Dzyaloshinskii-Moriya Interaction Constant Research Articles

Asymmetric magnetization switching and programmable complete Boolean logic enabled by long-range intralayer Dzyaloshinskii-Moriya interaction

After decades of efforts, some fundamental physics for electrical switching of magnetization is still missing. Here, we report the discovery of the long-range intralayer Dzyaloshinskii-Moriya interaction (DMI) effect, which is the chiral coupling of orthogonal magnetic domains within the same magnetic layer via the mediation of an adjacent heavy metal layer. The effective magnetic field of the long-range intralayer DMI on the perpendicular magnetization is out-of-plane and varies with the interfacial DMI constant, the applied in-plane magnetic fields, and the magnetic anisotropy distribution. Striking consequences of the effect include asymmetric current/field switching of perpendicular magnetization, hysteresis loop shift of perpendicular magnetization in the absence of in-plane direct current, and sharp in-plane magnetic field switching of perpendicular magnetization. Utilizing the intralayer DMI, we demonstrate programable, complete Boolean logic operations within a single spin-orbit torque device. These results will stimulate investigation of the long-range intralayer DMI effect in a variety of spintronic devices.

Electric manipulation of the magnetization in heterostructure Pt/Co/Bi2Se3

Spin–orbit torque (SOT) can provide efficient electrical manipulation of magnetism via applying electrical current to breaking the symmetry of damping-like torque. In the heterojunction of heavy and ferromagnetic metal, Dzyaloshinskii–Moriya interaction (DMI) is one of the key ingredients for stabilizing chiral spin structures, like chiral domain walls. Meanwhile, materials with larger charge-spin conversion rates are also highly expected for the efficient SOT. In this paper, spin–orbit torque magnetic switching is observed in the perpendicularly magnetized Pt/Co/Bi2Se3 and shows relatively high efficiency with low critical switching current density of about 5 × 105 A cm−2. The SOT efficiency and DMI in perpendicularly magnetized Pt/Co/Bi2Se3 were quantitatively investigated by electrical detection of the effective spin Hall field. The DMI constant is about 2.6 mJ m−2, and the effective spin Hall angle of Pt/Co/Bi2Se3 is about 0.14. The work also demonstrates that the Bi2Se3 layer takes the main responsibility for SOT, and the Pt/Co interface is the main source of DMI in Pt/Co/Bi2Se3 structures, which makes it possible to achieve independent optimization of DMI and SOT in the Pt/Co/Bi2Se3 structure at room temperature for the advanced application of spintronic devices.

Anisotropic creep velocity of Dzyaloshinskii domain walls

We have measured the field-driven velocity of chiral Néel domain walls (DWs) stabilized by the Dzyaloshinskii–Moriya interaction (DMI) in a Pt/Co/Ta/Pt film with perpendicular magnetic anisotropy. A simple model based on the universal creep theory allows us to describe the anisotropic propagation of a DW along the contour of a bubble domain, driven by an out-of-plane field in the presence of a static in-plane field. This model is used to obtain the DMI constant from the measurement of the DW propagation with only one value of the in-plane field, simplifying the existing method relying on several measurements. The DMI constant extracted from the model is in good agreement with independent measurements.

Field-free domain wall spin torque nano-oscillators with multimodal real-time modulation and high-quality factor

We report on a magnetic domain wall (DW)-based spin torque nano-oscillator (STNO) with real-time multimodal frequency modulation characteristics by engineering the synergistic effect of shape anisotropy, Dzyaloshinskii-Moriya interaction (DMI), and spin-transfer torque. The achieved manageable oscillation and precession of magnetic DW motivate us to implement such attributes into the developed STNO under a low current density of ∼107 A/cm2, which demonstrates outstanding functionality of multimodal real-time modulation ranging from few GHz and sub-THz with corresponding few tens and >104 quality factor (fSTNO/Δf) in absence of external magnetic field. Furthermore, the dynamic process of DW motion and magnetic moment precession under different modes has been revealed systematically, and the frequency dependence of various physical parameters including damping constant, uniaxial anisotropy constant, saturation magnetization, exchange stiffness, and DMI constant has also been summarized in detail. Such a DW-based device enriches the STNO family and promises great potential with a broad spectrum of applications in microwave generators and neuromorphic computing.

