Dzyaloshinkii-Moriya Interaction Research Articles

Micromagnetics simulations and phase transitions of ferromagnetics with Dzyaloshinskii–Moriya interaction

Magnetic skyrmions widely exist in a diverse range of magnetic systems, including chiral magnets with a non-centrosymmetric structure characterized by Dzyaloshinkii–Moriya interaction (DMI). In this study, we propose a generalized semi-implicit backward differentiation formula projection method, enabling the simulations of the Landau–Lifshitz (LL) equation in chiral magnets in a typical time step-size of 1 ps, markedly exceeding the limit subjected by the reported numerical methods of typically 0.1 ps. Using micromagnetics simulations, we show that the LL equation with strong DMI reveals an intriguing dynamic instability in magnetization configurations as the damping varies. Both the isolated skyrmionium and skyrmionium clusters can be consequently produced using a simple initialization strategy and a specific damping parameter. Assisted by the string method, the transition path between skyrmion and skyrmionium, along with the escape of a skyrmion from the skyrmion clusters, are then thoroughly examined. The numerical methods developed in this work not only provide a reliable paradigm to investigate the skyrmion-based textures and their transition paths, but also facilitate the understandings for magnetization dynamics in complex magnetic systems.

Phase diagram of chiral magnets via Green’s function method

In this paper, Green’s function method is applied to study the ferromagnetic system with Dzyaloshinkii–Moriya (DM) interaction in both two-dimension (2D) and three-dimension chiral magnets. Relevant properties in 2D magnets are calculated, such as the susceptibility, correlation function and analytical expressions of phase boundary. Based on the theoretical results, a new phase is predicted in the window of strong DM interaction characterized by a negative winding number. In addition, helical state in pure 2D material only appears at zero temperature. The analysis on correlation function shows a special symmetry of transverse spin correlation, which corresponds to the skyrmion phase. The results also prove the instability of helical state and its lifetime is numerically computed. Different from 2D magnets, helical state in 3D exists in the window of a lower Zeeman energy and has a long lifetime. DM interaction also reduces Curie temperature because of the spatial symmetry breaking.

Skyrmion crystal under D3h point group: Role of out-of-plane Dzyaloshinskii-Moriya interaction

The Dzyaloshinkii-Moriya (DM) interaction that originates from relativistic spin-orbit coupling in noncentrosymmetric magnets is a source of topological spin textures. We theoretically investigate the possibility of a skyrmion crystal by focusing on the role of the out-of-plane DM interaction that is different from the polar- and chiral-type DM interaction. By performing the simulated annealing for a spin model on a triangular lattice belonging to the $D_{3h}$ point group, we construct low-temperature magnetic phase diagrams in an applied magnetic field. As a result, we find the instability toward different skyrmion crystals under in-plane and out-of-plane magnetic fields, where the key ingredients to stabilize the SkX are different according to the magnetic field direction; the SkX is stabilized under the out-of-plane DM interaction for the in-plane magnetic field, while it is stabilized by additionally introducing an easy-axis anisotropy for the out-of-plane magnetic field. We also discuss the possible multiple-$Q$ states other than the skyrmion crystals in the presence of the out-of-plane DM interaction. Our result indicates that noncentrosymmetric magnetic materials with the out-of-plane DM interaction are potential candidates to host the skyrmion crystals.

Engineering the Spin-Orbit-Torque Efficiency and Magnetic Properties of Tb / Co Ferrimagnetic Multilayers by Stacking Order

