Search Results (29)

We numerically investigate the effect of multi-spin interactions on the stability of skyrmion crystals and other multiple-Q magnetic states, with a particular emphasis on the momentum-resolved bicubic interaction. By performing simulated annealing for an effective spin model that incorporates bilinear, biquadratic, and bicubic interactions on a two-dimensional triangular lattice, we construct the corresponding low-temperature phase diagram. Our results reveal that a positive bicubic interaction stabilizes a skyrmion crystal with a skyrmion number of two, whereas a negative bicubic interaction favors a single-Q spiral state. Moreover, we demonstrate that the stability region of the field-induced skyrmion crystal with the skyrmion number of one is largely enlarged in the presence of a positive bicubic interaction. Full article

We investigate the role of high-harmonic wave-vector interactions, which affect the stability of the single-Q spiral state and often result in the formation of multiple-Q states. By performing simulated annealing for an effective spin model on a two-dimensional square lattice, we examine the modulation of the single-Q spiral spin configuration by the high-harmonic wave-vector interaction. As a result, we find that the interactions at particular high-harmonic wave vectors affect the stability of the single-Q spiral state. In particular, the incorporation of interactions at high-harmonic wave vectors formed by the sum of two mutually perpendicular ordering wave vectors can lead to the emergence of three double-Q states and a square skyrmion crystal. The present study unveils the importance of high-harmonic wave-vector interactions in order to realize complicated noncoplanar spin textures. Full article

We study the topological defects and spin structures of rotating SU(3) spin–orbit-coupled spin F$=1$ Bose–Einstein condensates (BECs) in an in-plane quadrupole field with ferromagnetic spin interaction, and the BECs is confined by a harmonic trap. Without rotation, as the quadrupole field strength is increased, the spin F$=1$ BECs with SU(3) spin–orbit coupling (SOC) evolves from the initial Thomas–Fermi phase into the stripe phase; then, it enters a vortex–antivortex cluster state and eventually a polar-core vortex state. In the absence of rotation with the given quadrupole field, the enhancing SU(3) SOC strength can cause a phase transition from a central Mermin–Ho vortex to a vortex–antivortex cluster, subsequently converting to a bending vortex–antivortex chain. In addition, when considering rotation, it is found that this system generates the following five typical quantum phases: a three-vortex-chain cluster structure with mutual angles of approximately ${\displaystyle \frac{2\pi }{3}}$, a tree-fork-like vortex chain cluster, a rotationally symmetric vortex necklace, a diagonal vortex chain cluster, and a density hole vortex cluster. Particularly, the system exhibits unusual topological structures and spin textures, such as a bending half-skyrmion–half-antiskyrmion (meron–antimeron) chain, three half-skyrmion (meron) chains with mutual angles of an approximately ${\displaystyle \frac{2\pi }{3}}$, slightly curved diagonal half-skyrmion (meron) cluster lattice, a skyrmion–half-skyrmion (skyrmion-meron) necklace, and a tree-fork-like half-skyrmion (meron) chain cluster lattice. Full article

We conduct a numerical investigation into the stability of a quadruple-Q skyrmion crystal, a structure generated by the superposition of four spin density waves traveling in distinct directions within three-dimensional space, hosted on a centrosymmetric body-centered tetragonal lattice. Using simulated annealing applied to an effective spin model that includes momentum-resolved bilinear and biquadratic interactions, we construct a magnetic phase diagram spanning a broad range of model parameters. Our study finds that a quadruple-Q skyrmion crystal does not emerge within the phase diagram when varying the biquadratic interaction and external magnetic field. Instead, three distinct quadruple-Q states with topologically trivial spin textures are stabilized. However, we demonstrate that the quadruple-Q skyrmion crystal can become the ground state when an additional high-harmonic wave–vector interaction is considered. Depending on the magnitude of this interaction, we obtain two types of quadruple-Q skyrmion crystals exhibiting the skyrmion numbers of one and two. These findings highlight the emergence of diverse three-dimensional multiple-Q spin states in centrosymmetric body-centered tetragonal magnets. Full article

I revisit the well-known phase transition between the hexagonal skyrmion lattice and the homogeneous state within the phenomenological Dzyaloshinskii theory for chiral magnets, which includes only the exchange, Dzyaloshinskii–Moriya, and Zeeman energy contributions. I show that, in a narrow field range near the saturation field, the hexagonal skyrmion order gradually transforms into a square arrangement of skyrmions. Then, by the second-order phase transition during which the lattice period diverges, the square skyrmion lattice releases a set of repulsive isolated skyrmions. On decreasing the magnetic field, isolated skyrmions re-condense into the square lattice at the same critical field as soon as their eigen-energy becomes negative with respect to the field-aligned state. The underlying reason for the reorientation transition between two skyrmion orders can be deduced from the energy density distribution within isolated skyrmions surrounded by the homogeneous state. When the negative energy within the ring-shaped area at the skyrmion outskirt outweighs the positive energy amount around the skyrmion axis, skyrmions tend to form the square lattice, in which the overlap of skyrmion profiles results in smaller energy losses as compared with the hexagonal crystal. With the further decreasing field, the hexagonal lattice achieves smaller energy density in comparison with the square one due to the denser packing of individual skyrmions. Full article

