Dzyaloshinskii-Moriya Interaction Research Articles

Dynamic Susceptibility of Skyrmion Crystal

Using stereographic projection approach, we develop a theory for calculation of dynamic susceptibility tensor of Skyrmion crystals (SkX), formed in thin ferromagnetic films with Dzyaloshinskii–Moriya interaction and in the external magnetic field. Staying whenever possible within analytical framework, we employ the model ansatz for static SkX configuration and discuss small fluctuations around it. The obtained formulas are numerically analyzed in the important case of uniform susceptibility, accessible in magnetic resonance experiments. We show that, in addition to three characteristic magnetic resonance frequencies discussed earlier both theoretically and experimentally, one should also expect several resonances of smaller amplitude at somewhat higher frequencies.

Bloch points in nanostrips

Complex magnetic materials hosting topologically non-trivial particle-like objects such as skyrmions are under intensive research and could fundamentally change the way we store and process data. One important class of materials are helimagnetic materials with Dzyaloshinskii-Moriya interaction. Recently, it was demonstrated that thin nanodisks consisting of two layers with opposite chirality can host a single stable Bloch point of two different types at the interface between the layers. Using micromagnetic simulations we show that FeGe nanostrips consisting of two layers with opposite chirality can host multiple coexisting Bloch points in an arbitrary combination of the two different types. We show that the number of Bloch points that can simultaneously coexist depends on the strip geometry and the type of the individual Bloch points. Our simulation results allow us to predict strip geometries suitable for an arbitrary number of Bloch points. We show an example of an 80-Bloch-point configuration verifying the prediction.

Effect of the Dzyaloshinskii-Moriya interaction on quantum speed limit and orthogonality catastrophe

We study the effect of the Dzyaloshinskii-Moriya (DM) interaction on the quantum speed limit (QSL) and orthogonality catastrophe (OC) in XY spin chains. With an initial sudden quench, the general expressions of fidelity and QSL time are derived in terms of the antisymmetric quasiparticle excitation spectra. The numerical and analytical studies show that depending on the system parameters, the DM interaction has various influences on QSL and fidelity. In general, the OC is witnessed and QSL time vanishes in the thermodynamic limit as the variance of the quenched Hamiltonian in ground states scales with the system size, and the conclusion is independent of the DM interaction strength. However, it is interesting to note that the QSL can uniquely detect the critical points and lines induced by the DM interaction. We further analyze the actual evolution speed, a measure of the criticality, and find its direct correspondence with the OC. We also study an interesting phenomenon arising from the magnetic field and DM interaction in the presence of classical noise. Notably, we find that the system dynamic is fault tolerant when the system is subject to a uniform classical noise in the DM interaction strength.

Asymptotic Stability of Precessing Domain Walls for the Landau–Lifshitz–Gilbert Equation in a Nanowire with Dzyaloshinskii–Moriya Interaction

We consider a ferromagnetic nanowire and we focus on an asymptotic regime where the Dzyaloshinskii-Moriya interaction is taken into account. First we prove a dimension reduction result via $$\Gamma $$ -convergence that determines a limit functional E defined for maps $$m:\mathbb {R}\rightarrow \mathbb {S}^2$$ in the direction $$e_1$$ of the nanowire. The energy functional E is invariant under translations in $$e_1$$ and rotations about the axis $$e_1$$ . We fully classify the critical points of finite energy E when a transition between $$-e_1$$ and $$e_1$$ is imposed; these transition layers are called (static) domain walls. The evolution of a domain wall by the Landau–Lifshitz–Gilbert equation associated to E under the effect of an applied magnetic field $$h(t)e_1$$ depending on the time variable t gives rise to the so-called precessing domain wall. Our main result proves the asymptotic stability of precessing domain walls for small h in $$L^\infty ([0, +\infty ))$$ and small $$H^1(\mathbb {R})$$ perturbations of the static domain wall, up to a gauge which is intrinsic to invariances of the functional E.

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.

Terahertz Spin Current Dynamics in Antiferromagnetic Hematite.

An important vision of modern magnetic research is to use antiferromagnets (AFMs) as controllable and active ultrafast components in spintronic devices. Hematite (α-Fe2 O3 ) is a promising model material in this respect because its pronounced Dzyaloshinskii-Moriya interaction leads to the coexistence of antiferromagnetism and weak ferromagnetism. Here, femtosecond laser pulses are used to drive terahertz (THz) spin currents from α-Fe2 O3 into an adjacent Pt layer. Two contributions to the generation of the spin current with distinctly different dynamics are found: the impulsive stimulated Raman scatting that relies on the AFM order and the ultrafast spin Seebeck effect that relies on the net magnetization. The total THz spin current dynamics can be manipulated by a medium-strength magnetic field below 1 T. The control of the THz spin current achieved in α-Fe2 O3 opens the pathway toward tailoring the exact spin current dynamics from ultrafast AFM spin sources.