We measure the spin-orbit torques (SOTs), current-induced switching, and domain wall (DW) motion in synthetic ferrimagnets consisting of $\mathrm{Co}$/$\mathrm{Tb}$ layers with differing stacking order grown on a $\mathrm{Pt}$ underlayer. We find that the SOTs, magnetic anisotropy, compensation temperature, and SOT-induced switching are highly sensitive to the stacking order of $\mathrm{Co}$ and $\mathrm{Tb}$ and to the element in contact with $\mathrm{Pt}$. Our study further shows that $\mathrm{Tb}$ is an efficient SOT generator when in contact with $\mathrm{Co}$, such that its position in the stack can be adjusted to generate torques additive to those generated by $\mathrm{Pt}$. With optimal stacking and layer thickness, the dampinglike SOT efficiency reaches 0.3, which is more than twice that expected from the $\mathrm{Pt}$/$\mathrm{Co}$ bilayer. Moreover, the magnetization can be easily switched by the injection of pulses with current density of about (0.5--$2)\ifmmode\times\else\texttimes\fi{}{10}^{7}\phantom{\rule{0.2em}{0ex}}\mathrm{A}/{\mathrm{cm}}^{2}$ despite the extremely high perpendicular magnetic anisotropy barrier (up to 7.8 T). Efficient switching is due to a combination of large SOTs and low saturation magnetization owing to the ferrimagnetic character of the multilayers. We observe current-driven DW motion in the absence of any external field, which is indicative of homochiral N\'eel-type DWs stabilized by the interfacial Dzyaloshinkii-Moriya interaction. These results show that the stacking order in transition metal/rare-earth synthetic ferrimagnets plays a major role in determining the magnetotransport properties relevant for spintronic applications.

Dzyaloshinskii-Moriya anisotropy effect on field-induced magnon condensation in the kagome antiferromagnet α−Cu3.26Mg0.74(OH)6Br2

We performed a comprehensive electron spin resonance, magnetization and heat capacity study on the field-induced magnetic phase transitions in the kagome antiferromagnet $\alpha-Cu_3Mg(OH)_6Br_2$. With the successful preparation of single crystals, we mapped out the magnetic phase diagrams under the $c$-axis and $ab$-plane directional magnetic fields $B$. For $B\|c$, the three-dimensional (3D) magnon Bose-Einstein condensation (BEC) is evidenced by the power law scaling of the transition temperature, $T_c\propto (B_c-B)^{2/3}$. For $B\|ab$, the transition from the canted antiferromagetic (CAFM) state to the fully polarized (FP) state is a crossover rather than phase transition, and the characteristic temperature has a significant deviation from the 3D BEC scaling. The different behaviors of the field-induced magnetic transitions for $B\|c$ and $B\|ab$ could result from the Dzyaloshinkii-Moriya (DM) interaction with the DM vector along the $c$-axis, which preserves the $c$-axis directional spin rotation symmetry and breaks the spin rotation symmetry when $B\|ab$. The 3D magnon BEC scaling for $B\|c$ is immune to the off-stoichiometric disorder in our sample $\alpha-Cu_{3.26}Mg_{0.74}(OH)_6Br_2$. Our findings have the potential to shed light on the investigations of the magnetic anisotropy and disorder effects on the field-induced magnon BEC in the quantum antiferromagnet.

Towards hexagonal C2v systems with anisotropic Dzyaloshinkii-Moriya interaction: Characterization of epitaxial Co(101¯0)/Pt(110) multilayer films

Ferromagnet/heavy metal (FM/HM) multilayer thin films with ${C}_{2v}$ symmetry have the potential to host antiskyrmions and other chiral spin textures via an anisotropic Dzyaloshinkii-Moriya interaction (DMI). Here, we present a candidate material system that also has a strong uniaxial magnetocrystalline anisotropy aligned in the plane of the film. This system is based on a new Co/Pt epitaxial relationship, which is the central focus of this work: hexagonal closed-packed $\mathrm{Co}(1\phantom{\rule{0.16em}{0ex}}0\phantom{\rule{0.16em}{0ex}}\overline{1}\phantom{\rule{0.16em}{0ex}}0)[0\phantom{\rule{0.16em}{0ex}}0\phantom{\rule{0.16em}{0ex}}0\phantom{\rule{0.16em}{0ex}}1]$ $\ensuremath{\parallel}$ face-centered cubic $\mathrm{Pt}(1\phantom{\rule{0.16em}{0ex}}1\phantom{\rule{0.16em}{0ex}}0)[0\phantom{\rule{0.16em}{0ex}}0\phantom{\rule{0.16em}{0ex}}1]$. We characterized the crystal structure and magnetic properties of our films using x-ray diffraction techniques and magnetometry, respectively, including $q$-scans to determine stacking fault densities and their correlation with the measured magnetocrystalline anisotropy constant and thickness of Co. In future ultrathin multilayer films, we expect this epitaxial relationship to further enable an anisotropic DMI while supporting interfacial perpendicular magnetic anisotropy. The anticipated confluence of these properties, along with the tunability of multilayer films, make this material system a promising testbed for unveiling new spin configurations in FM/HM films.

