Magnetic Solitons Research Articles

Damping-like effects in Heisenberg spin chain caused by the site-dependent bilinear interaction

We investigate a continuous Heisenberg spin chain equation which models the local magnetization in ferromagnet with time- and site-dependent inhomogeneous bilinear interaction and time-dependent spin-transfer torque. By establishing the gauge equivalence between the spin chain equation and an integrable generalized nonlinear Schrödinger equation, we present explicitly a novel nonautonomous magnetic soliton solution for the spin chain equation. The results display how the dynamics of the magnetic soliton can be controlled by the bilinear interaction and spin-polarized current. Especially, we find that the site-dependent bilinear interaction may break some conserved quantity, and give rise to damping-like effect in the spin evolution.

Phase diagram, stability and magnetic properties of nonlinear excitations in spinor Bose–Einstein condensates

We present the phase diagram, the underlying stability and magnetic properties as well as the dynamics of nonlinear solitary wave excitations arising in the distinct phases of a harmonically confined spinor F = 1 Bose–Einstein condensate. Particularly, it is found that nonlinear excitations in the form of dark–dark–bright solitons exist in the antiferromagnetic and in the easy-axis phase of a spinor gas, being generally unstable in the former while possessing stability intervals in the latter phase. Dark–bright–bright solitons can be realized in the polar and the easy-plane phases as unstable and stable configurations respectively; the latter phase can also feature stable dark–dark–dark solitons. Importantly, the persistence of these types of states upon transitioning, by means of tuning the quadratic Zeeman coefficient from one phase to the other is unravelled. Additionally, the spin-mixing dynamics of stable and unstable matter waves is analyzed, revealing among others the coherent evolution of magnetic dark–bright, nematic dark–bright–bright and dark–dark–dark solitons. Moreover, for the unstable cases unmagnetized or magnetic droplet-like configurations and spin-waves consisting of regular and magnetic solitons are seen to dynamically emerge remaining thereafter robust while propagating for extremely large evolution times. Interestingly, exposing spinorial solitons to finite temperatures, their anti-damping in trap oscillation is showcased. It is found that the latter is suppressed for stronger bright soliton component ‘fillings’. Our investigations pave the wave for a systematic production and analysis involving spin transfer processes of such waveforms which have been recently realized in ultracold experiments.

Возможность управления динамикой и структурой магнитного солитона в трехслойной ферромагнитной структуре

The generation and excitation of a magnetic soliton in a three-layer ferromagnet by constant magnetic fields and fields of variable frequency and small amplitude in the presence of dissipation in the system are considered. The analysis of the solutions of the equation of motion in an alternating field shows the possibility of increasing the amplitude of the magnetic soliton over time under certain conditions. The resonant effect is also affected by the geometric parameters of the thin layer: at a large layer width, the translational mode of the soliton oscillations is also excited.

Relativistic kinematics of a magnetic soliton.

A tenet of special relativity is that no particle can exceed the speed of light. In certain magnetic materials, the maximum magnon group velocity serves as an analogous relativistic limit for the speed of magnetic solitons. Here, we drive domain walls to this limit in a low-dissipation magnetic insulator using pure spin currents from the spin Hall effect. We achieve record current-driven velocities in excess of 4300 meters per second-within ~10% of the relativistic limit-and we observe key signatures of relativistic motion associated with Lorentz contraction, which leads to velocity saturation. The experimental results are well explained through analytical and atomistic modeling. These observations provide critical insight into the fundamental limits of the dynamics of magnetic solitons and establish a readily accessible experimental framework to study relativistic solitonic physics.

Two-dimensional overdamped simulations of droplet solitons activated by spin transfer torque

We present overdamped micromagnetic simulations of the time evolution of magnetic droplet solitons which are formed in a thin film with perpendicular magnetic anisotropy by injecting a spin polarized current through a circular nanocontact. The overdamped dynamics help explore the effective energy landscape of these structures and permit identification of stationary states that are either energy extrema or saddle configurations. Our micromagnetic simulations start with configurations that are numerical solutions of a one-dimensional model where the magnetization depends only on the radial distance to the center of the nanocontact. We verify that these solutions correspond either to energy minima or saddle states, and use them to estimate thermal activation barriers for various current strengths. From the two-dimensional micromagnetic simulations, we identify a new persistent state which does not appear in the one-dimensional model.