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.

Ab initio exploration of short-pitch skyrmion materials: Role of orbital frustration

In recent years, the skyrmion lattice phase with a short lattice constant has attracted attention due to its high skyrmion density, making it a promising option for achieving high-density storage memory and for observing novel phenomena like the quantized topological Hall effect. Unlike conventional non-centrosymmetric systems where the Dzyaloshinsky–Moriya interaction plays a crucial role, the short pitch skyrmion phase requires a quadratic magnetic interaction J(q) with a peak at finite-Q, and weak easy-axis magnetic anisotropy is also critical. Thus, conducting first-principles evaluations is essential for understanding the formation mechanism as well as for promoting the discovery of new skyrmion materials. In this Perspective, we focus on recent developments of the first-principles evaluations of these properties and apply them to the prototype systems GdT2X2 and EuT2X2, where T denotes a transition metal and X represents Si or Ge. In particular, based on the spin density functional theory with the Hubbard correction combined with the Liechtenstein method in the Wannier tight-binding model formalism, we first show that the Hubbard U and Hund’s coupling is essential to stabilize a skyrmion lattice state by enhancing the easy-axis anisotropy. We then discuss mechanisms of finite-Q instability and show that competition among Gd-5d orbitals determines whether ferromagnetism or a finite-Q structure is favored in GdT2Si2 with T= Fe and Ru. Our systematic calculations reveal that GdRu2X2, GdOs2X2, and GdRe2X2 are promising, while GdAg2X2, GdAu2X2, and EuAg2X2 are possible candidates as the skyrmion host materials. Analysis based on a spin spiral calculation for the candidate materials is also presented.

Separation of Rare-Earth and Transition-Metal Contributions to the Interfacial Dzyaloshinskii-Moriya Interaction in Ferrimagnetic Co - Gd Alloys

Ferrimagnetic materials composed of rare earth (RE) and transition metals (TM) are of great interest for spintronic devices due to their tunable net moments and magnetic transport behaviors. Here we experimentally study the Dzyaloshinskii-Moriya interaction (DMI) in $\mathrm{Co}\text{\ensuremath{-}}\mathrm{Gd}$ ferrimagnets and find that the DMI strength increases substantially as the temperature approaches its moment compensation point. By subtracting the contribution of Heisenberg exchange coupled $\mathrm{Co}$-$\mathrm{Co}$ moments mediated by $\mathrm{Pt}$ from the total DMI strength, we observe a relationship ${D}_{\text{Co - Gd}}\ensuremath{\sim}{M}_{s}^{0.2\ifmmode\pm\else\textpm\fi{}0.06}$. The lower order indicates the weaker Heisenberg exchange compared with $\mathrm{Co}$-$\mathrm{Co}$ moments in $\mathrm{Co}\text{\ensuremath{-}}\mathrm{Gd}$ alloys. Our results reveal the intrinsic physics of DMI in RE-TM alloys by separating the different contributions of TM-TM and RE-TM sublattice moments from the total DMI and show the promising prospect for the fabrication of skyrmions in RE-TM ferrimagnets near the compensation point.

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.

Between waves and patterns: Spin wave freezing in films with Dzyaloshinskii-Moriya interaction

The relationship between waves and static pattern formation is an intriguing effect and remains unexplained in many areas of physics, including magnetism. We study the spin-wave-mediated spin reorientation transition (SRT) in magnetic films with uniaxial magnetic anisotropy and Dzyaloshinskii-Moriya interaction (DMI). In particular, we show that propagating spin waves can freeze in the SRT, causing periodic magnetic domains to arise, which is reminiscent of the wave amplitude distribution. This process can take place under the influence of a change in the magnetic field, but also of other parameters. Interestingly, at the SRT, DMI nonreciprocity leads to the emergence of flowing magnetization patterns, which suggests a spontaneous breaking of translational symmetry, and the formation of magnonic space-time crystals. The described phenomena are general and should take place in a large family of magnetic materials. Therefore, the results should be of great importance for the further development of spintronics and magnonics.

