Dzyaloshinskii Moriya Research Articles

Dynamics of hybrid magnetic skyrmion driven by spin–orbit torque in ferrimagnets

Precise control of skyrmion dynamics is essential for the future spintronic device design based on the magnetic skyrmions. In this work, we propose a scheme to implement hybrid magnetic skyrmions (HMS) in ferrimagnets and we study the dynamics of the HMS driven by spin–orbit torque. It is revealed that the skyrmion Hall effect depends on the skyrmion helicity and the net angular momentum (δs), allowing the effective modulation of the HMS motion through tuning Dzyaloshinskii–Moriya interaction and δs. Moreover, the Magnus force for finite δs suppresses the transverse motion and enhances the longitudinal propagation, resulting in the decrease in Hall angle accompanying faster dynamics than that in antiferromagnets. Thus, the Hall effect can be suppressed through selecting suitable materials to better control the HMS motion. Finally, we propose a convenient skyrmion diversion scheme through modulating the helicity and Hall angle of the HMS, benefiting the future spintronic device design.

Anisotropic Interlayer Dzyaloshinskii–Moriya Interaction in Synthetic Ferromagnetic/Antiferromagnetic Sandwiches

AbstractThe interfacial Dzyaloshinskii–Moriya interaction (DMI) in ferromagnetic/non‐magnetic‐metal bilayers is essential to stabilize chiral spin textures for potential applications. Recent works reveal that the interlayer DMI is beneficial to designing 3D chiral spin textures that possess fundamental importance and the associated technological promises. Here, the interlayer DM constants are determined quantitatively in synthetic ferromagnetic/antiferromagnetic Pt/Co/Pt/Ru/Pt/Co/Ta structures. The results demonstrate that the interlayer DMI shows uniaxial anisotropic characteristics. The first‐principles calculations elucidate that the anisotropic interlayer DMI is induced by the in‐plane symmetry breaking along two high symmetric directions, which favors the magnetization of adjacent ferromagnetic layers canting in different directions. The anisotropic interlayer DMI is also confirmed by spin‐orbit torque driven asymmetric magnetization switching. Moreover, the interlayer DMI can be tuned by the Ru‐layer‐thickness and beneficial to designing 3D spin textures for future spintronic devices.

Anomalous Spin Textures in a 2D Topological Superconductor Induced by Point Impurities

AbstractTopological superconductors are foreseen as good candidates for the search of Majorana zero modes, where they appear as edge states and can be used for quantum computation. In this context, it becomes necessary to study the robustness and behavior of electron states in topological superconductors when a magnetic or non‐magnetic impurity is present. The focus is on scattering resonances in the bands and on spin texture to know what the spin behavior of the electrons in the system will be. It is found that the scattering resonances appear outside the superconducting gap, thus providing evidence of topological robustness. Non‐trivial and anisotropic spin textures related to the Dzyaloshinskii–Moriya interaction are also found. The spin textures show a Ruderman–Kittel–Kasuya–Yosida interaction governed by Friedel oscillations. It is believed that the results are useful for further studies which consider many‐point‐impurity scattering or a more structured impurity potential with a finite range.

Dzyaloshinskii–Moriya interactions in Nd2Fe14B as the origin of spin reorientation and the rotating magnetocaloric effect

In this study, the mechanism of spin reorientation in Nd2Fe14B, which is the host crystal of prevalently employed neodymium permanent magnets, was investigated by combining first–principles calculations and Monte Carlo simulations. Spin reorientation is thought to originate from crystal field effects and has not received significant attention from researchers because it is an undesirable property in hard magnet applications. Similarly, Dzyaloshinskii–Moriya interactions are often ignored in rare–earth bulk systems, including permanent magnets such as Nd2Fe14B, because it is believed that magnetic anisotropy is more dominant than Dzyaloshinskii–Moriya interactions. However, in this study, for the first time, we found that the spin reorientation in Nd2Fe14B is caused by Dzyaloshinskii–Moriya interactions. Furthermore, we found that the spin reorientation in Nd2Fe14B results in the rotating magnetocaloric effect, which might be used for practical applications. We also found that the Dzyaloshinskii–Moriya interactions non-negligibly affect the physical properties of magnetic materials.

