Chiral magnetic skyrmions with arbitrary topological charge

Abstract

We show that continuous and spin-lattice models of chiral ferro-and antiferromagnets provide the existence of an infinite number of stable soliton solutions of any integer topological charge. A detailed description of the morphology of new skyrmions and the corresponding energy dependencies are provided. The considered model is general, and is expected to predict a plethora of particle-like states which may occur in various chiral magnets including atomic layers, e.g., PdFe/Ir(111), rhombohedral GaV4S8 semiconductor, B20-type alloys as Mn1−xFexGe, Mn1−xFexSi, Fe1−xCoxSi, Cu2OSeO3, acentric tetragonal Heusler compounds.

Gauged sigma models and magnetic Skyrmions

“…to obtain a well-defined variational problem. Clearly, (13) reduces to (12) for the simple gauge field (7). Adding the term (13) to the energy (3) has a number of advantages, at least from an analytical point of view.…”

“…1, we show examples of such solutions in a model with standard DM term (n, ∇ × n) and the potential 1 2 (1 − n 3 ) 2 . They include the axisymmetric skyrmion configuration (which has topological charge Q = 1 in our conventions), a line defect (Q = 0), an anti-skyrmion configuration (Q = 1) as well as bags and multi-(anti)-skyrmion configurations which show qualitative features of the configurations studied numerically in [12] and [13].…”

Spirit : Multifunctional framework for atomistic spin simulations

“…The functionality of the aforementioned softwares can be greatly extended by adding an interactive graphical user interface (GUI) that can be used to control calculations in real time -to not only change parameters, but also interact with the spin texture as demonstrated for example in Ref. 10. Together with such a GUI, Spirit unifies various computational methods that are commonly applied to atomistic (and in part also to micromagnetic) simulations: Monte Carlo and Landau Lifshitz Gilbert (LLG) dynamics, 11 the geodesic nudged elastic band (GNEB) method 12 , minimum mode following 13 (MMF), harmonic transition-state theory 14 (HTST), and the visualization of eigenmodes.…”

Turning a chiral skyrmion inside out

“…It is assumed that magnetization remains homogeneous along the thickness, t. The DMI term w(n) is defined by combinations of Lifshitz invariants, ΛThe re-sults presented in this letter are valid for a wide class of chiral magnets of different crystal symmetries with: Néeltype modulations [22][23][24] The last term in (1) represents the potential energy term including uniaxial anisotropy, U a = K (1 − n 2 z ) and the Zeeman energy -the interaction with an external magnetic field, U Z = M s B · n. The distances, magnetic fields and energies are given in dimensionless units relative to: the equilibrium period of helical spin spiral [29,30],the critical field [30], B D = D 2 /(2M s A) and the energy of saturated state, E 0 = 2At, respectively. The dimensionless magnetic field h = B/B D and anisotropy u = K/ (M s B D ) are unique control parameters of the system.For direct energy minimization of (1) we use a nonlinear conjugate gradient (NCG) method implemented for NVIDIA CUDA architecture and optimized for the best performance by the advanced numerical scheme atlas [31,32]. We use a fourth-order finite-difference scheme on a regular square grid with periodical boundary conditions [32].…”

“…The dimensionless magnetic field h = B/B D and anisotropy u = K/ (M s B D ) are unique control parameters of the system.For direct energy minimization of (1) we use a nonlinear conjugate gradient (NCG) method implemented for NVIDIA CUDA architecture and optimized for the best performance by the advanced numerical scheme atlas [31,32]. We use a fourth-order finite-difference scheme on a regular square grid with periodical boundary conditions [32]. The typical size of the simulated domain is ∼ 10L D ×10L D with a mesh density ∆l given in the number of nodes per L D , varying from 32 to 1024.…”