Magnetic Solitons Research Articles

Solitons in low-dimensional magnets: Elementary excitations with a nontrivial dispersion law

Solitons are known to play the role of elementary excitations for one-dimensional ordered systems, like atomic chains with charge or spin ordering. The main characteristic of solitons is their dispersion relation, dependence of soliton energy on the linear momentum. Topological kink-type solitons are the simplest and most important for the description of many physical properties of one-dimensional magnets. Here we provide a detailed analysis of solitons in some general class of magnets, ferrimagnets with the spin compensation point. The nonlinear spin dynamics of ferrimagnets are examined using a nonlinear sigma-model for the antiferromagnetic vector, which is a generalization of the Landau-Lifshitz equation for ferromagnets and sigma-model for the antiferromagnets. The characteristic features of this equation are governed by the value of the compensation parameter, describing the rate of compensation of spins of sublattices. The dispersion relation for kink-type solitons appears to be quite nontrivial, including periodic dispersion law for continuum model of magnet or the presence of ending point for kink spectrum.

Two types of metastable hopfions in bulk magnets

Localized magnetic topological solitons with Hopf index of 1 in an unbounded bulk magnet are studied theoretically, starting with the classical micromagnetic Hamiltonian. It is shown analytically that (like Bloch and Néel walls in classical magnetism) there are two possible stable configurations of these nanoobjects, which are equivalent topologically. Their stability regions are plotted on a phase diagram in the magnetic field — uniaxial anisotropy space for different normalized magnetostatic interaction strengths. For some parameters both types of hopfions can be stable.

Generation and routing of nanoscale droplet solitons without compensation of magnetic damping

A magnetic droplet soliton is a localized dynamic spin state which can serve as a nanoscale information carrier and nonlinear oscillator. The present opinion is that the formation of droplet solitons requires the compensation of magnetic damping by a torque created by a spin-polarized electric current or pure spin current. Here, we demonstrate theoretically that nanoscale droplet solitons can be generated and routed in ferromagnetic nanostructures with voltage-controlled magnetic anisotropy in the presence of uncompensated magnetic damping. Performing micromagnetic simulations for the MgO/Fe/MgO trilayer with almost perpendicular-to-plane magnetization, we reveal the formation of the droplet soliton under a nanoscale gate electrode subjected to a subnanosecond voltage pulse. The soliton lives up to 50 ns at room temperature and can propagate over micrometer distances in a ferromagnetic waveguide due to nonzero gradient of the demagnetizing field. Furthermore, we show that electrical routing of the soliton to different outputs of a spintronic device can be realized with the aid of an additional semiconducting nanostripe electrode creating controllable gradient of the perpendicular magnetic anisotropy.

Atomic-scale spin-wave polarizer based on a sharp antiferromagnetic domain wall

We theoretically study the scattering of spin waves from a sharp domain wall in an antiferromagnetic spin chain. While the continuum model for an antiferromagnetic material yields the well-known result that spin waves can pass through a wide domain wall with no reflection, here we show that, based on the discrete spin Hamiltonian, spin waves are generally reflected by a domain wall with a reflection coefficient that increases as the domain-wall width decreases. Remarkably, we find that, in the interesting case of an atomically sharp domain wall, the reflection of spin waves exhibits strong dependence on the state of circular polarization of the spin waves, leading to mainly reflection for one polarization while permitting partial transmission for the other, thus realizing an atomic-scale spin-wave polarizer. The polarization of the transmitted spin wave depends on the orientation of the spin in the sharp domain wall, which can be controlled by an external field or spin torque. Our utilization of a sharp antiferromagnetic domain wall as an atomic-scale spin-wave polarizer leads us to envision that ultra-small magnetic solitons such as domain walls and skyrmions may enable realizations of atomic-scale spin-wave scatterers with useful functionalities.