Evidence of Strong Dzyaloshinskii–Moriya Interaction at the Cobalt/Hexagonal Boron Nitride Interface

The Dzyaloshinskii-Moriya interaction (DMI) and perpendicular magnetic anisotropy (PMA) were measured on four series of Co films (1-2.2 nm thick) grown on Pt or Au and covered with h-BN or Cu. Clean h-BN/Co interfaces were obtained by exfoliating h-BN and transferring it onto the Co film in situ in the ultra-high-vacuum evaporation chamber. By comparing h-BN and Cu-covered samples, the DMI induced by the Co/h-BN interface was extracted and found to be comparable in strength to that of the Pt/Co interface, one of the largest known values. The strong observed DMI despite the weak spin-orbit interaction in h-BN supports a Rashba-like origin in agreement with recent theoretical results. Upon combination of it with Pt/Co in Pt/Co/h-BN heterostructures, even stronger PMA and DMI are found which stabilizes skyrmions at room temperature and a low magnetic field.

Helimagnet-based nonvolatile multi-bit memory units

In this Letter, we present a design of a helimagnet-based emerging memory device that is capable of storing multiple bits of information per device. The device consists of a helimagnet layer placed between two ferromagnetic layers, which allows us to lock-in specific spin configurations. The bottom pinned layer has high anisotropy energy or stays exchange biased, which keeps its spin configuration fixed on a specific direction, while the top layer is free to rotate under the influence of in-plane magnetic fields. We begin by finding the relaxed spin structure, which is the result of the competition between the Dzyaloshinskii–Moriya interaction (DMI) and exchange energy and is referred to as the equilibrium state (“0”). The writing of a memory state is simulated by applying an in-plane field that rotates and transforms the spin configurations of the memory device. Our results indicate that stable configurations can be achieved at rotations of an integer multiple of 180° (corresponding to states “−2,” “−1,” “1,” “2,” etc.), where the anisotropy stabilizes the free layer and, thus, the exchange coupled helimagnet. These states are separated by magnetic energy barriers and intermediate, unstable spin configurations tend to revert to their adjacent states. By simply changing the direction of the field, we can achieve multi-bit data storage per unit memory cell. The maximum number of bits is reached when the anisotropy energy barriers cannot withstand the strong DMI energy. Reading can be done by evaluating the different resistance states due to the twisted spin texture.

Robustness of the Skyrmion Phase in a Frustrated Heisenberg Antiferromagnetic Layer against Lattice Imperfections and Nanometric Domain Sizes

By employing GPU-implemented hybrid Monte Carlo simulations, we study the robustness of the skyrmion lattice phase (SkX) in a frustrated Heisenberg antiferromagnetic (AFM) layer on a triangular lattice with a Dzyaloshinskii–Moriya interaction in the external magnetic field against the presence of lattice imperfections (nonmagnetic impurities) and lattice finiteness. Both features are typical of experimentally accessible magnetic materials and require theoretical investigation. In the pure model of infinite size, SkX is known to be stabilized in a quite wide temperature-field window. We first study the effects of such imperfections on the SkX stability and compare them with those in the nonfrustrated ferromagnetic counterpart. The partial results of this part appeared in the conference proceedings [M. Mohylnaand M. Žukovič, Proceedings of the 36th International ECMS International Conference on Modelling and Simulation, ECMS, 2022]. We further look into whether SkX can also persist in finite clusters, i.e., zero-dimensional systems of nanometric sizes. In general, both the presence of magnetic vacancies as well as the finiteness of the system tend to destabilize any ordering. We show that in the present model, SkX can survive, albeit in a somewhat distorted form, in the impure infinite system up to a fairly large concentration of impurities, and, in the pure finite systems, down to sizes comprising merely tens of particles. Distortion of the SkX phase due to the formation of bimerons, reported in the ferromagnetic model, was not observed in the present frustrated AFM case.