Net Dzyaloshinskii–Moriya interaction in defect-enriched ferromagnet

The Dzyaloshinskii–Moriya interaction (DMI), which typically occurs in lattices without space inversion symmetry, can also be induced in a highly symmetric lattice by local symmetry breaking due to any lattice defect. We recently presented an experimental study of polarized small angle neutron scattering (SANS) on the nanocrystalline soft magnet Vitroperm (Fe73Si16B7Nb3Cu1), where the interface between the FeSi nanoparticles and the amorphous magnetic matrix serves as such a defect. The SANS cross sections exhibited the polarization-dependent asymmetric term originating from the DMI. One would naturally expect the defects characterized by a positive and a negative DMI constant D to be randomly distributed and this DMI-induced asymmetry to disappear. Thus, the observation of such an asymmetry indicates that there exists an extra symmetry breaking. In the present work we experimentally explore the possible causes by measuring the DMI-induced asymmetry in the SANS cross sections of the Vitroperm sample tilted in different directions with respect to the external magnetic field. Furthermore, we analyzed the scattered neutron beam using a spin filter based on polarized protons and confirm that the asymmetric DMI signal originates from the difference between the two spin-flip scattering cross-sections.

Dynamic Transformation of Domain Walls in Chiral Ferrimagnets

The dynamics of domain walls in ferrimagnets in which spatial dynamics invariance is violated because of the presence of the chiral Dzyaloshinskii–Moriya interaction with energy linear in sublattice spin density gradients is investigated theoretically. Analysis is performed based on numerical integration of equations in the sigma model generalized to the case of a ferrimagnet near the sublattice spin compensation point. It is shown that in contrast to conventional or chiral ferromagnets, chiral ferrimagnets can exhibit effects of dynamic transformation of the domain wall structure with the formation of more complex walls with a nonmonotonic behavior of the spin density in a wall upon an increase in the wall velocity. These effects are possible in a quite narrow neighborhood of the compensation point, and the width of this region increases upon an increase in the Dzyaloshinskii–Moriya interaction constant.

Modulation of Spin-Orbit Torque and Large Enhancement of Perpendicular Magnetic Anisotropy in W/Co20Fe60B20/MgO by Ir Insertion Layer

Iridium ($\mathrm{Ir}$) is a 5d heavy metal with strong spin-orbit coupling (SOC), which introduces various intriguing phenomena when interacting with a ferromagnetic layer. In this study, we utilize $\mathrm{Ir}$ as an insertion layer in $\mathrm{W}/\mathrm{Ir}({t}_{\mathrm{Ir}})/{\mathrm{Co}}_{20}{\mathrm{Fe}}_{60}{\mathrm{B}}_{20}/\mathrm{Mg}\mathrm{O}$ heterostructures to tune SOC and study its influence on the spin-orbit torque (SOT), perpendicular magnetic anisotropy (PMA), and Dzyaloshinskii-Moriya interaction (DMI). The SOT efficiency decreases first and then increases with an increase of $\mathrm{Ir}$ insertion layer thickness because of the opposite spin Hall angle between $\mathrm{W}$ and $\mathrm{Ir}$, and the sign changes when the thickness of $\mathrm{Ir}$ is 1.5 nm, which is close to the spin diffusion length of $\mathrm{Ir}$ of 1.35 nm. Importantly, a 0.25-nm-thick $\mathrm{Ir}$ layer enhances largely the effective PMA by 140%--350% under different annealing temperatures compared with that of a sample without insertion. Meanwhile, the DMI constant is also enhanced. The enhancement of PMA and DMI is likely due to the enhancement of interfacial SOC when $\mathrm{Ir}$ diffuses into ${\mathrm{Co}}_{20}{\mathrm{Fe}}_{60}{\mathrm{B}}_{20}$ and leads to the formation of ${\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Ir}}_{x}$. These results provide an effective method to tune SOC by inducing a dusting layer with strong SOC to meet different requirements in spintronic devices like small magnetic tunnel junctions.