Experimental observation of vortex rings in a bulk magnet

Vortex rings are remarkably stable structures occurring in numerous systems: for example in turbulent gases, where they are at the origin of weather phenomena [1]; in fluids with implications for biology [2]; in electromagnetic discharges [3]; and in plasmas [4]. While vortex rings have also been predicted to exist in ferromagnets [5], they have not yet been observed. Using X-ray magnetic nanotomography [6], we imaged three-dimensional structures forming closed loops in a bulk micromagnet, each composed of a vortex-antivortex pair. Based on the magnetic vorticity, a quantity analogous to hydrodynamic vorticity, we identify these configurations as magnetic vortex rings. While such structures have been predicted to exist as transient states in exchange ferromagnets [5], the vortex rings we observe exist as stable, static configurations, whose stability we attribute to the dipolar interaction. In addition, we observe stable vortex loops intersected by magnetic singularities [7], at which the magnetisation within the vortex and antivortex cores reverses. We gain insight into the stability of these states through field and thermal equilibration protocols. These measurements pave the way for the observation of complex three-dimensional solitons in bulk magnets, as well as for the development of applications based on three-dimensional magnetic structures.

Magnetic soliton rectifier via phase synchronization

Most of the existing research on the dynamics of magnetic solitons such as a domain wall (DW) has focused on the effect of DC forces, where the induced velocity is determined by the force strength. Here we show that AC forces such as an oscillating magnetic field or current are also able to move a DW straight via synchronization between the DW angle and the phase of the AC force. The resulting DW velocity is solely proportional to the driving frequency of the AC force, but the strength of the AC field just affects the frequency range for criteria for the phase-locking behavior. The AC-force-driven DW motion is shown to exhibit a phase locking-unlocking transition, a critical phenomenon akin to the Walker breakdown of a DC-bias-driven DW motion. Our work shows that a DW can be driven straight by synchronizing its angle to AC forces and thereby demonstrates a proof-of-concept of magnetic soliton rectifiers (i.e., DC motion induced by AC forces), shedding a light on the hitherto overlooked utility of internal degree of freedom for driving magnetic textures.

Tuning Magnetic Droplets in Nanocontact Spin-Torque Oscillators Using Electric Fields

Reliable in situ control of spin wave (SW) excitation between localized and propagating SW modes is of great interest for both fundamental and applied spintronics and magnonics. While spin-transfer-torque-generated SWs can typically be tuned directly via the driving current, the frequency of the highest intensity SWs, achieved in the strongly self-localized magnetic droplet soliton, is virtually current independent, as the droplet frequency is given by the intrinsic material properties. Here, we demonstrate, using micromagnetic simulations, how the droplet frequency can be efficiently tuned by an applied voltage through the effect of electric field (E-field)-dependent perpendicular magnetic anisotropy (PMA). It is found that as the PMA decreases, the droplet begins to distort and eventually collapses to give way to propagating SWs. However, due to the geometrically confined structures, the radially propagating SWs are reflected by the periphery boundary of the sample, and then the forward and backward SWs superpose to produce a series of standing SWs. The node number of the standing SWs strongly depends on the sample size as well as the applied E field. These findings provide a deeper understanding of magnetic excitation properties, which will be helpful for designing advanced spintronic devices.

Coupled-oscillator collective mode of a magnetic chiral soliton lattice

The collective excitation modes of a magnetic chiral soliton lattice (CSL) are numerically studied. We perform micromagnetic simulations of a monoaxial chiral helimagnet with an external magnetic field that forms the CSL. Due to the repulsive interaction between solitons through a ferromagnet state, collective modes described by the coupled oscillator are excited. These modes exist at a frequency of $\ensuremath{\sim}1\phantom{\rule{0.28em}{0ex}}\mathrm{GHz}$ while the conventional ferromagnetic resonant mode exists at a frequency of $\ensuremath{\sim}10\phantom{\rule{0.28em}{0ex}}\mathrm{GHz}$ as measured in experiments [F. Goncalves et al., Phys. Rev. B 95, 104415 (2017)]. In contrast to ferromagnetic resonance, the resonant frequency of the coupled-oscillator mode decreases by increasing the magnetic field. We clarified that the coupling energy between solitons becomes weak by increasing the distance between solitons. We also investigate the resonant condition of a precessional mode of the CSL measured in experiments.

Magnetic droplet solitons

Magnetic droplet solitons are dynamical magnetic textures that form due to an attractive interaction between spin waves in thin films with perpendicular magnetic anisotropy. Spin currents and the spin torques associated with these currents enable their formation as they provide a means to excite non-equilibrium spin-wave populations and compensate their decay. Recent years have seen rapid advances in experiments that realize and study magnetic droplets. Important advances include the first direct x-ray images of droplets, determination of their threshold and sustaining currents, measurement of their generation and annihilation time, and evidence for drift instabilities, which can limit their lifetime. This perspective discusses these studies and contrasts these solitons to other types of spin-current excitations, such as spin-wave bullets, and static magnetic textures, including magnetic vortices and skyrmions. Magnetic droplet solitons can also serve as current controlled microwave frequency oscillators with potential applications in neuromorphic chips as nonlinear oscillators with memory.

