Chiral Soliton Research Articles

Formation, propagation, and excitation of matter solitons and rogue waves in chiral BECs with a current nonlinearity trapped in external potentials.

In this paper, we investigate formation and propagation of matter solitons and rogue waves (RWs) in chiral Bose-Einstein condensates modulated by different external potentials, modeled by the chiral Gross-Pitaevskii (GP) equation with the current nonlinearity and external potentials. On the one hand, the introduction of two potentials (Pöschl-Teller and harmonic-Gaussian potentials) enables the discovery of exact soliton solutions in both focusing and defocusing cases. We analyze the interplay effects of current nonlinearity and potential on soliton stability via associated Bogoliubov-de Gennes equations. Moreover, multiple families of numerical solitons (ground-state and dipole modes) trapped in potentials are found, exhibiting distinctive structures. The interactions between solitons trapped in potentials are studied, which exhibit the inelastic trajectories and repulsive interactions. On the other hand, we introduce the time-dependent potentials such that the controlled RWs are found in both focusing and defocusing GP equations with current nonlinearity. Furthermore, through the interaction between potentials and current nonlinearity, it is possible to enlarge the region of modulational instability, leading to the generation of RWs and chiral solitons. High-order RWs are generated from several Gaussian perturbations on a continuous wave. The presence of current nonlinearity disrupts the structures of these high-order RWs, causing them to undergo a transform into chiral lower-amplitude solitons. Finally, various types of soliton excitations are investigated by varying the strengths of potential and current nonlinearity, showing the abundant dynamic transforms of chrital matter solitons.

Presence of a chiral soliton lattice in the chiral helimagnet MnTa3S6

Chiral helimagnetism was investigated in transition-metal intercalated dichalcogenide single crystals of MnTa3S6. Small-angle neutron scattering (SANS) experiments revealed the presence of harmonic chiral helimagnetic order, which was successfully detected as a pair of satellite peaks in the SANS pattern. The magnetization data are also supportive of the presence of chiral soliton lattice (CSL) phase in MnTa3S6. The observed features are summarized in the phase diagram of MnTa3S6, which is in strong contrast with that observed in other dichalcogenides such as CrNb3S6 and CrTa3S6. The presence of the remanent state provides tunable capability of the number of chiral solitons at zero magnetic field in the CSL system, which may be useful for memory device applications.

Revealing inverted chirality of hidden domain wall states in multiband systems without topological transition

Chirality, a fundamental concept from biological molecules to advanced materials, is prevalent in nature. Yet, its intricate behavior in specific topological systems remains poorly understood. Here, we investigate the emergence of hidden chiral domain wall states using a double-chain Su-Schrieffer-Heeger model with interchain coupling specifically designed to break chiral symmetry. Our phase diagram reveals single-gap and double-gap phases based on electronic structure, where transitions occur without topological phase changes. In the single-gap phase, we reproduce chiral domain wall states, akin to chiral solitons in the double-chain model, where chirality is encoded in the spectrum and topological charge pumping. In the double-gap phase, we identify hidden chiral domain wall states exhibiting opposite chirality to the domain wall states in the single-gap phase, where the opposite chirality is confirmed through spectrum inversion and charge pumping as the corresponding domain wall slowly moves. By engineering gap structures, we demonstrate control over hidden chiral domain states. Our findings open avenues to investigate novel topological systems with broken chiral symmetry and potential applications in diverse systems.

Surface barrier effect as evidence of chiral soliton lattice formation in chiral dichalcogenide CrTa3S6 crystals

The formation of chiral magnetic soliton lattice (CSL) is investigated in monoaxial chiral dichalcogenide CrTa3S6 crystals in terms of a surface barrier, which prevents the penetration of chiral solitons into the system and is an intrinsic origin of hysteresis for the continuous phase transition of nucleation-type, as discussed in the system of quantized vortices in type-II superconductors. The magnetoresistance (MR) was examined with microfabricated platelet samples in different dimensions with regard to the c-axis direction of the crystal. The CSL formation was confirmed by the discrete MR changes, reflecting the number of chiral solitons, as well as by the presence of a surface barrier, recognized as a fixed ratio of critical magnetic fields during the hysteresis field cycle. We also argue the influence of the surface barrier in bulk CrTa3S6 crystals.

