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Register a new userDiffusion of a magnetic skyrmion in 2-dimensional space
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Two-dimensional magnetic skyrmions are particle-like magnetic domains in magnetic thin films. The kinetic property of the magnetic skyrmions at finite temperature is well described by the Thiele equation, including a stochastic field and a finite mass. In this paper, the validity of the constant-mass approximation is examined by comparing the Fourier spectrum of Brownian motions described by the Thiele equation and the Landau-Lifshitz-Gilbert equation. Then, the 4-dimensional Fokker-Planck equation is derived from the Thiele equation with a mass-term. Consequently, an expression of the diffusion flow and diffusion constant in a tensor form is derived, extending Chandrasekhars method for Thiele dynamics.
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We show that, in strongly chaotic dynamical systems, the average particle velocity can be calculated analytically by consideration of Brownian dynamics in phase space, the method of images and use of the classical diffusion equation. The method is demonstrated on the simplified Fermi-Ulam accelerator model, which has a mixed phase space with chaotic seas, invariant tori and Kolmogorov-Arnold-Moser (KAM) islands. The calculated average velocities agree well with numerical simulations and with an earlier empirical theory. The procedure can readily be extended to other systems including time-dependent billiards.
Since the 1950s Heisenberg and others have attempted to explain the appearance of countable particles in quantum field theory in terms of stable localized field configurations. As an exception Skyrmes model succeeded to describe nuclear particles as localized states, so-called skyrmions, within a non-linear field theory. Skyrmions are a characteristic of non-linear continuum models ranging from microscopic to cosmological scales. Skyrmionic states have been found under non-equilibrium conditions, or when stabilised by external fields or the proliferation of topological defects. Examples are Turing patterns in classical liquids, spin textures in quantum Hall magnets, or the blue phases in liquid crystals, respectively. However, it is believed that skyrmions cannot form spontaneous ground states like ferromagnetic or antiferromagnetic order in magnetic materials. Here, we show theoretically that this assumption is wrong and that skyrmion textures may form spontaneously in condensed matter systems with chiral interactions without the assistance of external fields or the proliferation of defects. We show this within a phenomenological continuum model, that is based on a few material-specific parameters that may be determined from experiment. As a new condition not considered before, we allow for softened amplitude variations of the magnetisation - a key property of, for instance, metallic magnets. Our model implies that spontaneous skyrmion lattice ground states may exist quite generally in a large number of materials, notably at surfaces and in thin films as well as in bulk compounds, where a lack of space inversion symmetry leads to chiral interactions.
We consider the motion of a test particle in a one-dimensional system of equal-mass point particles. The test particle plays the role of a microscopic piston that separates two hard-point gases with different concentrations and arbitrary initial velocity distributions. In the homogeneous case when the gases on either side of the piston are in the same macroscopic state, we compute and analyze the stationary velocity autocorrelation function C(t). Explicit expressions are obtained for certain typical velocity distributions, serving to elucidate in particular the asymptotic behavior of C(t). It is shown that the occurrence of a non-vanishing probability mass at zero velocity is necessary for the occurrence of a long-time tail in C(t). The conditions under which this is a $t^{-3}$ tail are determined. Turning to the inhomogeneous system with different macroscopic states on either side of the piston, we determine its effective diffusion coefficient from the asymptotic behavior of the variance of its position, as well as the leading behavior of the other moments about the mean. Finally, we present an interpretation of the effective noise arising from the dynamics of the two gases, and thence that of the stochastic process to which the position of any particle in the system reduces in the thermodynamic limit.
The problem of characterizing low-temperature spin dynamics in antiferromagnetic spin chains has so far remained elusive. We reinvestigate it by focusing on isotropic antiferromagnetic chains whose low-energy effective field theory is governed by the quantum non-linear sigma model. We outline an exact non-perturbative theoretical approach to analyse the low-temperature behaviour in the vicinity of non-magnetized states, and obtain explicit expressions for the spin diffusion constant and the NMR relaxation rate, which we compare with previous theoretical results in the literature. Surprisingly, in SU(2)-invariant spin chains in the vicinity of half-filling we find a crossover from the semi-classical regime to a strongly interacting quantum regime characterized by zero spin Drude weight and diverging spin conductivity, indicating super-diffusive spin dynamics. The dynamical exponent of spin fluctuations is argued to belong to the Kardar-Parisi-Zhang universality class. Furthermore, by employing numerical tDMRG simulations, we find robust evidence that the anomalous spin transport persists also at high temperatures, irrespectively of the spectral gap and integrability of the model.
Supplementary information for our manuscript, entitled Spontaneous Skyrmion Ground States of Magnetic Metals, cond-mat/0603103, is presented. The physical nature of the gradient terms of our generalized micromagnetic model for ferromagnets with softened longitudinal fluctuations is explained. The relationship of our micromagnetic model with the spin fluctuation theory of itinerant-electron magnets is discussed. Experimental estimates of the parameter eta, which accounts for an effective reduced longitudinal stiffness, are presented for real materials from published polarized neutron scattering experiments on EuS, Ni and MnSi. The available experimental data clearly show that eta is significantly reduced for the latter two systems. It is suggested that particle-hole excitations are at the root of this longitudinal softness in itinerant-electron ferromagnets. The current status of the experimental evidence supporting spontaneous, amorphous skyrmion textures in MnSi and other materials is reviewed. Finally, we also address the general potential of skyrmion textures in chiral magnets for other fields of physics.
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