An emergence of chiral helimagnetism or ferromagnetism governed by Cr intercalation in a dichalcogenide CrNb3S6

A synthesis of single crystals of chiral dichalcogenides TM3X6 (T: 3d transition metal, M: Nb or Ta, X: S or Se) remains an intriguing issue for the investigation of emergent quantum properties such as chiral helimagnetism. In this study, we investigated a correlation between the quantity of Cr intercalation x and the magnetic property in single crystals of a chromium (Cr) intercalated chiral disulfide CrxNb3S6 in order to optimize the synthesis condition for the intercalation-controlled single crystals. The magnetic properties, including a magnetic transition temperature Tc, take different values depending on the samples. We systematically grew single crystals of CrxNb3S6 with x ranged from 0.89 to 1.03 and found that the amount of the Cr intercalation x is an essential factor in controlling the magnetic properties of the grown crystals. The magnetization anomaly, which appears in the temperature dependence as evidence of the formation of chiral magnetic soliton lattice (CSL), was observed only in a narrow region of x from 0.98 to 1.03. The single crystals with x being 0.98 and 0.99 showed the CSL behavior with the highest Tc of 133 K. These results indicate that the small number of defects on the sites for T ions dramatically affects the quality of the single crystals in the synthesis of TM3S6. We also discuss the importance of synthesizing enantiopure single crystals of chiral dichalcogenides in order to observe chiral physical properties unique to chiral compounds such as magneto-chiral effect and chiral-induced spin selectivity.

Dynamics of Dzyaloshinskii domain walls for ferrimagnets with compensation of angular momentum

Dzyaloshinskii domain walls in chiral ferrimagnets, with a violation of spatial inversion symmetry due to Dzyaloshinskii–Moriya interaction, are studied theoretically. The dynamics of domain walls with non-small velocity is investigated by means of qualitative and numerical analysis of the sigma-model equation, generalized for accounting for chiral interactions and not complete compensation of sublattice angular momenta. Domain wall critical velocity, the maximal velocity that the domain wall can move, its energy and linear momentum are determined. Domain wall dispersion relation, the dependence of the energy on the linear momentum, is constructed. Forced motion of domain walls with accounting for weak dissipation processes is investigated by means of collective variable approach. We found quite a complicated picture of the dynamics of domain walls in chiral ferrimagnet that can be of interest for general theory of magnetic solitons and useful for applications. In addition to the increasing of the critical velocity of the domain wall when approaching angular momentum compensation point, which is the well-known sequence of the exchange enhancement effect, even the qualitative picture of domain wall states is changing. The main difference is that a few different types of domain walls appear, forming a sequence of states with a characteristic complication of the wall structure (formation of cluster domain walls) together with an increase in their energy. Both factors, the exchange enhancement of the limiting domain wall velocity and the destruction of integrability, turn out to be important here. In particular, the critical velocities of cluster domain walls, as well as the maximal values of their linear momenta, appear to be higher (sometimes, a few times higher) than for standard domain walls. This effect is absent for domain walls, known for non-integrable models of ferromagnets. The presence of cluster domain walls can be of interest for the problem, how to increase the maximal velocity of motion for domain walls.

Creating arbitrary sequences of mobile magnetic skyrmions and antiskyrmions

Magnetic skyrmions and their antiparticles, the antiskyrmions, are stable magnetic solitons existing down to the nanometer scale. Their stability and size as well as the possibility to propel them by, e.g., electric currents make them promising candidates for use in memory devices, such as racetrack memories. Skyrmions and antiskyrmions share those same advantages individually, but may annihilate each other when they coexist in the same device. Yet, combining them to represent logical bits of 0 (skyrmion) and 1 (antiskyrmion) in one device opens new possibilities to create new types of densely packed racetrack memory devices. For this, a controlled creation and annihilation procedure, i.e., a writing or deletion operation, is necessary. Here, we propose a method to create arbitrary sequences of coexisting skyrmions and antiskyrmions by rotations of the magnetic moments at the edge of a rectangular slab. The skyrmions and antiskyrmions remain stable and do not annihilate each other.

