The profile of chiral skyrmions

arXiv: Mesoscale and Nanoscale Physics, 2020

We study the structure of an axially symmetric magnetic skyrmion in a ferromagnet with the Dzyaloshinskii-Moriya interaction. We examine the regime of large skyrmions and we identify rigorously the critical value of the dimensionless parameter at which the skyrmion radius diverges to infinity, while the skyrmion energy converges to zero. This critical value coincides with the expected transition point from the uniform phase, which accommodates the skyrmion as an excited state, to the helical phase, which has negative energy. We give the profile field at the skyrmion core, its outer field, and the intermediate field at the skyrmion domain wall. Moreover, we derive an explicit formula for the leading asymptotic behavior of the energy as well as the leading term and first asymptotic correction for the value of the critical parameter. The key leading to the results is a parity theorem that utilizes exact formulae for the asymptotic behavior of the solutions of the static Landau-Lifshitz...

Physical Review B, 2015

We study the dynamics of skyrmions in Dzyaloshinskii-Moriya materials with easy-axis anisotropy. An important link between topology and dynamics is established through the construction of unambiguous conservation laws obtained earlier in connection with magnetic bubbles and vortices. In particular, we study the motion of a topological skyrmion with skyrmion number Q = 1 and a non-topological skyrmionium with Q = 0 under the influence of an applied field gradient. The Q = 1 skyrmion undergoes Hall motion perpendicular to the direction of the field gradient with a drift velocity proportional to the gradient. In contrast, the non-topological Q = 0 skyrmionium is accelerated in the direction of the field gradient, thus exhibiting ordinary Newtonian motion. When the applied field is switched off the Q = 1 skyrmion is spontaneously pinned around a fixed guiding center, whereas the Q = 0 skyrmionium moves with constant velocity v. We give a systematic calculation of a skyrmionium traveling with any constant velocity v that is smaller than a critical velocity vc.

Physical Review B, 2020

We present a novel approach to understanding the extraordinary diversity of magnetic skyrmion solutions. Our approach combines a new classification scheme with efficient analytical and numerical methods. We introduce the concept of chiral kinks to account for regions of disfavoured chirality in spin textures, and classify two-dimensional magnetic skyrmions in terms of closed domain walls carrying such chiral kinks. In particular, we show that the topological charge of magnetic skyrmions can be expressed in terms of the constituent closed domain walls and chiral kinks. Guided by our classification scheme, we propose a method for creating hitherto unknown magnetic skyrmions which involves initial spin configurations formulated in terms of holomorphic functions and subsequent numerical energy minimization. We numerically study the stability of the resulting magnetic skyrmions for a range of external fields and anisotropy parameters, and provide quantitative estimates of the stability range for the whole variety of skyrmions with kinks. We show that the parameters limiting this range can be well described in terms of the relative energies of particular skyrmion solutions and isolated stripes with and without chiral kinks.

SciPost Physics

Skyrmions in antiferromagnetic (AFM) materials with the Dzyaloshinskii-Moriya (DM) interaction are expected to exist for essentially the same reasons as in DM ferromagnets (FM). It is shown that skyrmions in antiferromagnets with the DM interaction can be traveling as solitary waves with velocities up to a maximum value that depends on the DM parameter. Their configuration is found numerically. The energy and the linear momentum of an AFM skyrmion lead to a proper definition of its mass. We give the details of the energy-momentum dispersion of traveling skyrmions and explore their particle-like character based on exact relations. The skyrmion number, known to be linked to the dynamics of topological solitons in FM, is, here, unrelated to the dynamical behavior. As a result, the solitonic behavior of skyrmions in AFM is in stark contrast to the dynamical behavior of their FM counterparts.

Journal of Physics D: Applied Physics

We have performed micromagnetic simulations to study the formation of skyrmions in ferromagnetic elements with different shapes having perpendicular anisotropy. The strength of Dzyaloshinskii-Moriya interaction (D) and uniaxial anisotropy (K) are varied to elucidate the regime in which skyrmion formation can take place. It is found that for a certain combination of D and K skyrmion formation does not happen. Further we also observed that for large D and small K values, finite size effect dominates which in turn hinders formation of typical Néel (spherical) skyrmions. However the resulting magnetic phase is skyrmionic in nature and has different shape. We also have found that the shape of the magnetic nano element has a significant role in determining the final magnetic state in addition to the competing D and K values.