Synthesis, crystal structures, thermal and magnetic properties of Mn(NCS)2 coordination compounds with 3-cyanopyridine

The reaction of Mn(NCS)2 and 3-cyanopyridine in different solvents leads to the formation of pure Mn(NCS)2(3-cyanopyridine)4 (1), Mn(NCS)2(3-cyanopyridine)2(H2O)2-bis(3-cyanopyridine) solvate (2) and Mn(NCS)2(3-cyanopyridine)(H2O) (4). In further investigations single crystals of Mn(NCS)2(3-cyanopyridine)2(H2O)2 (3) were accidentally obtained, but this compound cannot be prepared pure. Compounds 1-3 consist of discrete complexes with octahedrally coordinated Mn cations, whereas in compound 4 the Mn cations are linked by single µ-1,3-bridging thiocyanate anions into chains, that are further connected into layers by the 3-cyanopyridine coligands. Thermogravimetric measurements reveal that upon heating compound 1 loses some of the 3-cyanopyridine ligands and transforms into [(Mn(NCS)2)3(3-cyanopyridine)4]n (5), which is isotypic to the corresponding Cd compound reported in the literature. In this structure, the Mn cations are linked by pairs of thiocyanate anions into chains that are further connected into layers by every second 3-cyanopyridine coligand. When compound 2 is heated, a transformation into the complex 1 is observed, that upon further heating transforms into 5. Magnetic measurements for compound 4 show that the Mn-NCS-Mn exchange is dominant and antiferromagnetic, and susceptibility dependence in the paramagnetic phase is well described by the Heisenberg spin chain model. Below 2.77 K, the Mn(II) spins in 4 are ordered with a weak ferromagnetic component due to the Dzyaloshinskii-Moriya interaction.

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.

Electrically function-switchable magnetic domain-wall memory.

Versatile memory is strongly desired for end users, to protect their information in the information era. In particular, bit-level switchable memory that can be switched from rewritable to read-only function would allow end users to prevent important data being tampered with. However, no such switchable memory has been reported. We demonstrate that the rewritable function can be converted into read-only function by applying a sufficiently large current pulse in a U-shaped domain-wall memory, which comprises an asymmetric Pt/Co/Ru/AlOx heterostructure with strong Dzyaloshinskii-Moriya interaction. Wafer-scale switchable magnetic domain-wall memory arrays on 4-inch Si/SiO2 substrate are demonstrated. Furthermore, we confirm that the information can be stored in rewritable or read-only states at bit level according to the security needs of end users. Our work not only provides a solution for personal confidential data, but also paves the way for developing multifunctional spintronic devices.

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.

Emergence of Sizeable Interfacial Dzyaloshinskii-Moriya Interaction at Cobalt/Fullerene Interface

The interfacial Dzyaloshinskii-Moriya interaction (iDMI) originating from a heavy-metal/ferromagnet (FM) interface plays a crucial role in stabilizing chiral spin textures in magnetic multilayers. Recently, graphene based on the low-spin-orbit-coupling (SOC) element carbon ($\mathrm{C}$) has shown a significant iDMI owing to the Rashba SOC when deposited on top of $\mathrm{Co}$. A similar enhanced SOC has been reported earlier for other $\mathrm{C}$ allotropes, namely fullerene (${\text{C}}_{60}$) and carbon nanotubes, and a sizeable DMI can be expected to emerge from them. In this context, we elucidate the magnetization-reversal mechanism, the domain-wall (DW) dynamics, and the strength of the iDMI in a $\mathrm{Pd}(4.0\phantom{\rule{0.2em}{0ex}}\mathrm{nm})/\mathrm{Co}(0.5\phantom{\rule{0.2em}{0ex}}\mathrm{nm})/{\text{C}}_{60}({t}_{{\mathrm{C}}_{60}})/\text{Pd}(2.0\phantom{\rule{0.2em}{0ex}}\mathrm{nm})$ system with varying ${t}_{{\mathrm{C}}_{60}}$. The field-induced DW velocity measured in the creep region shows a DW velocity 2 orders of magnitude higher for a sample with 1.6 nm of ${\text{C}}_{60}$, due to a lower depinning field and spin-dependent hybridization at the $\text{Co}/{\text{C}}_{60}$ interface. Further, DMI measurements performed by use of the asymmetric DW expansion method exhibit a systematic increase in the iDMI from $\ensuremath{-}0.07$ to $\ensuremath{-}0.46\phantom{\rule{0.2em}{0ex}}\mathrm{mJ}/{\mathrm{m}}^{2}$ with an increase in ${t}_{{\mathrm{C}}_{60}}$. Such an enhanced iDMI turns an achiral Bloch wall into a chiral N\'eel wall. The emergence of a finite DMI (${D}_{\mathrm{Co}/{\mathrm{C}}_{60}}\ensuremath{\sim}\ensuremath{-}0.11\phantom{\rule{0.2em}{0ex}}\mathrm{mJ}/{\mathrm{m}}^{2}$) from the $\text{Co}/{\text{C}}_{60}$ interface is particularly encouraging for the use of $\mathrm{C}$-based materials in chiral-DW-based device applications.

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.