We investigate the stability tendency of a magnetic skyrmion crystal in noncentrosymmetric tetragonal systems with the Dzyaloshinskii–Moriya interaction. We show that the stability region of the square skyrmion crystal on a square lattice depends on the Ising-type magnetic anisotropic interaction by performing the simulated annealing for the spin model. The easy-axis anisotropic interaction tends to narrow the region where the square skyrmion crystal is stabilized when the magnetic field is applied in the out-of-plane direction. In contrast, the easy-plane anisotropic interaction tends to enlarge the stability region. Meanwhile, the square skyrmion crystal induced by the easy-axis anisotropic interaction is robust compared with that induced by the easy-plane anisotropic interaction when the magnetic field is tilted from the out-of-plane to the in-plane direction. The results indicate that the instability toward the square skyrmion crystal in noncentrosymmetric crystals is sensitive to both magnetic anisotropy and magnetic fields. Full article

In this study, we investigate the stability of a magnetic skyrmion crystal with short-period magnetic modulations in a centrosymmetric body-centered tetragonal system. By performing the simulated annealing for the spin model, incorporating the effects of the biquadratic interaction and high-harmonic wave–vector interaction in momentum space, we find that the double-Q square skyrmion crystal consisting of two spin density waves is stabilized in an external magnetic field. We also show that double-Q states appear in both low- and high-field regions; the low-field spin configuration is characterized by an anisotropic double-Q modulation consisting of a superposition of the spiral wave and sinusoidal wave, while the high-field spin configuration is characterized by an isotropic double-Q modulation consisting of a superposition of two sinusoidal waves. Furthermore, we show that the obtained multiple-Q instabilities can be realized for various ordering wave vectors. The results provide the possibility of realizing the short-period skyrmion crystals under the body-centered tetragonal lattice structure. Full article

Previous studies have demonstrated that the surface curvature of cylindrical magnetic nonawires can induce fascinating dynamic magnetization properties. It was recently proposed that ferromagnetic nanotubes can be utilized as skyrmion guides, enabling the avoidance of the annihilation of skyrmions in the lateral boundaries as in flat thin-film strips. In this work, we demonstrate via micromagnetic simulation that multiple skyrmions can be stabilized in a cross-section of a ferromagnetic nanotube with interfacial Dzyaloshinskii–Moriya interaction (iDMI). When uniformly arranged, these skyrmions together can perform as a crystal lattice for spin waves (SWs) propagating in the nanotube. Our simulations show that the skyrmion lattice can contribute a chiral effect to the SW passing through, namely a circular polarization of the SW. The handedness of the polarization is found to be determined by the polarity of the skyrmions. A physical explanation of the observed effect is provided based on the exchange of angular momentum between SWs and skyrmions during the scattering process. Our results display more possibilities to exploit magnetic nanotubes as SW and skyrmion guide in the development of novel spintronic devices. Full article

I revisit the well-known structural transition between hexagonal and square skyrmion lattices and subsequent first-order phase transition into the tilted ferromagnetic state as induced by the increasing easy-plane anisotropy in quasi-two-dimensional chiral magnets. I show that the hexagonal skyrmion order first transforms into a rhombic skyrmion lattice, which, adjusts into a perfect square arrangement of skyrmions (“a square meron-antimeron crystal”) within a narrow range of anisotropy values. These transitions are mediated by merons and anti-merons emerging in the boundaries between skyrmion cells; energetically unfavorable anti-merons annihilate, whereas pairs of neighboring merons merge. The tilted ferromagnetic state sets in via mutual annihilation of oppositely charged merons; as an outcome, it contains bimeron clusters (chains) with the attracting inter-soliton potential. Additionally, I demonstrate that domain-wall merons are actively involved in the dynamic response of the square skyrmion lattices. As an example, I theoretically study spin–wave modes and their excitations by AC magnetic fields. Two found resonance peaks are the result of the complex dynamics of the domain-wall merons; whereas in the high-frequency mode the merons rotate counterclockwise, as one might expect, in the low-frequency mode merons are instead created and annihilated consistently with the rotational motion of the domain boundaries. Full article

We investigate the emergence of magnetic skyrmion crystals with swirling topological spin textures in itinerant magnets with an emphasis on momentum-resolved multi-spin interactions. By performing the simulated annealing for the effective spin model with the two-spin and four-spin interactions on a two-dimensional triangular lattice, we show that various types of four-spin interactions become the microscopic origin of the magnetic skyrmion crystal with the skyrmion numbers of one and two. We find that the four-spin interactions between the different wave vectors lead to the skyrmion crystal with the skyrmion number of one, whereas those at the same wave vectors lead to the skyrmion crystals with the skyrmion number of one and two. Our results indicate that the multi-spin interactions arising from the itinerant nature of electrons provide rich topological spin textures in magnetic metals. Full article

