Magnon modes and magnon-vortex scattering in two-dimensional easy-plane ferromagnets

Abstract

We calculate the magnon modes in the presence of a vortex on a circular system, combining analytical calculations in the continuum limit with a numerical diagonalization of the discrete system. The magnon modes are expressed by the S-matrix for magnon-vortex scattering, as a function of the parameters and the size of the system and for different boundary conditions. Certain quasi-local translational modes are identified with the frequencies which appear in the trajectory X(t) of the vortex center in recent Molecular Dynamics simulations of the full many-spin model. Using these quasilocal modes we calculate the two parameters of a 3 rd -order equation of motion for X(t). This equation was recently derived by a collective variable theory and describes very well the trajectories observed in the simulations. Both parameters, the vortex mass and the factor in front of ··· X, depend strongly on the boundary conditions. 75.10. Hk,75.40.Gb,75.40.Mg,02.60.Cb

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].…”

Inhomogeneous states in a small magnetic disk with single-ion surface anisotropy

“…The simplest way to describe analytically lattice effects and, in particular, to investigate the local stability of metastable states, is to introduce an effective periodical potential (Peierls-Nabarro potential) into the continuum model. Schnitzer shows, 36 see also, 31 that for in-plane vortices this potential is independent of the values of out-of-plane anisotropy parameters (for λ < 0.8) and can be presented in the simplest form as U P N (x, y) = κJS 2 π[sin 2 (xπ/a) + sin 2 (yπ/a)], where the origin is chosen at the point which is equidistant from lattice sites, and the numeric parameter κ ≃ 0.200. 36 The potential minima are attained at all points like r = ne x + me y , where m, n are integers, |e x | = |e y | = a, and the saddle points are at (n + 1/2)e x + me y and ne x + (m + 1/2)e y .…”

“…This effect could be described as a change of the sign of the effective interaction between the vortex and the border at some value B = B c . (Let us remind that the case B = ∞ corresponds to fixed boundary conditions, while the case B = 0 corresponds to free boundary conditions, which are associated with repulsion and attraction of the vortex to the border, respectively, see 31 .) This effect is present also for big values of the radius, see Fig.…”

“…The first one is the characteristic radius R/r 0 , where r 0 = a J/K at λ = 1 or r 0 = 2a λ/(1 − λ) at K = 0 is the magnetic length, defined in the same way as for bulk materials. 31 The second parameter is the ratio of the exchange integral to the surface anisotropy B/J. To simplify analysis we consider a model with a purely planar spin distribution.…”

Soliton diffusion on the classical, isotropic Heisenberg chain

“…In [2], an exhaustive review of solitons in magnetic systems is given. More recent publications include [3][4][5][6][7][8]. A stronger emphasis on particle physics is put in [9].…”