Topological structures in chiral media: Effects of confined geometry.

We theoretically study orientational structures in chiral magnetics and cholesteric liquid crystal (CLC) nanosystems confined in the slab geometry. Our analysis is based on the model that, in addition to the exchange and the Dzyaloshinskii-Moriya interactions, takes into account the bulk and surface anisotropies. In CLC films, these anisotropies describe the energy of interaction with external magnetic/electric field and the anchoring energy assuming that magnetic/electric anisotropy is negative and the boundary conditions are homeotropic. We have computed the phase diagram and found that the ground state of the film is represented by various delocalized structures depending on the bulk and surface anisotropy parameters, κ^{b} and κ^{s}. These include the z helix and the z cone states, the oblique, and the x helicoids. The minimum energy paths connecting the ground state and metastable helicoids and the energy barriers separating these states are evaluated. We have shown that there is a variety of localized topological structures such as the skyrmion tube, the toron, and the bobber that can be embedded in different ground states including the z cone (conical phase) and tilted fingerprint states. We have also found the structure called the leech that can be viewed as an intermediate state between the toron and the skyrmion tube.

Equilibrium Skyrmion Lattice Ground State in a Polar Easy-plane Magnet.

The skyrmion lattice state (SkL), a crystal built of mesoscopic spin vortices, gains its stability via thermal fluctuations in all bulk skyrmion host materials known to date. Therefore, its existence is limited to a narrow temperature region below the paramagnetic state. This stability range can drastically increase in systems with restricted geometries, such as thin films, interfaces and nanowires. Thermal quenching can also promote the SkL as a metastable state over extended temperature ranges. Here, we demonstrate more generally that a proper choice of material parameters alone guarantees the thermodynamic stability of the SkL over the full temperature range below the paramagnetic state down to zero kelvin. We found that GaV4Se8, a polar magnet with easy-plane anisotropy, hosts a robust Néel-type SkL even in its ground state. Our supporting theory confirms that polar magnets with weak uniaxial anisotropy are ideal candidates to realize SkLs with wide stability ranges.

Edge states and skyrmion dynamics in nanostripes of frustrated magnets.

Magnetic skyrmions are particle-like topological excitations recently discovered in chiral magnets. Their small size, topological protection and the ease with which they can be manipulated by electric currents generated much interest in using skyrmions for information storage and processing. Recently, it was suggested that skyrmions with additional degrees of freedom can exist in magnetically frustrated materials. Here, we show that dynamics of skyrmions and antiskyrmions in nanostripes of frustrated magnets is strongly affected by complex spin states formed at the stripe edges. These states create multiple edge channels which guide the skyrmion motion. Non-trivial topology of edge states gives rise to complex current-induced dynamics, such as emission of skyrmion-antiskyrmion pairs. The edge-state topology can be controlled with an electric current through the exchange of skyrmions and antiskyrmions between the edges of a magnetic nanostructure.

Chiral Surface Twists and Skyrmion Stability in Nanolayers of Cubic Helimagnets.

Theoretical analysis and Lorentz transmission electron microscopy (LTEM) investigations in an FeGe wedge demonstrate that chiral twists arising near the surfaces of noncentrosymmetric ferromagnets [Meynell et al., Phys. Rev. B 90, 014406 (2014)] provide a stabilization mechanism for magnetic Skyrmion lattices and helicoids in cubic helimagnet nanolayers. The magnetic phase diagram obtained for freestanding cubic helimagnet nanolayers shows that magnetization processes differ fundamentally from those in bulk cubic helimagnets and are characterized by the first-order transitions between modulated phases. LTEM investigations exhibit a series of hysteretic transformation processes among the modulated phases, which results in the formation of the multidomain patterns.

Three-dimensional chiral skyrmions with attractive interparticle interactions.

We introduce a new class of isolated three-dimensional skyrmion that can occur within the cone phase of chiral magnetic materials. These novel solitonic states consist of an axisymmetric core separated from the host phase by an asymmetric shell. These skyrmions attract one another. We derive regular solutions for isolated skyrmions arising in the cone phase of cubic helimagnets and investigate their bound states.

Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet.

Multiply periodic states appear in a wide variety of physical contexts, such as the Rayleigh-Bénard convection, Faraday waves, liquid crystals and skyrmion crystals recently observed in chiral magnets. Here we study the phase diagram of an anisotropic frustrated magnet which contains five different multiply periodic states including the skyrmion crystal. We clarify the mechanism for stabilization of these states and discuss how they can be observed in magnetic resonance and electric polarization measurements. We also find stable isolated skyrmions with topological charge 1 and 2. Their spin structure, interactions and dynamics are more complex than those in chiral magnets. In particular, magnetic resonance in the skyrmion crystal should be accompanied by oscillations of the electric polarization with a frequency depending on the amplitude of the a.c. magnetic field. These results show that skyrmion materials with rich physical properties can be found among frustrated magnets. We formulate rules to help the search.

Theory of skyrmion states in liquid crystals.

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. Ackerman 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.