The motion of domain walls in thin garnet films was investigated numerically using Slonczewski's equations of wall motion for the case of periodic drive field. The type of the wall motion was analyzed by observation of phase trajectories and spatio-temporal diagrams. It was found that depending on the period and amplitude of the drive field the motion of the wall is periodic or chaotic, reflecting the character of the dynamical processes connected with horizontal Bloch lines in the wall.
Three spatially extended one-dimensional dynamical systems are examined by numerical simulations and the time-delay technique is applied to find their dynamics at different positions in space. On the basis of this technique the correlation dimension is calculated from time series obtained at different positions. It is found that the value of the correlation dimension may vary from one position to another, reflecting the spatial inhomogeneity of the system.
Simple models of nonlinear ferromagnetic resonance are considered which describe perpendicular resonance and parallel pumping with the rf field amplitude changing randomly and chaotically in time. On-off intermittency is obtained from the numerical solution of the equations of motion for the spin-wave amplitudes when the mean value of the rf field amplitude exceeds the Suhl instability threshold. Possible experimental applications are discussed.
Electronic structure and local magnetic moments for the epitaxially grown fcc Fe films included between the Cu(001) substrate and Cu(001) covering layers are calculated. The lattice constant of the Fe film is assumed to be equal to that of Cu homogeneously in the whole film. Interface parts of the Fe film are found to be ordered ferromagnetically, while inner part of the Fe film is obtained as ordered layer-by-layer antiferromagnetically for odd number of layers. For even number of Fe layers the most favourable configuration includes antiferromagnetism of inner layers with two middle layers coupled ferromagnetically.
The dynamics of a kicked, anisotropic, damped spin is reduced to a two-dimensional map. This map exhibits such features as bifurcation diagrams, regular or chaotic attractors/repellors and intermittent-like transitions between two strange attractors. With increase of damping a transition from chaos to the fixed point attractor occurs. On the contrary to the Hamiltonian case the type of magnetic anisotropy plays a crucial role for damped models.
General theory of nonlinear ferromagnetic resonance is presented for samples with the usual magnetostatic and exchange boundary conditions imposed at the sample surface. In such samples the Suhl instabilities and other nonlinear effects occur due to nonlinear interactions of magnetostatic or dipole-exchange modes. All relevant types of interactions are included in the Hamiltonian: with the pumping field, three- and four-mode ones. Analytic calculation of the Suhl thresholds in the three possible types of instabilities in perpendicular and parallel pumping is performed for the sample in the shape of a thin slab.
Chaotic dynamics and routes to chaos of domain walls in magnetic bubble garnet materials in the presence of in-plane fields were investigated numerically using Slonczewski's equations of motion. Connection between the structure of the wall and the character of the attractor was found. The in-plane field can play a role of the factor controlling chaos.
Very peculiar electronic structure and local magnetic moment distribution for fcc Fe ultrathin films of 1, 2, 3, and 4 monolayers of thickness, epitaxially grown on Cu(001) substrates and covered with some layers of Cu, are calculated. The lattice constant of the Fe film is assumed to be equal to that of Cu, homogeneously in the whole film. The competition between the surface ferromagnetism and bulk antiferromagnetism results in ferromagnetism of 2-monolayer film, asymmetric solution for 3-monolayer film and antisymmetric solution for 4-monolayer film.
Some non-trivial phenomena in chaos in ferromagnetic resonance above the first-order Suhl instability threshold are obtained numerically from a simple model of three interacting modes. They include sudden changes of the correlation dimension of the attractor and the largest Lyapunov exponent with the rise of the rf field amplitude. Numerical evidence is provided that these effects may result from the on-off intermittency in the system of interacting modes. These results are qualitatively similar to the experimental ones, known from the literature, obtained for in-plane magnetized thin films.
The route to chaos of domain wall in thin magnetic film, which is described by Słonczewski's equations of motion, is analyzed numerically. Hagedorn's model of surface stray field is applied. Ranges of periodic and chaotic wall motion as a function of constant in time, drive field are found. Comparison of results with those obtained for Hubert's model of the stray field is made.
Numerical simulations of noise-free stochastic resonance and aperiodic stochastic resonance in chaotic ferromagnetic resonance are presented. The model, based on three-magnon interactions between the externally excited uniform mode and pairs of spin waves, shows on-off intermittency. The rf magnetic field amplitude is slowly modulated by a small periodic or aperiodic signal, and the output signal, which reflects the occurrence of laminar phases and bursts in the time series of spin-wave amplitudes, is analyzed. On variation of the dc magnetic field the signal-to-noise ratio of the output signal and the correlation function between modulation and output signal pass a maximum, which indicates the occurrence of periodic and aperiodic stochastic resonance, respectively. The role of thermal magnon excitations in the occurrence of this maximum is clarified. The results are compared with experimental findings obtained in other types of intermittency.
Dynamics of a neural network in the form of a linear chain of artificial neurons S_i∈(-1,1) influenced by an external sinusoidal stimulation is investigated as a function of the range k of synaptic connections with random values. Time evolution of the network is periodic for small k, however, clusters of neurons oscillating with a triple period of external stimulation, with quasiperiodic or with chaotic time evolution may occur. For increasing k the number and width of the chaotic clusters increase and for k >4 the chaotic motion occurs in the whole network. A route to chaos in the considered system is discussed.
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