Homotopy transitions and 3D magnetic solitons

This work provides a concept for three-dimensional magnetic solitons based on mapping the homotopy path between various two-dimensional solutions onto the third spatial axis. The representative examples of statically stable configurations of that type in the model of an isotropic chiral magnet are provided. Various static and dynamic properties of such three-dimensional magnetic solitons are discussed in detail.

Skyrmion–antiskyrmion pair creation and annihilation in a cubic chiral magnet

A fundamental property of particles and antiparticles (such as electrons and positrons, respectively) is their ability to annihilate one another. A similar behaviour is predicted for magnetic solitons1—localized spin textures that can be distinguished by their topological index Q. Theoretically, magnetic topological solitons with opposite values of Q, such as skyrmions2 and their antiparticles (namely, antiskyrmions), are expected to be able to continuously merge and annihilate3. However, experimental verification of such particle–antiparticle pair production and annihilation processes has been lacking. Here we report the creation and annihilation of skyrmion–antiskyrmion pairs in an exceptionally thin film of the cubic chiral magnet of B20-type FeGe observed using transmission electron microscopy. Our observations are highly reproducible and are fully consistent with micromagnetic simulations. Our findings provide a new platform for the fundamental studies of particles and antiparticles based on magnetic solids and open new perspectives for practical applications of thin films of isotropic chiral magnets.

Magnetic soliton confinement and discretization effects in Cr1/3TaS2 nanoflakes

Magnetic soliton confinement and discretization effects in Cr1/3TaS2 nanoflakes

Inertial domain wall characterization in layered multisublattice antiferromagnets

The motion of a Néel-like 180∘ domain wall induced by a time-dependent staggered spin–orbit field in the layered collinear antiferromagnet Mn2Au is explored. Through an effective version of the two sublattice nonlinear σ-model which does not take into account the antiferromagnetic exchange interaction directed along the tetragonal c-axis, it is possible to replicate accurately the relativistic and inertial traces intrinsic to the magnetic texture dynamics obtained through atomistic spin dynamics simulations for quasistatic processes. In the case in which the steady-state magnetic soliton motion is extinguished due to the abrupt shutdown of the external stimulus, its stored relativistic exchange energy is transformed into a complex translational mobility, being the rigid domain wall profile approximation no longer suitable. Although it is not feasible to carry out a detailed follow-up of its temporal evolution in this case, it is possible to predict the inertial-based distance travelled by the domain wall in relation to its steady-state relativistic mass. This exhaustive dynamical characterization for different time-dependent regimes of the driving force is of potential interest in antiferromagnetic domain wall-based device applications.

Wiener Process Effects on the Solutions of the Fractional (2 + 1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation

The stochastic fractional (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation (SFHFSCE), which is driven in the Stratonovich sense by a multiplicative Wiener process, is considered here. The analytical solutions of the SFHFSCE are attained by utilizing the Jacobi elliptic function method. Various kinds of analytical fractional stochastic solutions, for instance, the elliptic functions, are obtained. Physicists can utilize these solutions to understand a variety of important physical phenomena because magnetic solitons have been categorized as one of the interesting groups of non-linear excitations representing spin dynamics in semi-classical continuum Heisenberg systems. To study the impact of the Wiener process on these solutions, the 3D and 2D surfaces of some achieved exact fractional stochastic solutions are plotted.

Thermal generation of droplet soliton in chiral magnet

Controlled creation of localized magnetic textures beyond conventional $\ensuremath{\pi}$-skyrmions is an important problem in the field of magnetism. Here, by means of spin dynamics simulations, Monte Carlo simulations, and harmonic transition state theory we demonstrate that an elementary chiral magnetic soliton with zero topological charge---the chiral droplet---can be created by thermal fluctuations in the presence of the tilted magnetic field. The proposed protocol relies on an unusual kinetics combining the effects of the entropic stabilization and low-energy barrier for the nucleation of a topologically trivial state. Following this protocol by varying temperature and the tilt of the external magnetic field, one can selectively generate chiral droplets or $\ensuremath{\pi}$-skyrmions in a single system. The coexistence of two distinct magnetic solitons establishes a basis for a rich magnetization dynamics and opens up the possibility for the construction of more complex magnetic textures such as skyrmion bags and skyrmions with chiral kinks.