Generalized Dzyaloshinskii–Moriya Interaction and Chirality-Induced Phenomena in Chiral Crystals

This paper is a review of recent advances in studies of the magnetic, electronic, spintronic, and phononic properties of chiral crystals, with a focus on the connection between the Dzyaloshinskii–Moriya interaction (DMI) and chirality in materials. Importantly, a microscopic DMI is elevated to a macroscopic Lifshitz invariant (LI) in chiral crystals, where mirror reflection and inversion symmetry are globally broken. As a consequence, chiral crystals exhibit nontrivial physical responses over a macroscopic scale. Indeed, in chiral magnetism, a chiral spin soliton lattice (CSL) appears in monoaxial chiral magnetic crystals and exhibits various nontrivial physical properties characterized by the coherent and topological nature of the CSL. This CSL isone of the prominent outcomes arising from the DMI and LI, as envisioned by Dzyaloshinskii in the 1960s. Furthermore, a giant spin polarization emerges over a macroscopic scale in a wide range of chiral materials from organic molecules to inorganic crystals. The first-order spatial dispersion, such as the LI, also appears in elastic or phonon degrees of freedom in chiral crystals. These examples show how a time-even pseudoscalar term, which corresponds to a generalized concept of the DMI and LI, is realized in chiral media.

Stability and asymptotic interactions of chiral magnetic skyrmions in a tilted magnetic field

Using a general framework, interaction potentials between chiral magnetic solitons in a planar system with a tilted external magnetic field are calculated analytically in the limit of large separation. The results are compared to previous numerical results for solitons with topological charge \pm 1±1. A key feature of the calculation is the interpretation of Dzyaloshinskii-Moriya interaction (DMI) as a background SO(3)SO(3) gauge field. In a tilted field, this leads to a U(1)U(1)-gauged version of the usual equation for spin excitations, leading to a distinctive oscillating interaction profile. We also obtain predictions for skyrmion stability in a tilted field which closely match numerical observations.

Chirality reversal of magnetic solitons in chiral Cr1/3TaS2

Ferromagnetism in two-dimensional (2D) materials provides an ideal platform to study emergent electromagnetic phenomena in low dimensions for future spintronics. In magnetic-element intercalated transition metal dichalcogenides, topologically nontrivial spin textures, such as chiral helimagnetic spin states and chiral soliton lattices, are realized due to the chiral lattice distortions induced by intercalated magnetic ions. Consequently, the magnetic chirality is predictably determined by the sign of antisymmetric exchange interaction (or Dzyaloshinskii–Moriya interaction, DMI) vector that is coupled to the underlying crystal chirality. Here, using cryogenic Lorentz phase microscopy, we directly observed the chirality reversal behavior of the chiral soliton lattices in Cr1/3TaS2 across the structural defects. We show that a partial 1 T stacking in 2H-TaS2 locally reduces DMI, leading to magnetic chirality reversal with direct atomic resolution imaging. Our experimental results show that manipulation of stacking sequence provides a viable way to control the chirality of topologically nontrivial soliton lattices in 2D magnets.

The Progress on Magnetic Material Thin Films Prepared Using Polymer-Assisted Deposition.

Polymer-assisted deposition (PAD) has been widely used in the preparation of high-quality oxides and sulfides for basic research and applications. Specifically, diverse PAD-prepared magnetic material thin films such as ZnO, Ga2O3, SrRuO3, LaCoO3, LaMnO3, Y3Fe5O12, MoS2, MoSe2, and ReS2 thin films have been grown, in which thickness-dependent, strain-modulated, doping-mediated, and/or morphology-dependent room-temperature ferromagnetism (RTFM) have been explored. Inspired by the discovery of intrinsic low-temperature FM in two-dimensional (2D) systems prepared using mechanical exfoliation, the search for more convenient methods to prepare 2D ferromagnetic materials with high-temperature FM has seen explosive growth, but with little success. Fortunately, the very recent synthesis of 2D NiO by PAD has shed light on this challenge. Based on these abovementioned developments, the difficulties of PAD when preparing a-few-nanometer single-crystalline materials and the opportunities in PAD for novel materials such as chiral magnetic soliton material Cr1/3NbS2 are discussed.

Quasicrystals in QCD

We study the ground state of the low energy dense QCD with the assumption of chiral condensates of quarks. Under an external magnetic field, mesons could form soliton lattices via the chiral anomaly. For such scenarios, we present a unified description of pions and η meson with a U(2) field in the framework of the chiral perturbation theory. Our result shows the ground state is a mixture of the magnetized domain walls formed by neutral pion π0 and η meson when they coexist. The winding number of the ground state would alter according to the strength of the magnetic field. When the magnetic field is strong or the chemical potential is large, the proportion of the mixture is determined by the decay constants and the contributions to the anomalous action of π0 and η meson. The resulting configuration is either a mixed soliton lattice or a quasicrystal which could be dubbed a “chiral soliton quasicrystal”.