Néel Skyrmion Bubbles in La0.7Sr0.3Mn1–xRuxO3 Multilayers

Ferromagnetic La0.7Sr0.3Mn1-xRuxO3 epitaxial multilayers with controlled variation of the Ru/Mn content were synthesized to engineer canted magnetic anisotropy and variable exchange interactions, and to explore the possibility of generating a Dzyaloshinskii-Moriya interaction. The ultimate aim of the multilayer design is to provide the conditions for the formation of domains with nontrivial magnetic topology in an oxide thin film system. Employing magnetic force microscopy and Lorentz transmission electron microscopy in varying perpendicular magnetic fields, magnetic stripe domains separated by Néel-type domain walls as well as Néel skyrmions smaller than 100 nm in diameter were observed. These findings are consistent with micromagnetic modeling, taking into account a sizable Dzyaloshinskii-Moriya interaction arising from the inversion symmetry breaking and possibly from strain effects in the multilayer system.

Magnetic skyrmion nucleation via current injection in confined nanotrack with modified perpendicular anisotropy region

Magnetic skyrmions, as spintronic information carriers, are promising for next-generation spin logic and memory devices. For such skyrmion-based devices, effective control of skyrmion nucleation and controllable motion in the nanotrack are of great importance. The ion irradiation process can modify magnetic properties, such as perpendicular magnetic anisotropy (PMA) and Dzyaloshinskii–Moriya interaction (DMI), at the nanoscale, which can be used to reduce the design complexity of devices. In this study, a nanoregion without PMA in the nanotrack is adopted as a skyrmion nucleation seed and a current-driven highly efficient, in-line, and on-demand skyrmion nucleation schematic is presented. A key factor for realizing this concept is that the disappearance of PMA and the existence of DMI induce magnetization tilts and create a chiral perpendicular stripe domain within the nucleation region. This stripe domain allows the effective control of the spin transfer torque, and it is ejected from the PMA-modified region and propelled into the nanotrack, forming a stable skyrmion. Our proposed device allows the controlled nucleation and propagation of a series of skyrmions, which allows binary information to be written in a controlled manner, consequently, yielding simple devices with two terminals. This study provides an efficient route for designing tunable skyrmionics-mechanic memory devices.

Control of magnetic states and spin interactions in bilayer CrCl3 with strain and electric fields: an ab initio study

Using ab initio density functional theory, we demonstrated the possibility of controlling the magnetic ground-state properties of bilayer CrCl_{3} by means of mechanical strains and electric fields. In principle, we investigated the influence of these two fields on parameters describing the spin Hamiltonian of the system. The obtained results show that biaxial strains change the magnetic ground state between ferromagnetic and antiferromagnetic phases. The mechanical strain also affects the direction and amplitude of the magnetic anisotropy energy (MAE). Importantly, the direction and amplitude of the Dzyaloshinskii–Moriya vectors are also highly tunable under external strain and electric fields. The competition between nearest-neighbor exchange interactions, MAE, and Dzyaloshinskii–Moriya interactions can lead to the stabilization of various exotic spin textures and novel magnetic excitations. The high tunability of magnetic properties by external fields makes bilayer CrCl_{3} a promising candidate for application in the emerging field of two-dimensional quantum spintronics and magnonics.

Spin chirality driven by the Dzyaloshinskii–Moriya interaction in one-dimensional antiferromagnetic chain

Dzyaloshinskii–Moriya (DM) interactions cause many interesting physical features, such as topologically nontrivial magnetic skyrmions and chiral domain walls. These interactions become more pronounced in low-dimensional systems. We investigated a one-dimensional Heisenberg spin-1/2 chain with an asymmetric DM interaction. The results show that, upon applying a nonzero DM interaction, the Néel ground state transitions to a spin chiral phase. Moreover, using the mean-field approximation, we obtain the dispersion of the energy spectrum, from which the z-axis spin chirality is calculated as a function of the strength of the DM interaction for low-lying excitations. The results indicate that the DM interaction facilitates chirality for Dz ≤ J and induces a spin-gapped chiral state.