Modulational instability induced generation of solitary wave profile of an anisotropic-ferromagnetic nanowire with asymmetric Dzyaloshinskii-Moriya interaction

We study the nanoscale magnetization evolution of a one dimensional ferromagnetic nanowire with the inclusion of next-nearest-neighbor interaction and Dzyaloshinkii-Moriya (DM) interaction. The system is modelled using Heisenberg Hamiltonian in the quasi classical approximation of spin operators. The dynamics of the system is found to be governed by generalized discrete nonlinear Schrodinger equation. Further we investigate analytically the modulational instability in ferromagnetic nanowire system, where the effect of next-nearest neighbour (NNN) interaction and DM interaction are taken into an account to show graphically the effect of interactions on Modulational Instability (MI) gain spectra.

Bloch Chirality Induced by an Interlayer Dzyaloshinskii-Moriya Interaction in Ferromagnetic Multilayers

Chiral spin textures stabilized by the interfacial Dzyaloshinkii-Moriya interaction, such as skyrmions and homochiral domain walls, have been shown to exhibit qualities that make them attractive for their incorporation in a variety of spintronic devices. However, for thicker multilayer films, mixed textures occur in which an achiral Bloch component coexists with a chiral Néel component of the domain wall to reduce the demagnetization field at the film surface. We show that an interlayer Dzyaloshinkii-Moriya interaction can break the degeneracy between Bloch chiralities. We further find large population asymmetries and chiral branching in the Bloch component of the domain walls in well-ordered Co/Pd multilayers. This asymmetry is a result of the combined effect of the demagnetization field and an interlayer Dzyaloshinkii-Moriya interaction, and is strongly related to film thickness and structural ordering. This work paves the way toward the utilization of this effect toward controlling Bloch chirality in magnetic multilayers.

Robust metastable skyrmions with tunable size in the chiral magnet FePtMo3N

Synthesis of new materials that can host magnetic skyrmions and their thorough experimental and theoretical characterization are essential for future technological applications. The $\beta$-Mn-type compound FePtMo$_3$N is one such novel material that belongs to the chiral space group $P4_132$, where the antisymmetric Dzyaloshinkii-Moriya interaction is allowed due to the absence of inversion symmetry. We report the results of small-angle neutron scattering (SANS) measurements of FePtMo$_3$N and demonstrate that its magnetic ground state is a long-period spin helix with a Curie temperature of 222~K. The magnetic field-induced redistribution of the SANS intensity showed that the helical structure transforms to a lattice of skyrmions at $\sim$13~mT at temperatures just below $T_{\text C}$. Our key observation is that the skyrmion state in FePtMo$_3$N is robust against field cooling down to the lowest temperatures. Moreover, once the metastable state is prepared by field cooling, the skyrmion lattice exists even in zero field. Furthermore, we show that the skyrmion size in FePtMo$_3$N exhibits high sensitivity to the sample temperature and can be continuously tuned between 120 and 210~nm. This offers new prospects in the control of topological properties of chiral magnets.

Ultrafast domain wall motion in ferrimagnets induced by magnetic anisotropy gradient

The ultrafast magnetic dynamics in compensated ferrimagnets not only provides information similar to antiferromagnetic dynamics, but more importantly opens new opportunities for future spintronic devices [Kim et al., Nat. Mater. 16, 1187 (2017)]. One of the most essential issues for device design is searching for low-power-consuming and high-efficient methods of controlling domain wall. In this work, we propose to use the voltage-controlled magnetic anisotropy gradient as an excitation source to drive the domain wall motion in ferrimagnets. The ultrafast wall motion under the anisotropy gradient is predicted theoretically based on the collective coordinate theory, which is confirmed by the atomistic micromagnetic simulations. The antiferromagnetic spin dynamics is realized at the angular momentum compensation point, and the wall shifting has a constant speed under small gradient and can be slightly accelerated under large gradient due to the broadened wall width during the motion. For nonzero net angular momentum, the Walker breakdown occurs at a critical anisotropy gradient significantly depending on the second anisotropy and interfacial Dzyaloshinkii-Moriya interaction, which is highly appreciated for further experiments including the materials selection and device geometry design. More importantly, this work unveils a low-power-consuming method of controlling the domain wall in ferrimagnets, benefiting to future spintronic applications.

