"Polymerization" of Bimerons in Quasi-Two-Dimensional Chiral Magnets with Easy-Plane Anisotropy.

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.

Precursor skyrmion states near the ordering temperatures of chiral magnets.

In noncentrosymmetric magnets, chiral Dzyaloshinskii-Moriya interactions (DMI) provide a distinctive mechanism for the stabilization of localized skyrmion states in two and three dimensions with a fixed sense of rotation. Near the ordering transition, the skyrmion strings develop attractive skyrmion-skyrmion interactions and ultimately become confined in extended clusters or textures [A. O. Leonov and U. K. Rößler, Nanomaterials, 2023, 13, 891], which is a consequence of the coupling between the magnitude and the angular part of the order parameter. Multi-skyrmionic states built from isolated skyrmions (IS) can form multiple modulated magnetic phases that may underlie the exotic magnetic phenomena of "partial order" or the field-driven "A-phase" observed in MnSi and other cubic helimagnets. Based on the standard phenomenological Dzyaloshinskii model, we obtain numerically exact solutions for skyrmion lattices (SkL), formulate their basic properties, and elucidate physical mechanisms of their formation and stability. Our detailed numerical studies show that the bound skyrmion states arise as hexagonal lattices of ±π-skyrmions (with the magnetization in the center along or opposite to the magnetic field) or square staggered lattices of π/2-skyrmions, which contain defect lines with zero modulus value and thus may form thermodynamically stable states only near the ordering temperature. In the simplest case of a two-dimensional (2D) skyrmionic texture, the structure is homogeneous in the third dimension (3D). The skyrmions preserve an ideal axisymmetric "double twist" core in condensed phases, while continuation into a space-filling texture is frustrated. The evolution of skyrmion lattices in an increasing magnetic field leads to a succession of phase transitions of first or second kind between diverse textures and finally ends due to the formation of isolated skyrmion-filaments with fixed radius and shape embedded in a homogeneously magnetized matrix. In the framework of the phenomenological model including only isotropic interactions (exchange, Zeeman, and DM energy contributions), the considered skyrmion lattices are only metastable states as the competing conical one-dimensional spiral forms the equilibrium state. But due to the weak couplings between skyrmions, secondary effects like anisotropies can stabilize skyrmionic textures as compared to simple helices. Also the topological nature of skyrmion condensates makes the magnetization processes in chiral magnets history-dependent and hysteretic.

Harnessing Skyrmion Hall Effect by Thickness Gradients in Wedge-Shaped Samples of Cubic Helimagnets.

The skyrmion Hall effect, which is regarded as a significant hurdle for skyrmion implementation in thin-film racetrack devices, is theoretically shown to be suppressed in wedge-shaped nanostructures of cubic helimagnets. Under an applied electric current, ordinary isolated skyrmions with the topological charge 1 were found to move along the straight trajectories parallel to the wedge boundaries. Depending on the current density, such skyrmion tracks are located at different thicknesses uphill along the wedge. Numerical simulations show that such an equilibrium is achieved due to the balance between the Magnus force, which instigates skyrmion shift towards the wedge elevation, and the force, which restores the skyrmion position near the sharp wedge boundary due to the minimum of the edge-skyrmion interaction potential. Current-driven dynamics is found to be highly non-linear and to rest on the internal properties of isolated skyrmions in wedge geometries; both the skyrmion size and the helicity are modified in a non-trivial way with an increasing sample thickness. In addition, we supplement the well-known theoretical phase diagram of states in thin layers of chiral magnets with new characteristic lines; in particular, we demonstrate the second-order phase transition between the helical and conical phases with mutually perpendicular wave vectors. Our results are useful from both the fundamental point of view, since they systematize the internal properties of isolated skyrmions, and from the point of view of applications, since they point to the parameter region, where the skyrmion dynamics could be utilized.

Mechanism of Skyrmion Attraction in Chiral Magnets near the Ordering Temperatures.

Isolated chiral skyrmions are investigated within the phenomenological Dzyaloshinskii model near the ordering temperatures of quasi-two-dimensional chiral magnets with Cnv symmetry and three-dimensional cubic helimagnets. In the former case, isolated skyrmions (IS) perfectly blend into the homogeneously magnetized state. The interaction between these particle-like states, being repulsive in a broad low-temperature (LT) range, is found to switch into attraction at high temperatures (HT). This leads to a remarkable confinement effect: near the ordering temperature, skyrmions exist only as bound states. This is a consequence of the coupling between the magnitude and the angular part of the order parameter, which becomes pronounced at HT. The nascent conical state in bulk cubic helimagnets, on the contrary, is shown to shape skyrmion internal structure and to substantiate the attraction between them. Although the attracting skyrmion interaction in this case is explained by the reduction of the total pair energy due to the overlap of skyrmion shells, which are circular domain boundaries with the positive energy density formed with respect to the surrounding host phase, additional magnetization "ripples" at the skyrmion outskirt may lead to attraction also at larger length scales. The present work provides fundamental insights into the mechanism for complex mesophase formation near the ordering temperatures and constitutes a first step to explain the phenomenon of multifarious precursor effects in that temperature region.