Observation of the Chiral Soliton Lattice above Room Temperature

AbstractMagnetic chiral soliton lattices (CSLs) emerge from the helical phase in chiral magnets when magnetic fields are applied perpendicular to the helical propagation vector, and they show great promise for next‐generation magnetic memory applications. These one‐dimensional structures are previously observed at low temperatures in samples with uniaxial symmetry. Here, it is found that in‐plane fields are the key to stabilizing the CSL in cubic Co8Zn10Mn2 over the entire temperature range from 15 K to below the Curie temperature (365 K). Using small‐angle resonant elastic X‐ray scattering, it is observed that the CSL is stabilized with an arbitrary in‐plane propagation vector, while its thin plate geometry plays a deciding role in the soliton wavelength as a function of applied field. This work paves the way for high temperature, real world applications of soliton physics in future magnetic memory devices.

Crossover of critical behavior and nontrivial magnetism in the chiral soliton lattice host Cr1/3TaS2

The chiral magnetic soliton, a topological kinklike spin texture, has significant applications in spintronic components. In this work, a crossover of critical behavior is found in ${\mathrm{Cr}}_{1/3}{\mathrm{TaS}}_{2}$, a chiral magnetic soliton host with the highest ${T}_{C}$ to date. Angular-dependent magnetization reveals that ${\mathrm{Cr}}_{1/3}{\mathrm{TaS}}_{2}$ exhibits an easy orientation within the isotropic $ab$ plane, but displays anisotropy with the $c$ axis. By using a modified iterative method, two distinct sets of critical exponents, including ${\ensuremath{\beta}}_{\ensuremath{-}}=0.3190(1)$ and ${\ensuremath{\gamma}}_{\ensuremath{-}}=1.263(8)$ for $T\ensuremath{\le}{T}_{C}$, and ${\ensuremath{\beta}}_{+}=0.3475(2)$ and ${\ensuremath{\gamma}}_{+}=1.385(5)$ for $T\ensuremath{\ge}{T}_{C}$, are acquired on both sides of the transition. Analysis of the exponents indicates a crossover of the magnetic interaction from a three-dimensional Ising type below ${T}_{C}$ to a three-dimensional Heisenberg type above ${T}_{C}$, implying nontrivial magnetism in this system. Based on universality scaling, a detailed $H\ensuremath{-}T$ phase diagram around ${T}_{C}$ is constructed for $H\ensuremath{\perp}c$. The crossover of the critical behavior in ${\mathrm{Cr}}_{1/3}{\mathrm{TaS}}_{2}$ is peculiar to chiral magnetic soliton hosts, suggesting that the three-dimensional magnetic coupling is replaced by a one-dimensional one in the chiral magnetic soliton phase via a phase transition.

Crystal field excitation in the chiral helimagnet YbNi3Al9

A crystal field level scheme of a uniaxial chiral helimagnet $\mathrm{Yb}{\mathrm{Ni}}_{3}{\mathrm{Al}}_{9}$, exhibiting a chiral magnetic soliton lattice state by Cu substitution for Ni, has been determined by inelastic neutron scattering. The ground and the first excited doublets are separated by 44 K and are simply expressed as $\ensuremath{\alpha}|\ifmmode\pm\else\textpm\fi{}7/2\ensuremath{\rangle}+\ensuremath{\beta}|\ensuremath{\mp}5/2\ensuremath{\rangle}$, with $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ nearly equal to $\ifmmode\pm\else\textpm\fi{}1/\sqrt{2}$. The easy axis of the crystal field anisotropy is the $c$ axis when the excited levels are populated at high temperatures and high magnetic fields. On the other hand, the magnetism at low temperatures and low magnetic fields, where only the ground doublet is populated, is described by an easy-plane anisotropy which may be treated as an $S=1/2$ system with an anisotropic $g$ factor, ${g}_{xy}=3.02$ and ${g}_{z}=1.14$. An orbital-dependent exchange interaction is also discussed to explain the temperature dependence of the magnetic susceptibility based on this level scheme.

Islands of chiral solitons in integer-spin Kitaev chains

An intriguing chiral soliton phase has recently been identified in the $S=\frac{1}{2}$ Kitaev spin chain. Here we show that for $S$ = 1, 2, 3, 4, 5 an analogous phase can be identified, but contrary to the $S=\frac{1}{2}$ case the chiral soliton phases appear as islands within the sea of the polarized phase. In fact, a small field applied in a general direction will adiabatically connect the integer spin Kitaev chain to the polarized phase. Only at sizable intermediate fields along symmetry directions does the soliton phase appear centered around the special point ${h}_{x}^{★}={h}_{y}^{★}=S$ where two exact product ground states can be identified. The large-$S$ limit can be understood from a semiclassical analysis, and variational calculations provide a detailed picture of the $S=1$ soliton phase. Under open boundary conditions, the chain has a single soliton in the ground state, which can be excited, leading to a proliferation of in-gap states. In contrast, even length periodic chains exhibit a gap above a twice-degenerate ground state. The presence of solitons leaves a distinct imprint on the low-temperature specific heat.