Interlayer Dzyaloshinskii-Moriya Interactions

The interfacial Dzyaloshinkii-Moriya interaction defines a rotational sense for the spin structure in two-dimensional magnetic films and can be used to create chiral magnetic structures like spin spirals and skyrmions in those films. Here, we show by means of atomistic calculations that in heterostructures an interlayer coupling of the Dzyaloshinskii-Moriya type across a spacer can emerge. We quantify this interaction in the framework of the Lévy-Fert model for trilayers consisting of two ferromagnets separated by a nonmagnetic spacer and show that such an interlayer Dzyaloshinkii-Moriya interaction yields nontrivial three-dimensional spin textures across the entire trilayer, which evolve within as well as between the planes and, hence, combine intraplane and interplane chiralities. This analysis opens new perspectives for three-dimensional tailoring of magnetic chirality in multilayers.

Thermal entanglement in a five-qubit XXZ Heisenberg spin chain with the next nearest neighboring interaction

In the study of thermal entanglement of the Heisenberg spin chain model, one usually considers only the spin interaction between the nearest neighboring qubits. Actually, a generalized Heisenberg model, so-called J1-J2 Heisenberg model, which is constructed by considering the fact that not only the nearest neighboring but also the next nearest neighboring spin interaction also plays an important role. In J1-J2 Heisenberg model, due to the next nearest neighboring spin interaction, the frustration effect can occur and has an important influence on the magnetic properties of the model. In this paper we investigate the thermal entanglement of a five-qubit XXZ Heisenberg spin chain with the next nearest neighboring interaction in a magnetic field. Using the numerical method, we calculate the pairwise concurrences of the nearest neighbouring qubits and the next nearest neighboring qubits, abbreviated as C12 and C13 respectively. The numerical results show that the frustration parameter α has an important effect on the pairwise thermal entanglement. Moreover, C12 and C13 have different variations with the change of the frustration parameter α. Meanwhile, it is found that the temperature, magnetic field, Dzyaloshinkii-Moriya (DM) interaction and anisotropic parameter also have great effects on the thermal entanglement. The increasing of temperature can reduce the thermal entanglement. The magnetic field can enhance the thermal entanglement between both two nearest and next nearest neighboring qubits, but when the magnetic field becomes strong enough, only the thermal entanglement between the two nearest neighboring qubits is suppressed. A certain extent of DM interaction can enhance the thermal entanglement between the two nearest neighboring qubits. But for the next nearest neighboring qubits, without the magnetic field, the increasing of DM interaction mainly enlarge the entanglement vanishing area of frustration parameter α. When the system changes from anisotropic to isotropic state, the entanglement vanishing area also changes obviously for C12 and C13. Thus, we can choose appropriate magnetic field strength, temperature, frustration parameter, DM interaction parameter and anisotropic parameter to effectively control and enhance the thermal entanglement of the system.

Dzyaloshinskii–Moriya interaction induced domain wall depinning anomaly in ferromagnetic nanowire

Magnetic domain wall positional manipulation is usually through the introduction of potential trap. In this work, we show that the presence of interfacial Dzyaloshinkii–Moriya interaction leads to a different static depinning field for Néel domain walls with the same handedness in a notched magnetic nanowire. The difference in static depinning field is due to the Néel domain wall spin orientation. The spin orientation leads to different torques being exerted on the localized magnetic moments. This inherently imposes a spin orientation dependent diode-like behavior for domain walls in a notched nanowire. An equation which relates the difference in static depinning field to the notch geometry is derived. Micromagnetic simulation with varying damping constant reveals the influence of damping constant on the strength of depinning anomaly.

A skyrmion-based spin-torque nano-oscillator

A model for a spin-torque nano-oscillator based on the self-sustained oscillation of a magnetic skyrmion is presented. The system involves a circular nanopillar geometry comprising an ultrathin film free magnetic layer with a strong Dzyaloshinkii–Moriya interaction and a polariser layer with a vortex-like spin configuration. It is shown that spin-transfer torques due to current flow perpendicular to the film plane leads to skyrmion gyration that arises from a competition between geometric confinement due to boundary edges and the vortex-like polarisation of the spin torques. A phenomenology for such oscillations is developed and quantitative analysis using micromagnetics simulations is presented. It is also shown that weak disorder due to random anisotropy variations does not influence the main characteristics of the steady-state gyration.