Surface anchoring as a control parameter for shaping skyrmion or toron properties in thin layers of chiral nematic liquid crystals and noncentrosymmetric magnets.

Existence of topological localized states (skyrmions and torons) and the mechanism of their condensation into modulated states are the ruling principles of condensed matter systems, such as chiral nematic liquid crystals (CLCs) and chiral magnets (ChM). In bulk helimagnets, skyrmions are rendered into thermodynamically stable hexagonal skyrmion lattice due to the combined effect of a magnetic field and, e.g., small anisotropic contributions. In thin glass cells of CLCs, skyrmions are formed in response to the geometrical frustration and field coupling effects. By numerical modeling, I undertake a systematic study of skyrmion or toron properties in thin layers of CLCs and ChMs with competing surface-induced and bulk anisotropies. The conical phase with a variable polar angle serves as a suitable background, which shapes skyrmion internal structure, guides the nucleation processes, and substantializes the skyrmion-skyrmion interaction. I show that the hexagonal lattice of torons can be stabilized in a vast region of the constructed phase diagram for both easy-axis bulk and surface anisotropies. A topologically trivial droplet is shown to form as a domain boundary between two cone states with different rotational fashion, which underpins its stability. The findings provide a recipe for controllably creating skyrmions and torons, possessing the features on demand for potential applications.

Current-induced shuttlecock-like movement of non-axisymmetric chiral skyrmions.

Current-induced motion of non-axisymmetric skyrmions within tilted ferromagnetic phases of polar helimagnets with the easy plane anisotropy is studied by micromagnetic simulations. Such non-axisymmetric skyrmions consist of a circular core and a crescent-shaped domain-wall region formed with respect to the tilted surrounding state. Current-driven motion of non-axisymmetric skyrmions exhibits two distinct time regimes: initially the skyrmions rotate towards the current flow direction and subsequently move along the current with the skyrmionic crescent first. According to the Thiele equation, the asymmetric distribution of the topological charge and the dissipative force tensor play an important role for giving the different velocities for the circular and the crescent-shaped constituent parts of the skyrmion what underlies such a shuttlecock-like movement. Moreover, the current-velocity relation depends on the angle of the tilted ferromagnetic phase what makes in particular the transverse velocity of skyrmions sensitive to their field-driven configurational transformation. We also argue the possibility of magnetic racetrack waveguides based on complex interplay of robust asymmetric skyrmions with multiple twisted edge states.

Skyrmion flop transition and congregation of mutually orthogonal skyrmions in cubic helimagnets.

Magnetic chiral skyrmions are particle-like excitations with a topological charge, which are currently considered as promising objects for the next generation of magnetic memory, logic, and neuromorphic devices. In three-dimensional systems, they can form rather complex topological structures. In bulk helimagnets, elongated skyrmion tubes can be ordered either perpendicularly or parallel to an external magnetic field and such configurations coexist in a specific range of fields. We have shown that with an increase in the magnetic field, the transition from perpendicular to parallel ordering in a 3D skyrmion dimer occurs through an intermediate state with mutually orthogonal skyrmion tubes. In the system with three and more skyrmion tubes, we uncovered a surprisingly large diversity of superstructures and systemized the principles of their formation. The nascent conical state is shown to induce the field-dependent switch between favored skyrmion clusters and underlies attracting inter-skyrmion potential. We argue that our numerical simulations on skyrmion clusters are valid in a parameter range corresponding to the A-phase region of cubic helimagnets. Moreover, skyrmionic superstructures constitute a novel concept of spintronic devices based on gapless skyrmion motion along with each other.

New magnetic phase of the chiral skyrmion material Cu2OSeO3.

The lack of inversion symmetry in the crystal lattice of magnetic materials gives rise to complex noncollinear spin orders through interactions of a relativistic nature, resulting in interesting physical phenomena, such as emergent electromagnetism. Studies of cubic chiral magnets revealed a universal magnetic phase diagram composed of helical spiral, conical spiral, and skyrmion crystal phases. We report a remarkable deviation from this universal behavior. By combining neutron diffraction with magnetization measurements, we observe a new multidomain state in Cu2OSeO3. Just below the upper critical field at which the conical spiral state disappears, the spiral wave vector rotates away from the magnetic field direction. This transition gives rise to large magnetic fluctuations. We clarify the physical origin of the new state and discuss its multiferroic properties.