in the VTe2 monolayer using the Heisenberg Hamiltonian, which includes the ferromagnetic interaction J, magnetic anisotropy K, Dzyaloshinskii–Moriya interaction DMI, and the applied magnetic field B. We have numerically verified that the skyrmion can be created by the competition between these different interactions. At T = 0 K, the ground state (GS) is determined by minimizing the interaction energy and showing that the transition phase occurs at about Tc= 555 K. Also, we have demonstrated that if a magnetic field, has a direction opposite to the magnetic moment of the skyrmion center, attains a critical value Bc, the core of the skyrmion inverses the direction of its magnetization in order to recover the FM ground state. Moreover, we have studied the phase diagram in the plane (B,DMI). We have deduced that for a certain range of the DMI a skyrmion crystal can be stabilized within a certain range of the magnetic fields. Finally, we investigated the effect of the external magnetic field on the properties of the skyrmions, such as the skyrmion number (Nsky) and diameter (d).

Skyrmion size-tuning in two-dimensional antiferromagnetic monolayers by applying local spin-polarized current-induced spin-transfer torque

Antiferromagnetic (AFM) skyrmions exhibit a variety of outstanding features, including stability, non-volatility, processability, and resistance to the skyrmion Hall effect (SkHE). However, AFM skyrmions are insensitive to an external magnetic field, posing a major challenge for controlling their size. Tuning the key magnetic properties in AFM thin films is a feasible method for controlling skyrmion size, but it may also adversely affect other magnetic characteristics, such as the velocity and stability of the skyrmion, especially for small skyrmion sizes. In this study, we have investigated the size controllability of AFM skyrmions in the presence of the Dzyaloshinskii–Moriya interaction (DMI), applying a pure spin current in a bilayer structure consisting of a 2D AFM nanodisk placed over a thin coating of heavy metal (HM). The method relies on destabilizing the AFM lattice by targeting the 2D AFM nanodisk in a specific area defined by the diameter (dtr) using spin-polarized current-perpendicular-to-plane (CPP), causing a localized magnetization precession induced by spin-transfer torque (STT). As a result, a series of AFM skyrmions of different radii was stabilized depending on the diameter used without resorting to re-tuning the magnetic characteristics of the material. Moreover, we have found that for strong DMI, robust AFM skyrmions of small sizes can also be generated by adopting small diameters. Besides, the impact of spin current and nucleation time has been examined, and it was found that adjusting these parameters does not help to fine-tune the skyrmion size as much as it affects the nucleation process. Finally, we demonstrate how this method may be used to adjust both the radius and site of the skyrmion in the 2D AFM monolayer by simultaneously targeting different locations using pure spin currents. This method allows us to tune the AFM skyrmion size and to directly address the target skyrmion without disturbing the surrounding magnetic environment. Therefore, our results may pave the way for high-functional spintronics applications based on AFM skyrmions.