Transformation from Magnetic Soliton to Skyrmion in a Monoaxial Chiral Magnet.

Topological spin textures are of great interest for both fundamental physics and applications in spintronics. The Dzyaloshinskii-Moriya interaction underpins the formation of single-twisted magnetic solitons or multi-twisted magnetic skyrmions in magnetic materials with different crystallographic symmetries. However, topological transitions between these two kinds of topological objects have not been verified experimentally. Here, the direct observation of transformations from a chiral soliton lattice (CSL) to magnetic skyrmions in a nanostripe of the monoaxial chiral magnet CrNb3 S6 using Lorentz transmission electron microscopy is reported. In the presence of an external magnetic field, helical spin structures first transform into CSLs and then evolve into isolated elongated magnetic skyrmions. The detailed spin textures of the elongated magnetic skyrmions are resolved using off-axis electron holography and are shown to comprise two merons, which enclose their ends and have unit total topological charge. Magnetic dipolar interactions are shown to play a key role in the magnetic soliton-skyrmion transformation, which depends sensitively on nanostripe width. The findings here, which are consistent with micromagnetic simulations, enrich the family of topological magnetic states and their transitions and promise to further stimulate the exploration of their emergent electromagnetic properties.

Magnetic phase diagram of Cr1/3NbS2: SANS study

The magnetic structure of the Cr1/3NbS2 compound was studied with help of small-angle neutron scattering under an applied magnetic field in a wide temperature range below TN ​= ​130 К. At zero magnetic field the magnetic moments of Cr3+ ions build the helix structure with the wave vector k oriented along the c-axis of the chiral structure of P6322 space group. The detected diffraction ring is interpreted as scattering on the magnetic helices of randomly oriented crystallites within powder sample. The intensity of the diffraction peak decreases with temperature and dissolves at T ​= ​115 К. The magnetic field differently affects the crystallites with helix wave vector k along the field and those with k perpendicular to the field. The magnetic field, when applied, leads to appearance of the chiral soliton lattice in the grains with k oriented perpendicularly to the field. The period of the chiral soliton lattice increases rapidly as H approaches HC1 ​= ​0.25 ​T. The transition from chiral soliton lattice to the field-induced ferromagnet, however, is not homogeneous but is accompanied by strong ferromagnetic fluctuations in the wide field range around HC1. These fluctuations are well visible in the experiment as scattering centered at Q ​= ​0. In the grains with k parallel to the field, the chiral soliton lattice undergoes a series of transitions from helimagnet to the conical state, and then to the field-induced ferromagnet at HC2 ​= ​1.25 ​T. The period of the conical helix increases slightly (for 5%) with the field, while the transition to the field–induced ferromagnetic state is again accompanied by strong ferromagnetic fluctuations. The magnetic field–temperature phase diagrams for H perpendicular to the c-axis and for H parallel to the c-axis are plotted on the basis of the data obtained.

Interaction of chiral solitons in a Bose-Einstein Condensate under density-dependent gauge potential

The collision between two chiral solitons in a Bose-Einstein Condensate (BEC) under density-dependent gauge potential is studied. By means of Poincaré-Lighthill-Kuo (PLK) perturbation method, the different kinds of colliding chiral soliton pairs self-consistently excited upon the background of the system are obtained analytically. The coupling of the current nonlinearity induced by the gauge potential and mean-field atomic interaction results in rich collision dynamics of chiral soliton pairs. When the atomic interaction is repulsive, head-on collisions of dark-dark and dark-bright solitons are observed. However, when the atomic interaction is attractive, unidirectional chiral dark soliton pairs are excited, and overtaking collision between two chiral dark solitons takes place. The phase shifts following the collision of soliton pairs are derived analytically and confirmed numerically. Interestingly, due to the contribution of the density-dependent gauge potential, the phase shifts of the two interacting chiral solitons are different from each other. This is distinct from the case without the density-dependent gauge potential, where the phase shifts of the two colliding ordinary solitons are the same. Thus, phase shifts of interacting chiral soliton pairs can be used to identify the chiral properties of solitons in BEC under density-dependent gauge potential. Furthermore, both elastic and inelastic collisions of chiral solitons in the system are presented numerically. The phase diagram for occurrence of elastic and inelastic collisions of chiral soliton is obtained, which strongly depends on the strength of density-dependent gauge potential.