Robust nature of the chiral spin helix in CrNb3S6 nanostructures studied by off-axis electron holography

Magnetic soliton crystals with layered structures that host periodic chiral helimagnetic ordering are promising candidates for spintronic nanodevices. Among them, helimagnetic $\mathrm{Cr}{\mathrm{Nb}}_{3}{\mathrm{S}}_{6}$ is unique owing to its crystallographic chirality and monoaxial Dzyaloshinskii-Moriya interaction. It is crucial to explore its magnetic configurations and properties with respect to the temperature and thickness, especially in reduced dimensions. Here, the chiral helimagnetic ground state in $\mathrm{Cr}{\mathrm{Nb}}_{3}{\mathrm{S}}_{6}$ nanostructures is investigated using off-axis electron holography in the transmission electron microscope. The period of the helical state is found to be independent of both temperature and specimen thickness, while the temperature dependence of the saturation magnetization is shown to follow a classical Heisenberg spin model. Monte Carlo simulations based on a discrete classical Heisenberg model reproduce the experimental observations closely, confirming the applicability of a three-dimensional Heisenberg model even in a confined specimen geometry.

The origin of spin wave pulse-induced domain wall inertia

The fundamental problem of domain wall (DW) inertia—the property that gives to inertial behaviors remains unclear in the physics of magnetic solitons. To understand its nature as well as to achieve accurate DW positioning and efficient manipulation of domain wall motion (DWM), spin wave (SW) pulse-induced DW transient effect is studied both numerically and theoretically in a magnetic nanostrip. It is shown for the first time that there occurs inevitable deceleration/automotion after SW pulse, which indicates nonzero DW inertia. The induced DWM is revealed to relate to two factors: energy storing within DW and out-of-plane tilting of DW. To explain the DWM dynamics, a one-dimensional collective model is developed to account for the excitation of spin wave pulse. The model successfully bridges DW energy, DW tilting and DW displacement and provides descriptions in accordance with numerical findings. It is made clear that the DW automotion hence DW inertia originate from the process of DW relaxation toward equilibrium. The DW inertia is expressed in terms of effective mass and turns out to be a time-dependent function with damping constant α as the governing parameter, which opposes the nature of intrinsic mass. For case containing multiple DWs, the total effective mass is shown to concern the reached velocity and stored energy of DWs instead of the number of DWs, which is against common intuition.

Dipole-dominated dissipative magnetic solitons in quasi-one-dimensional spin-torque oscillators

It is well-known that a spin-transfer torque caused by a dc electric current can excite in a two-dimensional ferromagnetic film exchange-dominated magnetic solitons, often called “spin-wave bullets”, under the condition of a negative nonlinear shift of spin wave frequency. In this work, we demonstrate that in a quasi-one-dimensional (1D) case, e.g., in a nanowire spin-Hall oscillator, it is possible to excite a stable dissipative magnetic soliton, which is dominated by the dipole-dipole interaction. This dissipative magnetic soliton can be described in the framework of a 1D Ginzburg-Landau auto-oscillator model, and has the shape similar to that of the exchange-dominated spin wave bullet, but with a different spatial localization law. The influence of the dipolar interaction makes possible the stabilization of a dissipative soliton in a relatively large (micron-sized) active area of the oscillator, which is in a sharp contrast with the two-dimensional case, where the excitation of a stable spin-wave bullet was observed only in relatively small active areas having typical sizes of the order of 100 nm. The characteristics and possible applications of these dipole-dominated spin wave bullets are discussed.

Dynamics of pair of coupled nonlinear systems. I. Magnetic systems

In the framework of the Landau–Lifshitz equations for discrete systems, the dynamics of two classical magnetic moments modeling weakly coupled magnetic nanodots, layers of quasi-two-dimensional magnets and two-sublattice magnets are considered. Exact solutions of dynamic equations are found and investigated. Particular attention is paid to the study of essentially nonlinear inhomogeneous states with different levels of excitation for identical subsystems as a discrete analog for the magnetic solitons.

Observation of Magnetic Solitons in Two-Component Bose-Einstein Condensates.