Room temperature skyrmions in symmetric multilayers

We experimentally demonstrate the generation of skyrmions (166 ± 42 nm) by controlling and modulating the skyrmion stability parameter κ through changing the Co layer thickness in the multilayer with repetitions of the symmetric Pt/Co/Pt trilayer. The magnetic field dependence of skyrmion evolution is reversible. Dzyaloshinskii–Moriya interaction constant D is quantitatively measured by Brillouin spectroscopy to understand the mechanism. Surprisingly, the D value is high enough to generate skyrmions in a symmetric sandwich structure although the value is smaller than that in an antisymmetric Pt/Co/Ta trilayer. The decreased D value with the increase in the Co layer thickness indicates that the Dzyaloshinskii–Moriya interaction is still contributed from the interfaces. This work broadens the flexibility to generate skyrmions by engineering skyrmion-based devices with nominally symmetric multilayer without the requirement of very large DMI.

Influence of the anisotropy and the DMI constant on the magnetic skyrmions in elliptical and rectangular-shaped nanomagnets

Micromagnetic simulations have been used to study the influence of the anisotropy (K U ) and Dzyaloshinskii-Moriya interaction (DMI) constant on the stability and size of magnetic skyrmions in elliptical and rectangular-shaped nanostructures, in order to understand the role of the geometry on magnetic skyrmions. In order to compare the changes in the internal magnetic states for the elliptical and rectangular nanostructures, the lengths of the major and minor sides and axes of the rectangle and ellipse, respectively, are considered equal in values. For both types of geometries, micromagnetic simulations clearly demonstrate the influence of the K U and DMI constant on the stability and size of magnetic skyrmions. A plot of K U versus DMI for the range of 1.10 to 1.40 MJ/m3 and 0 to 6.0 mJ/m2, respectively, shows that the elliptical nanomagnets have a higher range of K U and DMI values to stabilize the skyrmions. It is also observed that for K U and DMI values of 1.30 MJ/m3 and 2.0 mJ/m2, respectively, the diameter of the skyrmions increases with the minor to the major length of the ellipse. These results have been explained in terms of the interplay between the different energies and the geometry of the nanostructure.

Omnidirectional flat bands in chiral magnonic crystals

The magnonic band structure of two-dimensional chiral magnonic crystals is theoretically investigated. The proposed metamaterial involves a three-dimensional architecture, where a thin ferromagnetic layer is in contact with a two-dimensional periodic array of heavy-metal square islands. When these two materials are in contact, an anti-symmetric exchange coupling known as the Dzyaloshinskii–Moriya interaction (DMI) arises, which generates nonreciprocal spin waves and chiral magnetic order. The Landau–Lifshitz equation and the plane-wave method are employed to study the dynamic magnetic behavior. A systematic variation of geometric parameters, the DMI constant, and the filling fraction allows the examination of spin-wave propagation features, such as the spatial profiles of the dynamic magnetization, the isofrequency contours, and group velocities. In this study, it is found that omnidirectional flat magnonic bands are induced by a sufficiently strong Dzyaloshinskii–Moriya interaction underneath the heavy-metal islands, where the spin excitations are active. The theoretical results were substantiated by micromagnetic simulations. These findings are relevant for envisioning applications associated with spin-wave-based logic devices, where the nonreciprocity and channeling of the spin waves are of fundamental and practical scientific interest.

Direct observation of the temperature dependence of the Dzyaloshinskii–Moriya interaction

In this work, we investigate the temperature dependence of the Dzyaloshinskii–Moriya interaction (DMI) in Co/Pt thin film by observing the asymmetric spin-wave dispersion using Brillouin light scattering. The DMI constant D reduce monotonously with the temperature increasing from room temperature to 393 K. By extracting the saturation magnetization M s and the uniaxial anisotropy K u, we find that D(T) ∝ K u (T)2.08±0.13 and D(T) ∝ M s (T)5.25±0.33. These observations indicate that temperature is a possible way to control the DMI. On the other hand, the temperature dependence of DMI in thin films may have significant influence for potential applications.

