Internal modes and magnon scattering on topological solitons in two-dimensional easy-axis ferromagnets

Abstract

We study the magnon modes in the presence of a topological soliton in a 2d Heisenberg easy-axis ferromagnet. The problem of magnon scattering on the soliton with arbitrary relation between the soliton radius R and the "magnetic length" ∆ 0 is investigated for partial modes with different values of the azimuthal quantum numbers m. Truly local modes are shown to be present for all values of m, when the soliton radius is enough large. The eigenfrequencies of such internal modes are calculated analytically on limiting case of a large soliton radius and numerically for arbitrary soliton radius. It is demonstrated that the model of an isotropic magnet, which admits an exact analytical investigation, is not adequate even for the limit of small radius solitons, R ≪ ∆ 0 : there exists a local mode with nonzero frequency. We use the data about local modes to derive the effective equation of soliton motion; this equation has the usual Newtonian form in contrast to the case of the easy-plane ferromagnet. The effective mass of the soliton is found. 75.10.Hk, 75.30.Ds, 75.70.Kw

Generalized Levinson theorem for singular potentials in two dimensions

“…At the same time it provides a method to count bound states. The method can be used in various 2D field theories with applications to the physics of 2D plasma [30,31], nuclear physics [32], quantum Hall effect [33], and 2D magnetism [34,35,36,37].…”

“…Potentials like (20) are of interest in field theories: in the (2+1) nonlinear σ-model of the n-field [32,35], in models of 2D easy-axis [36] and easy-plane ferromagnets in the cone state [37].…”

Scattering of high-energy magnons off a magnetic skyrmion

“…(33), we recover Eqs. (46) and (47). For the understanding of the universality of F ⊥ , it is also instructive to consider alternatively the right-hand side of the classical equations of motion (48).…”

“…[45][46][47][48] We introduce the local orthogonal frameê iêj = δ ij withê 1 ×ê 2 =ê 3 , whereê 3 (r) = n s (r) tracks the skyrmion profile. For the two orthogonal vectors we useê T 1 = (− sin ϕ, cos ϕ, 0) and e T 2 = (− cos θ cos ϕ, sin θ sin ϕ, cos θ).…”

Spin excitation spectrum in a magnetic nanodot with continuous transitions between the vortex, Bloch-type skyrmion, and Néel-type skyrmion states

“…Typically the Belavin-Polyakov (no magnetic anisotropy) solitons 17 and the precessional solitons in uniaxial "easy" axis ferromagnets 18 were considered. The need to consider precession of the magnetic solitons appeared due to the problem with the soliton stability in the absence of the high-order exchange or Dzyaloshinskii-Moriya exchange interaction.…”