Skyrmions and Their Sizes in Helimagnets

New Journal of Physics, 2016

We report the most precise observations to date concerning the spin structure of magnetic skyrmions in a nanowedge specimen of cubic B20 structured FeGe. Enabled by our development of advanced differential phase contrast (DPC) imaging (in a scanning transmission electron microscope (STEM)) we have obtained high spatial resolution quantitative measurements of skyrmion internal spin profile. For hexagonal skyrmion lattice cells, stabilised by an out-plane applied magnetic field, mapping of the in-plane component of magnetic induction has revealed precise spin profiles and that the internal structure possesses intrinsic six-fold symmetry. With increasing field strength, the diameter of skyrmion cores was measured to decrease and accompanied by a nonlinear variation of the lattice periodicity. Variations in structure for individual skyrmions across an area of the lattice were also studied utilising a new increased sensitivity DPC detection scheme and a variety of symmetry lowering distortions were observed. To provide insight into fundamental energetics we have constructed a phenomenological model, with which our experimental observations of spin profiles and field induced core diameter variation are in good agreement with predicted structure in the middle of the nanowedge crystal. In the vicinity of the crystal surfaces, our model predicts the existence of in-plane twisting distortions which our current experimental observations were not sensitive to. As an alternative to the requirement for as yet unidentified sources of magnetic anisotropy, we demonstrate that surface states could provide the energetic stabilisation needed for predomination over the conical magnetic phase.

Physical Review B, 1996

The classical ferromagnet is analyzed in two dimensions via a mean-field treatment of the CP 1 model valid in the limit of low temperature and of weak magnetic field. At high skyrmion densities, we find that the magnetization begins to decrease linearly with temperature, but it then crosses over to a Curie-law at higher temperature. The comparison of these results with recent Knight-shift experiments on the quantum Hall state is fair.

Physical Review B, 2019

We demonstrate a fast numerical method of theoretical studies of skyrmion lattice or spiral order in magnetic materials with Dzyaloshinsky-Moriya interaction. The method is based on the Fourier expansion of the magnetization combined with a minimization of the free energy functional of the magnetic material in Fourier space, yielding the optimal configuration of the system for any given set of parameters. We employ a Lagrange multiplier technique in order to satisfy micromagnetic constraints. We apply this method to a system that exhibits, depending on the parameter choice, ferromagnetic, skyrmion lattice, or spiral (helical) order. Known critical fields corresponding to the helical-skyrmion as well as the skyrmion-ferromagnet phase transitions are reproduced with high precision. Using this numerical method we predict new types of excited (metastable) states of the skyrmion lattice, which may be stabilized by coupling the skyrmion lattice with a superconducting vortex lattice. The method can be readily adapted to other micromagnetic systems. I.

JETP Letters, 2019

We consider multiskyrmion configurations in 2D ferromagnets with Dzyaloshinskii-Moriya (DM) interaction and the magnetic field, using the stereographic projection method. In the absence of DM interaction, D, and the field, B, the skyrmions do not interact and the exact multiskyrmion solution is a sum of individual projections. In certain range of B, D = 0, skyrmions become stable and form a hexagonal lattice. The shape of one skyrmion on the plane is fully determined by D and B. We describe multiskyrmion configurations by simple sums of individual skyrmion projections, of the same shape and adjusted scale. This procedure reveals pairwise and triple interactions between skyrmions, and the energy of proposed hexagonal structure is found in a good agreement with previous studies. It allows an effective theory of skyrmion structures in terms of variables, referring to individual skyrmions, i.e., their position, size and phase, elliptic distortions etc.

2020

Skyrmions were originally introduced in Particle Physics as a possible mechanism to explain the stability of particles. Lately the concept has been applied in Condensed Matter Physics to describe the newly discovered topologically protected magnetic configurations called the magnetic Skyrmions. This elementary review introduces the concept at a level suitable for beginning students of Physics.

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...

Physical Review B, 2014

The magnetic skyrmion, i.e., the nanometric swirling spin vortexlike object with the topolgical charge, is broadly observed in chiral-lattice cubic magnets, typically MnSi; where the cylindrical-shape skyrmions form the two-dimensional hexagonal crystal, in a very narrow temperature-magentic field window for bulk crystals but in a much wider one for tens of nanometer thin films under the perpendicular magnetic field applied. We have investigated the stability of two-dimensional skyrmion states emerging in epitaxial thin films of Mn 1−x Fe x Si with various thicknesses t and iron contents x (t = 10, 15, and 20 nm; x = 0, 0.02, and 0.04) by changing the magnetic-field direction. Topological Hall effect arising from the skyrmions is critically suppressed in the course of tilting the applied magnetic field from the normal vector, indicating the collapse of the skyrmion state. Utilizing this observation, the stable region of the skyrmions, which depends on the film thickness relative to the helimagnetic period, can be mapped out in the temperature-magnetic field plane.

arXiv: Mesoscale and Nanoscale Physics, 2019

By introducing nearest neighbor antiferromagnetic biqudratic together with usual ferromagnetic bilinear exchange interaction, we show that the corresponding magnetic system can host spin-spiral structures with shorter pitch length in comparison to usual Dzyaloshinskii-Moriya interaction. By the method of simulated annealing for the model which contains Dzyaloshinskii-Moriya interaction, magnetic anisotropy and magnetic field also, we obtain various noncollinear magnetic structures that are experimentally observed but most of which are not yet theoretically found for the presence of all or the absence of one or more of these parameters: spin-spiral; skyrmion lattice; isolated skyrmions; mixed phase of broken spirals, chiral bubbles, and skyrmions; meron lattice. Our findings based on the proposed model strikingly explain a large number of experiments on skyrmions and related magnetic phases.

Physica B: Condensed Matter, 2017

The stability of magnetic skyrmions against thermal fluctuations and external perturbations is investigated within the framework of harmonic transition state theory for magnetic degrees of freedom. The influence of confined geometry and atomic scale non-magnetic defects on the skyrmion lifetime is estimated. It is shown that a skyrmion on a track has lower activation energy for annihilation and higher energy for nucleation if the size of the skyrmion is comparable with the width of the track. Two mechanisms of skyrmion annihilation are considered: inside the track and escape through the boundary. For both mechanisms, the dependence of activation energy on the track width is calculated. Non-magnetic defects are found to localize skyrmions in their neighborhood and strongly decrease the activation energy for creation and annihilation. This is in agreement with experimental measurements that have found nucleation of skyrmions in presence of spin-polarized current preferably occurring near structural defects.

Physical Review B