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Skyrmions are important in topological quantum field theory for being soliton solutions of a nonlinear sigma model and in information technology for their attractive applications. Skyrmions are believed to be circular and stripy spin textures appeared in the vicinity of skyrmion crystals are termed spiral, helical, and cycloid spin orders, but not skyrmions. Here we present convincing evidences showing that those stripy spin textures are skyrmions, siblings of circular skyrmions in skyrmion crystals and cousins of isolated circular skyrmions. Specifically, isolated skyrmions are excitations when skyrmion formation energy is positive. The skyrmion morphologies are various stripy structures when the ground states of chiral magnetic films are skyrmions. The density of skyrmion number determines the morphology of condensed skyrmion states. At the extreme of one skyrmion in the whole sample, the skyrmion is a ramified stripe. As the skyrmion number density increases, individual skyrmion shapes gradually change from ramified stripes to rectangular stripes, and eventually to disk-like objects. At a low skyrmion number density, the natural width of stripes is proportional to the ratio between the exchange stiffness constant and Dzyaloshinskii-Moriya interaction coefficient. At a high skyrmion number density, skyrmion crystals are the preferred states. Our findings reveal the nature and properties of stripy spin texture, and open a new avenue for manipulating skyrmions, especially condensed skyrmions such as skyrmion crystals.
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A magnetic skyrmion is a topological object that can exist as a solitary embedded in the vast ferromagnetic phase, or coexists with a group of its siblings in various stripy phases as well as skyrmion crystals (SkXs). Isolated skyrmions and skyrmions in an SkX are circular while a skyrmion in other phases is a stripe of various forms. Unexpectedly, the sizes of the three different types of skyrmions depend on material parameters differently. For chiral magnetic films with exchange stiffness constant $A$, the Dzyaloshinskii-Moriya interaction (DMI) strength $D$, and perpendicular magnetic anisotropy $K$, $kappaequivpi^2D^2/(16AK)=1$ separates isolated skyrmions from condensed skyrmion states. In contrast to isolated skyrmions whose size increases with $D/K$ and is insensitive to $kappall1$ and stripe skyrmions whose width increases with $A/D$ and is insensitive to $kappagg1$, the size of skyrmions in SkXs is inversely proportional to the square root of skyrmion number density and decreases with $A/D$. This finding has important implications in our search for stable smaller skyrmions at the room temperature in applications.
Antiferromagnetic skyrmion crystals are magnetic phases predicted to exist in antiferromagnets with Dzyaloshinskii-Moriya interactions. Their spatially periodic noncollinear magnetic texture gives rise to topological bulk magnon bands characterized by nonzero Chern numbers. We find topologically-protected chiral magnonic edge states over a wide range of magnetic fields and Dzyaloshinskii-Moriya interaction values. Moreover, and of particular importance for experimental realizations, edge states appear at the lowest possible energies, namely, within the first bulk magnon gap. Thus, antiferromagnetic skyrmion crystals show great promise as novel platforms for topological magnonics.
Theory of interference-induced quantum corrections to conductivity is developed for two dimensional systems with chiral spin textures including skyrmions. The effect of exchange interaction between electrons and spin textures on weak localization of electronic waves is studied. The spin dephasing rates are calculated as functions of the spin texture size. The anomalous magnetoresistance is shown to be governed by the size and magnetization spatial distribution of the spin textures. The effect of average magnetization-induced spin splitting on weak localization is analyzed. The sign-alternating weak-antilocalization magnetoresistance is demonstrated for skyrmion crystals. We argue that analysis of the low-field magnetoresistance serves as an independent tool for an experimental detection of chiral spin textures and, in particular, skyrmions.
We investigate, within the framework of linear elasticity theory, edge Rayleigh waves of a two-dimensional elastic solid with broken time-reversal and parity symmetries due to a Berry term. As our prime example, we study the elastic edge wave traveling along the boundary of a two-dimensional skyrmion lattice hosted inside a thin-film chiral magnet. We find that the direction of propagation of the Rayleigh modes is determined not only by the chirality of the thin-film, but also by the Poisson ratio of the crystal. We discover three qualitatively different regions distinguished by the chirality of the low-frequency edge waves, and study their properties. To illustrate the Rayleigh edge waves in real time, we have carried out finite-difference simulations of the model. Apart from skyrmion crystals, our results are also applicable to edge waves of gyroelastic media and screened Wigner crystals in magnetic fields. Our work opens a pathway towards controlled manipulation of elastic signals along boundaries of crystals with broken time-reversal symmetry.
Within the Oseen-Frank theory we derive numerically exact solutions for axisymmetric localized states in chiral liquid crystal layers with homeotropic anchoring. These solutions describe recently observed two-dimensional skyrmions in confinement-frustrated chiral nematics [P. J. Acherman et al. Phys. Rev. E 90, 012505 (2014)]. We stress that these solitonic states arise due to a fundamental stabilization mechanism responsible for the formation of skyrmions in cubic helimagnets and other noncentrosymmetric condensed-matter systems.
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