Impact of the interfacial Dzyaloshinskii-Moriya interaction on the band structure of one-dimensional artificial magnonic crystals: A micromagnetic study

We present the results of a systematic micromagnetic study of the effect of the Dzyaloshinskii-Moriya interaction (DMI) on the spin wave band structure of two one-dimensional magnonic crystals (MCs), both with the same periodicity p = 300 nm, but different implementation of the DMI modulation. In the first system the artificial periodicity was achieved by modulating the interfacial DMI constant D, while in the second system also the sample morphology was modulated. Due to the folding property of the band structure in the dispersion relations of the magnonic crystals it is possible to extend the sensitivity of Brillouin light scattering towards weak DMI strength (D in the range from 0 to 0.5 mJ/m2), by measuring the frequency splitting of folded modes in high-order artificial Brillouin zones, since the splitting increases almost linearly with the band index. For relatively large values of the DMI (D in the range from 1.0 to 2.0 mJ/m2) the spin waves dispersion relations present flat modes for positive wavevectors, separated by forbidden frequency gaps whose amplitude depend on the value of D. These frequency gaps are more pronounced for the sample with morphology modulation. The non-reciprocal, localised, spatial profiles of these modes in both MCs are discussed with reference to spin waves in plain films and in isolated stripes of the same thickness.

Dzyaloshinskii-Moriya interaction and magnetic anisotropy in Pt/Co/Au trilayers modified by Ga+ ion irradiation

The influence of 30 keV Ga+ ion irradiation in the fluence range 0 ÷ 1·1016 ions/cm2 on magnetic properties of Pt(bottom)/Co(3 nm)/Au(top) trilayers grown by the molecular beam epitaxy was studied. Polar magnetooptical Kerr effect magnetometry and Brillouin light scattering spectrometry were used to measure the magnetic anisotropy and the strength of Dzyaloshinskii-Moriya interaction (DMI). The as-deposited sample exhibits in-plane magnetization with an effective anisotropy field of −0.35 ± 0.02 T. Magnetic anisotropy gradually grows as the ion fluence is increased and out-of-plane magnetic anisotropy appears for the fluence above ∼ 3·1015 ions/cm2. The frequency asymmetry in Stokes and anti-Stokes lines Δf, being a measure of DMI strength, was determined from Brillouin light scattering investigations as a function of applied fluence. The effective DMI constant is equal to −0.48 ± 0.05 mJ/m2 in the as-deposited sample. While increasing fluence the parameter Δf: (i) varies non-monotonically (with two maxima) for F smaller than F≈1015 ions/cm2 and (ii) gradually decreases to zero for higher fluences. Our results can be used for the adjustment of DMI interaction in the manufacturing of magnonic nano-devices.

Influence of the Dzyaloshinskii – Moriya interaction on the properties of magnetic states in nanostructures

Dzyaloshinskii – Moriya interaction (DMI) plays an important role in the formation of chiral spin textures useful in spintronics. Interfacial DMI is of great interest, as was recently shown, it leads to the stabilization of chiral spin textures not only in ferromagnetic metals, but also in insulator systems such as rare-earth iron garnets. In this paper, we explore transformations of uniform magnetic states induced by the DMI in ferrimagnetic system of restricted geometry. We show that change of the DMI constant induces a series of phase transitions in the square magnetic nanoelement: homogeneous magnetic state – vortex – skyrmion/meron – multidomains – domain structure (K>/<0) and construct phase diagrams in terms of “DMI constant – nanoelement size”. Our findings show that manifestation of DMI in a system of restricted geometry depends on the initial magnetic configuration stabilized by competition between exchange and relativistic interactions. The transformations of the “out – of - plane” and “in-plane” single-domain magnetic states induced by the DMI are considered, and their distinctive features are revealed. The influence of an electric field acting through inhomogeneous magnetoelectric interaction on localized magnetic states is discussed.