Critical behavior and phase diagram of layered ferromagnetic FeTa3S6 single crystals

The magnetization of the highly air-stable two-dimensional (2D) intrinsic ferromagnet ${\mathrm{FeTa}}_{3}{\mathrm{S}}_{6}$ single crystal has been systematically investigated. Magnetization measurement revealed paramagnetic to ferromagnetic (PM-FM) phase transition at around 35 K and a strong magnetic anisotropy along the crystallographic c axis ($H\ensuremath{\parallel}c$). The critical exponents $\ensuremath{\beta}$ = 0.189(2), $\ensuremath{\gamma}$ = 1.423(1), and $\ensuremath{\delta}=8.531(7)$ with ${T}_{c}$ = 35 K suggest that the spin interaction of a two-dimensional (2D) Ising type in ${\mathrm{FeTa}}_{3}{\mathrm{S}}_{6}$ coupled with long-range ($\ensuremath{\sigma}=1.581$) interaction. A comprehensive magnetic phase diagram based on detailed magnetization measurements and universality scaling of ${\mathrm{FeTa}}_{3}{\mathrm{S}}_{6}$ is constructed over three magnetic field regions. The magnetic phase diagram of ${\mathrm{FeTa}}_{3}{\mathrm{S}}_{6}$ is analogous to that of ${\mathrm{CrNb}}_{3}{\mathrm{S}}_{6}$, which exhibits a chiral magnetic soliton lattice. DFT simulation reveals that the large magnetic anisotropy energy in ${\mathrm{FeTa}}_{3}{\mathrm{S}}_{6}$ originates from the combined effects such as considerable orbital magnetic moment, host lattice spin-orbit coupling, and hybridization between host lattice $2\mathrm{H}\ensuremath{-}{\mathrm{TaS}}_{2}$ and the intercalated Fe component. Furthermore, the magnetic anisotropy ($\ensuremath{\parallel}$ c) in ${\mathrm{FeTa}}_{3}{\mathrm{S}}_{6}$ is due to the dominant contribution of the spin conserving process $\mathrm{\ensuremath{\Delta}}{S}_{z}$ = 0 in magnetic anisotropy energy, which differs from that of ${\mathrm{CrNb}}_{3}{\mathrm{S}}_{6}$, or ${\mathrm{MnNb}}_{3}{\mathrm{S}}_{6}$, where the spin flipping process $\mathrm{\ensuremath{\Delta}}{S}_{z}$ = 1 dominates, causing in-plane ($\ensuremath{\perp}$ c) magnetic anisotropy.

Angular-dependent magnetoresistance in Cr1/3NbS2 single crystals

We present a comprehensive study of angular-dependent magnetoresistance (MR) in the layered chiral helimagnet Cr1/3NbS2 (CNS), which realizes a magnetic soliton lattice. It was found that, at temperatures below Curie temperature, CNS showed a negative magnetoresistance related to the emergence of a chiral soliton lattice state when a magnetic field was applied parallel to the ab-plane (H ‖ ab-plane). When the magnetic field was applied parallel to the c-axis (H ‖ c-axis), however, the negative MR disappeared and a positive MR appeared around zero field at low temperatures. Detailed analysis and modeling indicate that the positive MR is due to the weak anti-localization effect arising from the strong spin–orbit coupling of CNS.