Physical Review B

The uniform motion of chiral magnetic skyrmions induced by a spin-transfer torque displays an intricate dependence on the skyrmions' topological charge and shape. We reveal surprising patterns in this dependence through simulations of the Landau-Lifshitz-Gilbert equation with Zhang-Li torque and explain them through a geometric analysis of Thiele's equation. Our results provide a universal geometrical understanding of the dependence of the skyrmion's velocity and Hall angle on the skyrmion's topological charge, shape, and orientation. The generality of our approach suggests the validity of our results for exchange-frustrated magnets, bubble materials, and other materials.

2020

We find numerically skyrmionic textures with skyrmion number Q = 0 in ferromagnets with the Dzyaloshinskii-Moriya interaction and perpendicular anisotropy. These have the form of a skyrmionantiskyrmion pair and may be called chiral droplets. They are stable in an infinite film as well as in disc-shaped magnetic elements. Droplets are found for values of the parameters close to the transition from the ferromagnetic to the spiral phase. We study their motion under spin-transfer torque. They move in the direction of the spin flow and, thus, their dynamics are drastically different than the Hall dynamics of the standard Q = 1 skyrmion.

Journal of Physics: Condensed Matter

By introducing biquadratic together with usual bilinear ferromagnetic nearest neighbor exchange interaction in a square lattice, we find that the energy of the spin-wave mode is minimized at a finite wavevector for a vanishingly small Dzyaloshinskii–Moriya interaction (DMI), supporting a ground state with spin-spiral structure whose pitch length is unusually short as found in some of the experiments. Apart from reproducing the magnetic structures that can be obtained in a canonical model with nearest neighbor exchange interaction only, a numerical simulation of this model with further introduction of magnetic anisotropy and magnetic field predicts many other magnetic structures some of which are already observed in the experiments. Among many observed structures, nanoscale skyrmion even at vanishingly small DMI is found for the first time in a model. The model provides the nanoscale skyrmions of unit topological charge at zero magnetic field as well. We obtain phase diagrams for all...

Journal of Magnetism and Magnetic Materials, 2020

The purpose of the research is the construction of the analytical model for description of a number of topological objects in a two-sublattice antiferromagnet with uniaxial magnetic anisotropy and Dzyaloshinskii-Moriya interaction (DMI) including vortices, antivortices, skyrmions, antiskyrmions, skyrmioniums and their bound states, which are the exact dynamic solutions of the nonlinear Landau-Lifshitz equations. "Relativistic contraction" of skyrmion-like topological object size in the direction of motion is demonstrated for "subcritical" case when its velocity is less than spin wave velocity in antiferromagnet. Lorentz-like "supercritical" transformation are found for skyrmion-like magnetic structures moving with velocity greater than spin wave velocity in antiferromagnet. In particular, the results of the analytical model are applied for an antiferromagnet in the form of cylindrical nanoshell; in this case, there are more than one solution of the nonlinear Landau-Lifshitz equations for the same boundary and initial conditions. It means that vortices, skyrmions, skyrmioniums and their bound states represent the ground state and the excited states in an antiferromagnetic cylindrical nanoshell. The particular cases of the exact static solutions of the nonlinear Landau-Lifshitz equations include the well-known one-dimensional solutions such as Bloch domain, Neel domain wall, Shirobokov domain structure, antiferromagnetic vortices, two-dimensional Belavin-Polyakov soliton, three-dimensional Hodenkov soliton and target type soliton. The results of this paper can be used for further development of theory of the antiferromagnetic soliton and skyrmion physics. Besides, the exact dynamic solutions of the nonlinear Landau-Lifshitz equations can serve as the reference solutions for testing the results of micromagnetic simulations. Recently, the direct observation of topological objects (skyrmions,

Physical Review Research, 2019

We find closed-form solution of the Euler equation for a chiral magnet in terms of a skyrmion or a meron depending on the relative strengths of magnetic anisotropy and magnetic field. We show that the relevant length scales for these solutions primarily depend on the strengths of Dzyaloshinskii-Moriya interaction through its ratios, respectively, with magnetic field and magnetic anisotropy. We thus unambiguously determine the parameter dependencies on the radius of the topological structures particularly of the skyrmions, showing an excellent agreement with experiments and firstprinciple studies. An anisotropic Dzyaloshinskii-Moriya interaction suitable for thin films made with Cnv symmetric materials is found to stabilize anti-skyrmion and anti-meron, which are prototypical for D 2d symmetric systems, depending on the degree of anisotropy. Based on these solutions, we obtain phase diagram by comparing the energies of various collinear and non-collinear competing phases.