The Dzyaloshinskii–Moriya interaction effects in antiferromagnetic Heisenberg model

The spin-1/2 antiferromagnetic (AFM) Heisenberg model is considered in the mean-field approximation in terms of the spin operators [Formula: see text] and [Formula: see text] in the matrix forms with the introduction of bilinear exchange interaction ([Formula: see text]), the Dzyaloshinskii–Moriya interaction (DMI) ([Formula: see text]) and external magnetic fields ([Formula: see text]) into the Hamiltonian in three dimensions. The thermal changes of sublattice magnetizations [Formula: see text] and [Formula: see text] are investigated in the isotropic case to identify the critical behaviors displayed by the system. The phase diagrams are illustrated on various planes of system parameters for given coordination numbers [Formula: see text] and 6. In addition, the graphs of the magnetization components in the same directions were drawn against each other and very interesting results were obtained. The model exhibits the ordered phases, i.e., AFM, ferromagnetic (FM), and a phase with random or oscillatory behavior (R). The phase transitions are observed between FM and R phases when for all [Formula: see text], between FM and AFM when [Formula: see text] only and, AFM and R at low temperatures for very small [Formula: see text] and [Formula: see text] values.

Carrier and thickness mediated ferromagnetism in chiral magnet Mn1/3TaS2 nanoflakes

Layered chiral magnets with broken spatial inversion symmetry (SIS) enable chiral spin textures to occur in atomically thin layers. However, most layered materials retain SIS during their crystallization. Here, we demonstrate that SIS can be broken in a layered transition metal dichalcogenide TaS2 by intercalating Mn atoms. A chiral magnetic phase in Mn1/3TaS2 has, thus, been realized. This phase enables a nonzero Dzyaloshinskii–Moriya interaction, which in turn gives rise to large topological Hall effects (THEs) below 50 K. Both the ferromagnetism and THE can be tuned at low temperatures by modulating the carrier density via a protonic gate. Measured at 20 K with Vg = −4.7 V applied to the gate and electron doping density of 1.7 × 1022 cm−3, the maximum THE was almost double that recorded with no gate voltage applied. By further reducing the sample thicknesses, both the Curie temperature Tc and the longitudinal magnetoresistance can be significantly modulated. This is consistent with the theory of critical behavior. Our work highlights the ability to control both magnetism and chiral spin textures in Mn1/3TaS2 nanoflakes. Applying this discovery may lead to a variety of practical van der Waals heterostructure devices.

Local quantum uncertainty of a two-qubit XY Heisenberg model with different Dzyaloshinskii–Moriya couplings

This study investigates the local quantum uncertainty ([Formula: see text]) of a two-qubit Heisenberg XY chain with different directions of Dzyaloshinskii–Moriya (DM) interactions. The DM interaction parameters and coupling coefficient J are demonstrated to be beneficial in managing correlation. The DM interaction’s x-axis parameter has more influence on correlation than the DM interaction’s z-axis. As a result, adjusting the direction of the DM interaction with the coupling coefficient J may produce a more efficient operation to enhance the correlation.

Hole doping induced ferromagnetism and Dzyaloshinskii–Moriya interaction in the two-dimensional group-IVA oxides

Based on the first-principles calculations, we examine the effect of hole doping on the ferromagnetism and Dzyaloshinskii–Moriya interaction (DMI) for PbSnO2, SnO2 and GeO2 monolayers. The nonmagnetic to ferromagnetic transition and the DMI can emerge simultaneously in the three two-dimensional IVA oxides. By increasing the hole doping concentration, we find the ferromagnetism can be strengthened for the three oxides. Due to different inversion symmetry breaking, isotropic DMI is found in PbSnO2, whereas anisotropic DMI presents in SnO2 and GeO2. More appealingly, for PbSnO2 with different hole concentrations, DMI can induce a variety of topological spin textures. Interestingly, a peculiar feature of synchronously switch of magnetic easy axis and DMI chirality upon hole doping is found in PbSnO2. Hence, Néel-type skyrmions can be tailored via changing hole density in PbSnO2. Furthermore, we demonstrate that both SnO2 and GeO2.with different hole concentrations can host antiskyrmions or antibimerons (in-plane antiskyrmions). Our findings demonstrate the presence and tunability of topological chiral structures in p-type magnets and open up new possibility for spintronics.

