When a magnetic skyrmion is modeled as a point particle, its dynamics depends on the precise definition of the skyrmion center. The guiding-center position, defined as the first moment of the skyrmion density, exhibits Thiele's massless dynamics; position based on the first moment of magnetization component $m_z$ shows Larmor oscillations characteristic of a massive particle. We show that, even with the latter definition, the Larmor oscillations may be absent for certain types of external forces such as adiabatic spin torque. We offer an alternative mechanical model of a skyrmion featuring two coupled massless particles.
We discuss models for massless Dirac fermions being subject to a perpendicular magnetic field in spherical geometry. These models are analogues of Haldane`s spherical construction for massful charge carriers. The single particle states constructed here are easily implemented in existing numerical code for many-body problems in conventional quantum Hall systems. Moreover, the many-body states of fully filled sublevels in the subspace of lowest Landau level index are skyrmions with respect to the layer spin.
The dynamics of a vortex in a thin-film ferromagnet resembles the motion of a charged massless particle in a uniform magnetic field. Similar dynamics is expected for other magnetic textures with a nonzero skyrmion number. However, recent numerical simulations revealed that skyrmion magnetic bubbles show significant deviations from this model. We show that a skyrmion bubble possesses inertia and derive its mass from the standard theory of a thin-film ferromagnet. Besides center-of-mass motion, other low energy modes are waves on the edge of the bubble traveling with different speeds in opposite…
An analytical expression is obtained for the mass of an isolated magnetic skyrmion and its linearized equation of motion. The magnetic skyrmion is viewed as a topologically protected spin-wave soliton in the magnetic ultrathin films stabilized by the interfacial-Dzyaloshinskii-Moriya interaction. The equations of motion are derived from the Landau-Lifshitz-Gilbert equation for both the skyrmion charge and magnetization centers. They are generalized Thiele equations, including the gyro-term, dissipation term, external force, acceleration term with the tensorial mass, and time derivatives of the…
We study the stability and energetics associated to skyrmions appear- ing as excitations on curved surfaces. Using a continuum model we show that the presence of cylindrically radial and azimuthal fields destabilizes the skyrmions that appear in the absence of an external field. Weak fields generate fractional skyrmions while strong magnetic fields yield stable 2{$π$}- skyrmions, which have their widths diminished by the magnetic field strength. Under azimuthal fields vortex appear as stable states on the curved surface.
We study the collective dynamics of a two-dimensional honeycomb lattice of magnetic skyrmions. By performing large-scale micromagnetic simulations, we find multiple chiral and non-chiral edge modes of skyrmion oscillations in the lattice. The non-chiral edge states are due to the Tamm-Shockley mechanism, while the chiral ones are topologically protected against structure defects and hold different handednesses depending on the mode frequency. To interpret the emerging multiband nature of the chiral edge states, we generalize the massless Thiele's equation by including a second-order inertial t…
We numerically examine a single skyrmion dynamics under the influence of triangular and honeycomb obstacle arrays at zero temperature. The skyrmion Hall angle $θ_{sk}$, that is the angle between the applied external drive and the direction of the skyrmion motion, increases in quantized steps or continuously as a function of the applied drive. For the obstacle arrays studied in this work, the skyrmion exhibits two main directional locking effects, where the skyrmion motion locks with $θ_{sk}=-30^\circ$ and $-60^\circ$. We show that these directions are privileged due to the obstacle landscape s…
Emergent crystals are periodic alignment of "emergent particles", i.e., localized collective behavior of atoms or their charges/spins/orbits. These novel states of matter, widely observed in various systems, may deform under mechanical forces with elasticity strikingly different from that of the underlying material. However, their nonlinear and critical behaviors under strong fields are hitherto unclear. Here we theoretically study the nonlinear elasticity and structural transitions of skyrmion crystals (SkX) suffering uniaxial distortion by using three different methods. Under moderate tensio…
We deal with magnetic structures that attain integer and half-integer skyrmion numbers. We model and solve the problem analytically, and show how the solutions appear in materials that engender distinct, very specific physical properties, and use them to describe their topological features. In particular, we found a way to model skyrmion with a large transition region correlated with the presence of a two-peak skyrmion number density. Moreover, we run into the issue concerning the topological strength of a vortex-like structure and suggest an experimental realization, important to decide how t…
Topologically stable field configurations appear in many fields of physics, from elementary particles to condensed matter and cosmology. During the last decade, chiral liquid crystals and chiral magnets took on the role of model objects for experimental investigation of topological solitons and understanding of their nonsingular field configurations. Here we introduce a paradigm of facile skyrmionic networks with mutually-orthogonal orientations of constituent isolated skyrmions. Such networks are envisioned as a novel concept of spintronic devices and are presumably responsible for precursor …
Ultrathin ferromagnets with frustrated exchange and the Dzyaloshinskii-Moriya interaction can support topological solitons such as skyrmions and antiskyrmions, which are metastable and can be considered particle-antiparticle counterparts. When spin-orbit torques are applied, the motion of an isolated antiskyrmion driven beyond its Walker limit can generate skyrmion-antiskyrmion pairs. Here, we use atomistic spin dynamics simulations to shed light on the scattering processes involved in this pair generation. Under certain conditions a proliferation of these particles and antiparticles can appea…
Since the 1950s, topological solitons have been used to describe elementary particles[1-3] and particle-like field configurations[4-13] that appear in almost all branches of physics ranging from subatomic to cosmological scales[3,14-16]. In this context, formation and annihilation of particles corresponds to topological phase transitions, whose actual process and mechanism remain elusive. Here, we show that annihilation of an isolated skyrmion in helimagnets as the applied magnetic field increases initiates at its center point by a local magnetization reversal. At the critical field, a soft mo…
The aim of this Tutorial is to give a pedagogical introduction into realizations of Majorana fermions, usually termed as Majorana bound states (MBS), in condensed matter systems with magnetic textures. We begin by considering the Kitaev chain model of 'spinless' fermions and show how two 'half' fermions can appear at chain ends due to interactions. By considering this model and its two-dimensional generalization, we emphasize intricate relation between topological superconductivity and possible realizations of MBS. We further discuss how 'spinless' fermions can be realized in more physical sys…
We report on the anomalous magnetization dynamics of the cycloidally-modulated spin textures under the influence of uniaxial anisotropy in multiferroic $\mathrm{GaV_4S_8}$. The temperature and field dependence of the linear ac susceptibility [$χ_{1ω}^{\prime}(T,H)$], ac magnetic loss [$χ_{1ω}^{\prime\prime}(T,H)$], and nonlinear ac magnetic response [$M_{3ω}(T,H)$] are examined across the magnetic phase diagram in the frequency range $f = 10-10000$ Hz. According to recent theory, skyrmion vortices under axial crystal symmetry are confined along specific orientations, resulting in enhanced robu…