Dynamically stable negative-energy states induced by spin-transfer torques

We investigate instabilities of the magnetic ground state in ferromagnetic metals that are induced by uniform electrical currents, and, in particular, go beyond previous analyses by including dipolar interactions. These instabilities arise from spin-transfer torques that lead to Doppler shifted spin waves. For sufficiently large electrical currents, spin-wave excitations have negative energy with respect to the uniform magnetic ground state, while remaining dynamically stable due to dissipative spin-transfer torques. Hence, the uniform magnetic ground state is energetically unstable, but is not able to dynamically reach the new ground state. We estimate this to happen for current densities $ j\gtrsim (1-D/D_c)10^{13} \mathrm{A/m^2} $ in typical thin film experiments, with $ D $ the Dzyaloshinskii-Moriya interaction constant, and $ D_c $ the Dzyaloshinskii-Moriya interaction that is required for spontaneous formation of spirals or skyrmions. These current densities can be made arbitrarily small for ultrathin film thicknesses at the order of nanometers, due to surface- and interlayer effects. From an analogue gravity perspective, the stable negative energy states are an essential ingredient to implement event horizons for magnons -- the quanta of spin waves -- giving rise to e.g. Hawking radiation and can be used to significantly amplify spin waves in a so-called black-hole laser.

МАГНИТНЫЕ ЭЛЕМЕНТЫ НЕЙРОННЫХ СЕТЕЙ. СВОЙСТВА МАГНИТНЫХ НЕОДНОРОДНОСТЕЙ В СИСТЕМАХ ОГРАНИЧЕННОЙ ГЕОМЕТРИИ

This paper discusses the prospects for using magnetic nanostructures as elements of neural networks. At present neural network learning programs are actively used in analyzing and processing large data arrays; however, the development of computer technologies based on the neural network principle still remains open. Possibilities for using magnetic elements as physical carriers of information bits in these systems attract much attention from researchers and technologists due to the presence of several easily controlled parameters (order parameter) in the magnetic system, possibilities for the dimensionality reduction in magnetic elements by using magnetic nanostructures (domain boundaries, vortices, ckyrmions), superquick switching between magnetic states and some other factors. One of the key aspects of research in this regard is to determine basic controlled magnetic parameters in restricted geometries and to identify ways of controlling these parameters through internal and external factors. The paper presents a research on the magnetic ground state in restricted geometries. It deals with the magnetic state rebuilding in the system under changes in both external factors (applied magnetic field, sample dimensions) and internal ones (magnetic anisotropy constant, Dzyaloshinskii-Moriya interaction constant). Calculations were performed within the framework of micromagnetic modelling using the Object Oriented MicroMagnetic Framework ( OOMMF) sogtware. It is shown that the anisotropic exchange interaction (Dzyaloshinskii-Moriya interaction) has a significant effect on the magnetization distribution in restricted geometries. Namely, when changing the value of the Dzyaloshinskii-Moriya constant in the system with uniaxial magnetic anisotropy there is a series of phase transitions observed between magnetic states of different types: transitions from the homogenous magnetic state into the skyrmion-type vortex state (domain structure with the skyrmion-type unidomain state) with subsequent domain structure reversal when changing the value of the Dzyaloshinskii-Moriya constant. In the case of magnetic anisotropy of easy -axis type, chirality and properties of the structures in question do not depend on the constant symbol of the Dzyaloshinskii-Moriya interaction.

Effect of the Interfacial Dzyaloshinskii–Moriya Interaction on the Spin Waves Eigenmodes of Isolated Stripes and Dots Magnetized In-Plane: A Micromagnetic Study

The influence of the Dzyaloshinskii–Moriya interaction (DMI) on the eigenmodes of magnetic nanostructures is attracting interest for both fundamental reasons and prospects in applications. In this study, the characteristics of spin waves eigenmodes in either long stripes or elliptical dots magnetized in-plane, with lateral dimensions of the order of 100 nm, are analyzed by micromagnetic simulations in presence of a sizeable DMI. Using the GPU-accelerated software MuMax3, we show that the eigenmodes spectrum is appreciably modified by the DMI-induced non-reciprocity in spin-waves propagation: the frequencies of the eigenmodes are red-shifted and their spatial profiles appreciable altered due to the lack of stationary character in the direction orthogonal to the magnetization direction. As a consequence, one finds a modification of the expected cross-section of the different modes in either ferromagnetic resonance or Brillouin light scattering experiments, enabling one to detect modes that would remain invisible without DMI. In this respect, the modifications of the spectrum can be directly connected to a quantitative estimation of the DMI constant. Moreover, it is seen that for sufficiently large values of the DMI constant, the low-frequency odd eigenmode changes its profile and becomes soft, reflecting the transition of the ground state from uniform to chiral.