Topological Magnon Bands in a Kagome Lattice Ferromagnet.

There is great interest in finding materials possessing quasiparticles with topological properties. Such materials may have novel excitations that exist on their boundaries which are protected against disorder. We report experimental evidence that magnons in an insulating kagome ferromagnet can have a topological band structure. Our neutron scattering measurements further reveal that one of the bands is flat due to the unique geometry of the kagome lattice. Spin wave calculations show that the measured band structure follows from a simple Heisenberg Hamiltonian with a Dzyaloshinkii-Moriya interaction. This serves as the first realization of an effectively two-dimensional topological magnon insulator--a new class of magnetic material that should display both a magnon Hall effect and protected chiral edge modes.

Quantum discord in spin-1/2 Heisenberg chains with Dzyaloshinkii–Moriya interaction

We have investigated the quantum discord (QD) of the thermal density matrix of spin-1/2 Heisenberg chains with Dzyaloshinskii–Moriya (DM) interaction. With fermionization technique, we study the mutual effect of DM interaction and the external magnetic field on the QD and the entanglement. Our analysis implies that the DM interaction can enhance the QD while the external magnetic field will shrink the QD. By a comparison between the entanglement and the QD, we find that the QD is more robust to the temperature and to the external magnetic field than the entanglement of formation (EoF) in the sense that the EoF takes a zero value while the QD does not for high temperature and strong external magnetic field. This point confirms the conclusion that there exist some separable states containing non-zero QD.

Collision of electromagnetic solitons in a weak ferromagnetic medium

We investigate the propagation dynamics of electromagnetic soliton in a weak ferromagnet with Dzyaloshinskii–Moriya interaction and uniaxial anisotropy along the propagation of electromagnetic (EM) wave. We perform the analysis in the framework of Landau–Lifshitz (LL) equation governing the spin evolution in ferromagnet and Maxwell (M) equations representing the electromagnetic wave propagation. We invoke the reductive perturbation method, and a nonuniform expansion is carried out on the coupled LLM equations which is reduced to a perturbed derivative nonlinear Schrödinger (pDNLS) equation for a new complex field that govern the spin excitations under the influence of EM wave. The pDNLS equation is systematically solved through the tangent-hyperbolic method and a class of soliton solutions are constructed. Further, the collision of EM wave soliton and the influence of Dzyaloshinkii–Moriya interaction is established via Hirota bilinerization method.

Phase diagram and magnetization plateaus in the SU(4) spin ladder with rung anisotropy

In this paper, we study a solvable SU(4) spin ladder with Dzyaloshinkii-Moriya interaction along the rung direction. Due to the rung anisotropy, the rung spin triplet is splitted into a singlet and a doublet. This splitting leads to some quantum phase transitions and the magnetization plateaus, with or without spin gap. Exact phase diagram and magnetization plateaus are presented based on the Bethe ansatz solutions. A magnetization line with $〈M〉=1/3$ is found in the Ising limit.

Magnetic-field induced gap and staggered susceptibility in the S = 1/2 chain [PM·Cu(NO3)2·(H2O)2]n(PM = pyrimidine)

Single-crystal magnetic susceptibility and specific heat studies of theone-dimensional copper complex[PM·Cu(NO3)2·(H2O)2]n (PM = pyrimidine) show that it behaveslike a uniform S = 1/2 antiferromagnetic Heisenberg chain, characterized bythe exchange parameter J/kB = 36 K. Specific heat measurements in theapplied magnetic field, however, reveal the formation of a field-induced spinexcitation gap, whose magnitude depends on the magnitude and direction of thefield. This behaviour is inconsistent with the ideal S = 1/2 Heisenberg chain.In the low-temperature region, a contribution to the susceptibility,approximately proportional to 1/T, is observed which varies strongly withthe varying direction of the magnetic field. The field-induced gap and the1/T contribution are largest for the same field direction. Previousobservations of a field-induced gap in the related compounds copper benzoateand Yb4As3 have been explained by the alternating g tensor andalternating Dzyaloshinkii-Moriya interaction, producing an effectivestaggered magnetic field at the Cu and Yb ions. We apply this model to [PM·Cu(NO3)2·(H2O)2]n and obtain aconsistent quantitative explanation of the low-temperature susceptibility, thefield-induced gap and their dependence on the magnetic-field direction.