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.

Investigation of Field-Free Switching of 2-D Material-Based Spin–Orbit Torque Magnetic Tunnel Junction

Spin Hall-assisted magnetization switching in a three-terminal magnetic tunnel junction (MTJ) has attracted much attention due to its high-speed magnetization switching, which enables low-power memory and logic applications. In this study, 2-D materials with high spin–orbit coupling (SOC) effects and high charge-to-spin conversion efficiency are used to assess the performance characteristics of spin–orbit torque MTJ (SOT-MTJ). External field-free switching in SOT-MTJ is accomplished by employing a standard MTJ structure with a bias magnetic layer on top of the structure that projects a dipolar magnetic field onto a free layer (FL). In addition, the Dzyaloshinskii–Moriya interaction (DMI), an asymmetric exchange interaction, is considered while evaluating the critical current density. We were able to demonstrate that the required critical current density decreases by 99.5%, while the switching speed increases by 86.67% in the proposed external field-free 2-D material-based SOT-MTJ. We have also shown the significance of DMI in the field-free switching of the magnetization without the requirement for additional mechanisms when the device shrank down to the subnanometer regime.

Formation of skyrmions in thin CoPt films with an atomic force microscope probe

Methods of magnetic force microscopy have been developed that make it possible to visualize the evolution of the domain structure when scanning a sample with a magnetic probe. These methods were used to study the processes of formation of skyrmions in thin CoPt films, a characteristic feature of which is the presence of the Dzyaloshinskii–Moriya interaction. A change in the position, shape, and size of skyrmions under the action of a spatially inhomogeneous magnetic field of the probe has been experimentally demonstrated.

Noncollinear twisted RKKY interaction on the optically driven SnTe(001) surface

The nontrivial spin texture on the (001) surface of topological crystalline insulator SnTe hosts exotic scientific importance and spintronic applications. Here, we study the effects of weak Floquet optical driving on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities on a doped SnTe(001) surface. Due to peculiar spin-orbit hybridization, we find a noncollinear twisted RKKY interaction with XYZ-Heisenberg, symmetric in-plane, and asymmetric Dzyaloshinskii-Moriya (DM) terms. We see that contributions from the $z$ $(x)$ component of the XYZ-Heisenberg (DM) interaction are dominant for most parameters. The interactions, including DM terms that are responsible for interesting spin textures, require doping in most cases. We propose to modify the interactions in situ via optical control of band structure, and thereby doping. A notable aspect of this control protocol is breaking of electron-hole symmetry, which stems from the DM interaction.

Linear response based theories for Dzyaloshinskii-Moriya interactions

We investigate abilities of various linear response based techniques for extracting parameters of antisymmetric Dzyaloshinskii-Moriya (DM) interactions from the first-principles electronic structure calculations. For these purposes, we further elaborate the idea of Sandratskii [Phys. Rev. B 96, 024450 (2017)], which states that $z$ component of the DM vector can be computed by retaining only spin-diagonal part of the spin-orbit (SO) coupling. We start our analysis with the magnetic force theorem (MFT), which relies on additional approximations resulting in the linear dependence of the exchange interactions on the response tensor, and compare it with the exact approach formulated in terms of the inverse response. We propose the downfolding procedure transferring the effect of these ligand spins into parameters of effective interactions between the localized spins. These techniques are applied for the series of CrCl$_3$ and CrI$_3$ based materials, including bulk, monolayer, bilayer, and three-layer systems. Particularly, we discuss how the DM interactions are induced by the inversion symmetry breaking at the surface or by the electric field. As long as the SO interaction of the heavy ligand atoms is taken into account in the calculations of the response tensor between the Cr $3d$ states, the MFT appears to be a good approximation for the DM interactions, being in contrast with the isotropic exchange, for which MFT and the exact method provide quite a different description. Finally, we discuss the relevance of our approach to other techniques ever proposed for calculations of the DM interactions. Particularly, we argue that the spin-current model for the DM interactions can be derived from the MFT based expression and is the relativistic counterpart of the double exchange, occurring in metallic systems in the limit of infinite exchange splitting.