Electron-spin interaction in the spin-Peierls phase of the organic spin chain ( o -DMTTF) 2X ( X =Cl, Br, I)

We investigate the electron spin resonance of the organic spin-Peierls chain ($o$-DMTTF)${}_{2}X$ with $X$ = Cl, Br, and I. We describe the temperature dependence of the spin gap during the phase transition and quantify the dimerization parameter $\ensuremath{\delta}$. At the lowest temperatures, the susceptibility is governed by defects in the spin dimerized chain. Such strongly correlated defects are the consequence of breaks in the translational symmetry of the chain. In the vicinity of the defects the spins are polarized antiferomagnetically forming a magnetic soliton: a spin $\frac{1}{2}$ quasiparticle of size ruled by $\ensuremath{\delta}$ pinned to the defects. For ($o$-DMTTF)${}_{2}\mathrm{Br}$ and ($o$-DMTTF)${}_{2}\mathrm{Cl}$, we show that the one-half of the total number of solitons are in isolation (as singles) whereas the other half form pairs (soliton dimers) with a strong magnetic coupling. The Rabi oscillations of both the single soliton and the soliton dimer are observed, which is a prerequisite in the context of quantum information.

Giant topological and planar Hall effect in Cr1/3NbS2

Cr$_{1/3}$NbS$_{2}$ is a transition metal dichalcogenide that has been of significant interest due to its ability to host a magnetic chiral soliton lattice. Conventional and planar Hall measurements provide valuable insight into the detection of exotic spin structures in chiral magnets. We show that the presence of a giant planar Hall effect can be attributed to a tilted soliton lattice in Cr$_{1/3}$NbS$_{2}$. Our detailed angular dependent study shows the planar Hall effect and anisotropic magnetoresistance are intrinsically linked in complex non-coplanar magnets. From the conventional Hall signal we show the presence of a giant unconventional, likely topological Hall component, that is the fingerprint of non-coplanar spin textures.

Magnetic solitons in an antiferromagnetic waveguide

The properties of transverse magnetic (TM) waves propagating along a single interface between two semi-infinite nonlinear antiferromagnetic materials are investigated. The surface waves exist in the form of bright magnetic solitons. The frequency characteristics for the passband and stopband are analytically studied. We discuss the possibility of controlling the bandwidth of the passband which is determined by the parameters of the materials composing the guiding structure. We expect that the theoretical findings could provide ideas for exploring potential applications in terahertz region.

Magnetic solitons in an immiscible two-component Bose-Einstein condensate

We investigate magnetic solitons in an immiscible binary Bose-Einstein condensate (BEC), where the intraspecies interactions are slightly weaker than the interspecies interactions. While their density and phase profiles are analogous to dark-bright solitons, other characteristic properties such as maximum velocities, widths, total density depletions, and in-trap oscillations are different. In the low-velocity regime, a magnetic soliton reduces to a traveling pair of magnetic domain walls. Collisional behaviors of the solitons are also briefly discussed. We further demonstrate that these solitonic states can be realized in a quasi-one-dimensional spin-1 ferromagnetic BEC with a weak spin interaction, e.g., a $^{87}\mathrm{Rb}$ BEC.

Magnetic lump motion in saturated ferromagnetic films.

In this paper, we study in detail the nonlinear propagation of a magnetic soliton in a ferromagnetic film. The sample is magnetized to saturation by an external field perpendicular to film plane. A generalized (2+1)-dimensional short-wave asymptotic model is derived. The bilinearlike forms of this equation are constructed and exact magnetic line soliton solutions are exhibited. It is observed that a series of stable lumps can be generated by an unstable magnetic soliton under Gaussian disturbance. Such magnetic lumps are highly stable and can maintain their shapes and velocities during evolution or collision. The interaction between lump and magnetic solitons, as well as the interaction between two lumps, are numerically investigated. We further discuss the nonlinear motion of lumps in ferrites with Gilbert damping and inhomogeneous exchange effects. The results show that the Gilbert-damping effects make the amplitude and velocity of the magnetic lump decay exponentially during propagation. And the shock waves are generated from a lump when quenching the strength of inhomogeneous exchange.