Domain-Wall Damping in Ultrathin Nanostripes with Dzyaloshinskii-Moriya Interaction

Asymmetrically sandwiched thin magnetic layers with perpendicular anisotropy and Dzyaloshinskii-Moriya interaction (DMI) is the prospective material science platform for spin-orbitronic technologies that rely on the motion of chiral magnetic textures, like skyrmions or chiral domain walls (DWs). The dynamic performance of a DW-based racetrack is defined by the strength of the DMI and the DW damping. The determination of the latter parameter is typically done based on technically challenging DW motion experiments. Here, we propose a method to access both the DMI constant and DW damping from static experiments by monitoring the tilt of magnetic DWs in nanostripes. We experimentally demonstrate that in perpendicularly magnetized ${\mathrm{//Cr}\mathrm{O}}_{x}\mathrm{/Co/Pt}$ stacks, DWs can be trapped on edge roughness in a metastable tilted state as a result of the DW dynamics driven by an external magnetic field. The measured tilt can be correlated to the DMI strength and DW damping in a self-consistent way in the frame of a theoretical formalism based on the collective coordinate approach.

Stability of skyrmion formation and its abnormal dynamic modes in magnetic nanotubes

We studied the stability of skyrmion formation and its abnormal dynamic motions in magnetic nanotubes with perpendicular magnetic anisotropy with respect to the tube surface. Unlike planar geometry, skyrmions, which are formed in an elliptical shape, are stabilized, to a greater or lesser degree, by the curved geometry, depending on the sign of the Dzyaloshinskii-Moriya Interaction (DMI) constant. The positive and negative signs of the DMI constant play a crucial role in the formation of skyrmions on the curved surface. These effects become stronger as the diameter of the tube decreases, quantitatively evidencing that the curvature-induced DM-like interaction also contributes to the stability of skyrmion formation. The dynamic modes of the skyrmion in the tubes are found to be as follows: two in-plane gyration modes in the counterclockwise (CCW) and clockwise (CW) rotation senses, and one out-of-plane breathing mode. On the other hand, in contrast to the planar geometry, the initial CCW gyration motion turns out to be a linear translational motion in the circumferential direction of the tube for cases where the strength of axial AC magnetic fields is greater than a threshold field strength. The direction of the translational motions is determined by the skyrmion helicity governed by the sign of the interfacial DMI constant. This work provides further physical insight into the static and dynamic properties of skyrmions formed in curved-geometry systems and also suggests its potential application to information processing devices.

Magnetic skyrmion states in cobalt nanodisk

Internal magnetic states and changes in the texture of the magnetization in cobalt nanodisks have been studied using micromagnetic simulations under two different initial conditions: a nucleated Bloch type skyrmion placed at the center of the cobalt disk and displaced 32 nm from the center. Analysis of simulation results clearly demonstrates that variations in values of the anisotropy (Ku) and Dzyaloshinskii-Moriya interaction (DMI) constants have strong influence on the internal magnetic states and the energy terms of the cobalt nanodisk. Of interest is the nucleation and stability of magnetic skyrmions as a function of the DMI constant. Micromagnetic analysis suggest that the interplay between demagnetizing, exchange and Dzyaloshinskii-Moriya energies induces a diagram with different textures of the magnetization including the Bloch and Néel type skyrmions, incomplete skyrmion and skyrmionium. If the initial Bloch skyrmion state is displaced 32 nm from the center, the diagram for the texture of the magnetization changes, creating a cycloid state for higher values of the DMI constant. The results have been discussed in function of the competition between the energy terms, and the initial magnetic states.