We experimentally investigate the dynamics of spin solitary waves (magnetic solitons) in a harmonically trapped, binary superfluid mixture. We measure the insitu density of each pseudospin component and their relative local phase via an interferometric technique we developed and as such, fully characterize the magnetic solitons while they undergo oscillatory motion in the trap. Magnetic solitons exhibit nondispersive, dissipationless longtime dynamics. By imprinting multiple magnetic solitons in our ultracold gas sample, we engineer binary collisions between solitons of either the same or opposite magnetization and map out their trajectories.

Microwave response of the chiral helimagnetic MnNb3S6

Chiral magnetic soliton (CMS), an isolated topological kink consisting of spins, has potential applications in spintronics. In this work, the microwave response of layered MnNb3S6, which is suggested as a candidate for CMS, is investigated by the electronic spin resonance (ESR). Angle-dependent ESR spectra show that the microwave response is strong for H ⊥ c while it is weak for H//c, where c is the c-axis of the single crystal. When H ⊥ c, two resonance lines are observed, which are marked as Hr1 for the higher field and Hr2 for the lower field. It is determined that Hr1 originates from the ferromagnetic resonance of forced ferromagnetic moments, which evolves into paramagnetic resonance above TC. Meanwhile, Hr2 existing only below TC fulfills the Goldstone excitation of CMS. The microwave response of MnNb3S6 supports the existence of CMS in MnNb3S6, and is proved to be an effective means for modulating and investigating CMS.

Giant, low-loss magnetic responses and ultraslow magnetic solitons via plasmon-induced transparency

The realization of advanced materials with strong, low-loss, and pure magnetic responses to radiation fields both in linear and nonlinear regimes is an important and long-standing goal for fundamental physics and practical applications. Here, we propose a physical scheme for obtaining such responses by using a metamaterial constructed by an array of unit cells consisting of two coupled varactor-loaded split-ring resonators working under the condition of plasmon-induced transparency (PIT). We show that the PIT in such metamaterial not only significantly suppresses radiation absorption but also greatly enhances magnetic Kerr nonlinearity, which may be many orders of magnitude larger than that obtained by conventional magnetic materials reported up to now. Based on such a nonlinear metamaterial, we further show that stable magnetic solitons with ultraslow propagation velocity and very low generation power can be created. Our research opens a route for designing novel metamaterial devices with strong, low-loss, pure, and actively tunable magnetic responses and for obtaining stable and low-power nonlinear magnetic pulses, which are promising for applications in information processing and transmission.

Tensile deformations of the magnetic chiral soliton lattice probed by Lorentz transmission electron microscopy

We consider the case of a chiral soliton lattice subjected to uniaxial elastic strain applied perpendicular to the chiral axis and derive through analytical modelling the phase diagram of magnetic states supported in the presence of an external magnetic field. The strain induced anisotropies give rise to three distinct non-trivial spin textures, depending on the nature of the strain, and we show how these states may be identified by their signatures in Lorentz transmission electron microscopy (TEM). Experimental TEM measurements of the Fresnel contrast in a strained sample of the prototypical monoaxial chrial helimagnet CrNb$_3$S$_6$ are reported and compare well with the modelled contrast. Our results demonstrate an additional degree of freedom that may be used to tailor the magnetic properties of helimagnets for fundamental research and applications in the areas of spintronics and the emerging field of strain manipulated spintronics.

Thermal activation barriers for creation and annihilation of magnetic droplet solitons in the presence of spin transfer torque

We study noise-induced creation and annihilation of magnetic droplet solitons in experimental parameter regions in which they are linearly stable against drift. Exploiting the rotational symmetry of the problem, we transform to the reference frame rotating with the droplet soliton and introduce an effective potential energy that accounts for the work done against spin-transfer torque to rotate the magnetization between two different orientations. We use this function to compute the activation barrier in both directions between the uniform magnetization state and the droplet soliton state for a variety of nanocontact radii and currents. We investigate droplet soliton structures with both zero and nonzero spin-torque asymmetry parameter. Our approach can be applied to estimate activation barriers for dynamical systems where non-gradient terms can be absorbed by changes of reference frames, and suggests a technique applicable to extended systems that may not be uniformly magnetized.

Symmetric and antisymmetric Dzyaloshinskii-Moriya solitons in anisotropic ferromagnetic wires

We theoretically investigate the effect of Dzyaloshinskii-Moriya interaction (DMI) on magnetic solitons in anisotropic ferromagnetic wires driven by the adiabatic spin-transfer torque. The DMI changes the formation region of soliton solution and the corresponding phase diagram is given for different types of soliton solutions. Also, it affects the processional frequency and the internal structure distortion of solitons. We show that the DMI decreases the energy for symmetric soliton while increases the energy for antisymmetric one. It implies that the DMI favours the more steady state of magnetization for the case of strong easy-axis anisotropy.