The structure of skyrmion and spiral solutions, investigated within the phenomenological Dzyaloshinskii model of chiral magnets near the ordering temperatures, is characterized by the strong interplay between longitudinal and angular order parameters, which may be responsible for experimentally observed precursor effects. Within the precursor regions, additional effects, such as pressure, electric fields, chemical doping, uniaxial strains and/or magnetocrystalline anisotropies, modify the energetic landscape and may even lead to the stability of such exotic phases as a square staggered lattice of half-skyrmions, the internal structure of which employs the concept of the “soft” modulus and contains points with zero modulus value. Here, we additionally alter the stiffness of the magnetization modulus to favor one- and two-dimensional modulated states with large modulations of the order parameter magnitude. The computed phase diagram, which omits any additional effects, exhibits stability pockets with a square half-skyrmion lattice, a hexagonal skyrmion lattice with the magnetization in the center of the cells parallel to the applied magnetic field, and helicoids with propagation transverse to the field, i.e., those phases in which the notion of localized defects is replaced by the picture of a smooth but more complex tiling of space. We note that the results can be adapted to metallic glasses, in which the energy contributions are the same and originate from the inherent frustration in the models, and chiral liquid crystals with a different ratio of elastic constants. Full article

We report our numerical results on the stability of the skyrmion crystal phase in an external magnetic field for both in-plane and out-of-plane directions in a centrosymmetric host. We analyze a spin model with the two-spin symmetric anisotropic exchange interaction that arises from relativistic spin–orbit coupling on a triangular lattice. By performing simulated annealing, we construct magnetic phase diagrams when the magnetic field is tilted from the out-of-plane field direction to the in-plane field direction. We find a different stability tendency of the skyrmion crystal phase according to the directions of the in-plane field, which provides a signal of the two-spin symmetric anisotropic exchange interaction for stabilizing the skyrmion crystal phase. Our results indicate that the mechanism of the skyrmion crystal phase triggered by the two-spin symmetric anisotropic exchange interaction can be experimentally tested by applying the in-plane magnetic field. Full article

We re-examine the internal structure of bimerons, which are stabilized in easy-plane chiral magnets and represent coupled states of two merons with the same topological charge $|1/2|$ but with opposite vorticity and the polarity. We find that, in addition to the vortices and antivortices, bimerons feature circular regions which are located behind the anti-vortices and bear the rotational sense opposite to the rotational sense chosen by the Dzyaloshinskii–Moriya interaction. In an attempt to eliminate these wrong-twist regions with an excess of positive energy density, bimerons assemble into chains, and as such exhibit an attracting interaction potential. As an alternative to chains, we demonstrate the existence of ring-shaped bimeron clusters of several varieties. In some rings, bimeron dipoles are oriented along the circle and swirl clockwise and/or counterclockwise (dubbed “roundabouts”). Moreover, a central meron encircled by the outer bimerons may possess either positive or negative polarity. In other rings, the bimeron dipoles point towards the center of a ring and consequently couple to the central meron (dubbed “crossings”). We point out that the ringlike solutions for baryons obtained within the Skyrme model of pions, although driven by the same tendency of the energy reduction, yield only one type of bimeron rings. The conditions of stability applied to the described bimeron rings are additionally extended to bimeron networks when bimerons fill the whole space of two-dimensional samples and exhibit combinations of rings and chains dispersed with different spatial density (dubbed bimeron “polymers”). In particular, bimeron crystals with hexagonal and the square bimeron orderings are possible when the sides of the unit cells represent chains of bimerons joined in intersections with three or four bimerons, respectively; otherwise, bimeron networks represent disordered bimeron structures. Moreover, we scrutinize the inter-transformations between hexagonal Skyrmion lattices and disordered bimeron polymers occuring via nucleation and mutual annihilation of merons within the cell boundaries. Our theory provides clear directions for experimental studies of bimeron orderings in different condensed-matter systems with quasi-two-dimensional geometries. Full article

This article presents a concise survey of basic discrete and semi-discrete nonlinear models, which produce two- and three-dimensional (2D and 3D) solitons, and a summary of the main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross–Pitaevskii (GP) equations with the Lee–Huang–Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole–dipole and quadrupole–quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (${\chi }^{\left(2\right)}$) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its $\mathcal{PT}$-symmetric version, a system of DNLS equations for the spin–orbit-coupled (SOC) binary Bose–Einstein condensate, and others. The article presents a review of the basic species of multidimensional discrete modes, including fundamental (zero-vorticity) and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and $\mathcal{PT}$-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others. Full article

Optical skyrmion lattices play an important role in photonic system design and have potential applications in optical transmission and storage. In this study, we propose a novel metasurface approach to calculating the dependence of the multi-beam interference principle and the angular momentum action in the spin–orbit interaction. The metasurface consists of nanopore structures, which are used to generate an optical skyrmion lattice. The superposition of optical vortex beams with circular polarization states is used to evaluate the evolution of the shape of the topological domain walls of the hexagonal skyrmion lattice. Our results show that the distribution of the skyrmion spin vector can be controlled by changing the lattice arrangement from triangular to hexagonal shapes. The distribution of skyrmion number at the microscale is further calculated. Our work has significant implications for the regulation of the shape of topological domain walls of skyrmion lattices, with potential applications in polarization sensing, nanopositioning, and super-resolution microimaging. Full article