arXiv subjects

F. G. Mertens

Publications and source records attributed to F. G. Mertens.

40 records · Page 3Linked to original sources

arXiv1999

Hierarchy of equations of motion for nonlinear coherent excitations applied to magnetic vortices

Starting from a travelling wave ansatz we show successively that the shape of a nonlinear excitation generally depends also on the 1st, 2nd, ... time derivative of the position X of the excitation. From the Hamilton equations we derive a hierarchy of equations of motion for X. The type of the excitation determines on which levels the hierarchy can be truncated consistently: "Gyrotropic" excitations are governed by odd-order equations, non-gyrotropic ones by even-order equations. Examples for the latter case are kinks in 1-dimensional models and planar vortices of the 2D anisotropic (easy-plane) Heisenberg model. The non-planar vortices of this model are the simplest gyrotropic example. For this case we solve the Hamilton equations for a finite system with one vortex and free boundary conditions and calculate the parameters of the 3rd-order equation of motion. This equation yields trajectories which are a superposition of two cycloids with different frequencies, which is in full agreement with computer simulations of the full many-spin model. Finally we demonstrate that the additional effects from the 5th-order equation are negligible.

cond-mat↗

arXiv1999

Low Temperature Static and Dynamic Behavior of the Two-Dimensional Easy-Axis Heisenberg Model

We apply the self-consistent harmonic approximation (SCHA) to study static and dynamic properties of the two-dimensional classical Heisenberg model with easy-axis anisotropy. The static properties obtained are magnetization and spin wave energy as functions of temperature, and the critical temperature as a function of the easy-axis anisotropy. We also calculate the dynamic correlation functions using the SCHA renormalized spin wave energy. Our analytical results, for both static properties and dynamic correlation functions, are compared to numerical simulation data combining cluster-Monte Carlo algorithms and Spin Dynamics. The comparison allows us to conclude that far below the transition temperature, where the SCHA is valid, spin waves are responsible for all relevant features observed in the numerical simulation data; topological excitations do not seem to contribute appreciably. For temperatures closer to the transition temperature, there are differences between the dynamic correlation functions from SCHA theory and Spin Dynamics; these may be due to the presence of domain walls and solitons.

cond-mat↗

arXiv1999

Noise-induced switching between vortex states with different polarization in classical two-dimensional easy-plane magnets

In the 2-dimensional anisotropic Heisenberg model with XY-symmetry there are non-planar vortices which exhibit a localized structure of the z-components of the spins around the vortex center. We study how thermal noise induces a transition of this structure from one polarization to the opposite one. We describe the vortex core by a discrete Hamiltonian and consider a stationary solution of the Fokker-Planck equation. We find a bimodal distribution function and calculate the transition rate using Langer's instanton theory (1969). The result is compared with Langevin dynamics simulations for the full many-spin model.

cond-mat↗

arXiv1998

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

We calculate the magnon modes in the presence of a vortex in 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 quasi-local modes we calculate the two parameters of a 3rd-order quation 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 a factor on the third time derivative of X(t), depend strongly on the boundary conditions.

cond-mat.mtrl-sci↗