On the investigation of chiral solitons via modified new Kudryashov method

Purpose: This study includes the examination of the cases where the [Formula: see text]-dimensional chiral nonlinear Schrödinger equation also has Bohm potential. This review is not to obtain different soliton solutions for both cases but to obtain a certain type of soliton and to observe the effect of the problem parameters. By using the modified new Kudryashovs scheme. This observation also includes how the soliton behavior is effective by comparing the [Formula: see text]-dimensional chiral nonlinear Schrödinger equation (C-NLSE) and [Formula: see text]-dimensional chiral nonlinear Schrödinger equation with Bohm potential (C-NLSE-BP), especially by examining the Bohm potential parameter. Methodology: In order to apply the proposed analytical method which is the modified Kudryasovs scheme (m-NKM), as in many studies, the nonlinear partial ordinary differential equation (NLPDE) is first converted into nonlinear ordinary differential equation form (NLODE) by using wave transform. Then, in order to determine which degree the solution function to be proposed will be, the balancing constant is calculated. The next step is to determine the unknown parameters of the problem by applying the m-NKM on NODE, obtaining solution sets, and combine the solution of the Riccati equation, which is the basis of the method, with the proposed solution function and wave transform. Obtaining the optical solution by providing the main NLPDE is the next step that follows this stage. The final stage is the graphical analysis and interpretation of the parameter effect for both problems using the obtained solution function. Findings: The examination of the case with and without Bohm potential was carried out on the behavior of the bright soliton shape, which is one of the basic soliton shapes that many effects can be clearly studied on it. It was successfully shown that both equation parameters and the Bohm potential had a significant effect on the soliton behavior, graphical presentations were made and interpreted in detail. Originality: Such an examination has not been studied before in the literature for the investigated equations.

Field-induced chiral soliton phase in the Kitaev spin chain

A chiral phase of topological solitons is identified at finite intermediate fields in the Kitaev spin chain. The excitation spectrum in the soliton phase is strongly dependent on the boundary conditions.

Soliton locking phenomenon in bulk single crystal of monoaxial chiral magnet MnNb3S6

MnNb3S6 is a monoaxial chiral magnet and stabilizes magnetic solitons in the presence of a magnetic field (H). The number of solitons can be controlled by varying H. Furthermore, MnNb3S6 exhibits magnetization relaxation due to soliton annihilation, that is, a nonequilibrium chiral soliton lattice (CSL) state. In this study, we observed soliton locking phenomena in a CSL state on bulk MnNb3S6 crystal, as on micro-processed crystals of CrNb3S6. Thus, we could create nonequilibrium and equilibrium CSL states and switch between them. A numerical simulation revealed that the soliton number was preserved in the soliton locking region; thus, magnetization relaxation was not observed.

Magnetic ground state dependent magnetostriction effects on the chiral magnet CrNb3S6

A prototype of the monoaxial chiral magnet ${\mathrm{CrNb}}_{3}{\mathrm{S}}_{6}$ exhibited two magnetostriction (MS) effects: (1) spontaneous MS due to the exchange interaction and spin-orbit coupling (SOC) at zero dc magnetic field ($H$) [Phys. Rev. B 102, 014446 (2020)] and (2) paramagnetic MS due to SOC and Zeeman energy at room temperature [Phys. Rev. B 105, 104412 (2022)]. ${\mathrm{CrNb}}_{3}{\mathrm{S}}_{6}$ has various magnetic structures, such as helimagnetic, first chiral soliton lattice (CSL-1), second CSL (CSL-2), CSL-2 with irreversibility, and forced ferromagnetic phases, resulting from the Dzyaloshinskii--Moriya interaction as a function of $H$ below the magnetic ordering temperature (${T}_{\mathrm{c}}$). In this study, we conducted powder x-ray diffraction analyses to investigate the effects of $H$ and temperature ($T$) on the MS at the atomic level. The $T$ dependence of the lattice constants reveals that below ${T}_{\mathrm{c}}$, the MS depends on the magnetic structure. The MS below ${T}_{\mathrm{c}}$ is discussed in this study in terms of both the hybridization between the ${z}^{2}$ orbital of $\mathrm{Nb}(4f)$ and delocalized ${a}_{1}$ orbital of Cr and the structural symmetry of the ${\mathrm{CrS}}_{6}$ octahedron.