Non-Markovian magnetization dynamics for uniaxial nanomagnets

A stochastic approach for the description of the time evolution of the magnetization of nanomagnets is proposed, that interpolates between the Landau-Lifshitz-Gilbert and the Landau-Lifshitz-Bloch approximations, by varying the strength of the noise. Its finite autocorrelation time, i.e. when it may be described as colored, rather than white, is, also, taken into account and the consequences, on the scale of the response of the magnetization are investigated. It is shown that the hierarchy for the moments of the magnetization can be closed, by introducing a suitable truncation scheme, whose validity is tested by direct numerical solution of the moment equations and compared to the averages obtained from a numerical solution of the corresponding colored stochastic Langevin equation. This comparison is performed on magnetic systems subject to both an external uniform magnetic field and an internal one-site uniaxial anisotropy.Comment: 4 pages, 3 figure

Quantum Magnets and Matrix Lorenz Systems

The Landau--Lifshitz--Gilbert equations for the evolution of the magnetization, in presence of an external torque, can be cast in the form of the Lorenz equations and, thus, can describe chaotic fluctuations. To study quantum effects, we describe the magnetization by matrices, that take values in a Lie algebra. The finite dimensionality of the representation encodes the quantum fluctuations, while the non-linear nature of the equations can describe chaotic fluctuations. We identify a criterion, for the appearance of such non-linear terms. This depends on whether an invariant, symmetric tensor of the algebra can vanish or not. This proposal is studied in detail for the fundamental representation of $\mathfrak{u}(2)=\mathfrak{u}(1)\times\mathfrak{su}(2)$. We find a knotted structure for the attractor, a bimodal distribution for the largest Lyapunov exponent and that the dynamics takes place within the Cartan subalgebra, that does not contain only the identity matrix, thereby can describe the quantum fluctuations.Comment: 5 pages, 3 figures. Uses jpconf style. Presented at the ICM-SQUARE 4 conference, Madrid, August 2014. The topic is a special case of the content of 1404.7774, currently under revisio

A functional calculus for the magnetization dynamics

A functional calculus approach is applied to the derivation of evolution equations for the moments of the magnetization dynamics of systems subject to stochastic fields. It allows us to derive a general framework for obtaining the master equation for the stochastic magnetization dynamics, that is applied to both, Markovian and non-Markovian dynamics. The formalism is applied for studying different kinds of interactions, that are of practical relevance and hierarchies of evolution equations for the moments of the distribution of the magnetization are obtained. In each case, assumptions are spelled out, in order to close the hierarchies. These closure assumptions are tested by extensive numerical studies, that probe the validity of Gaussian or non--Gaussian closure Ans\"atze.Comment: 17 pages, 5 figure

Closing the hierarchy for non-Markovian magnetization dynamics

We propose a stochastic approach for the description of the time evolution of the magnetization of nanomagnets, that interpolates between the Landau--Lifshitz--Gilbert and the Landau--Lifshitz--Bloch approximations, by varying the strength of the noise. In addition, we take into account the autocorrelation time of the noise and explore the consequences, when it is finite, on the scale of the response of the magnetization, i.e. when it may be described as colored, rather than white, noise and non-Markovian features become relevant. We close the hierarchy for the moments of the magnetization, by introducing a suitable truncation scheme, whose validity is tested by direct numerical solution of the moment equations and compared to the average deduced from a numerical solution of the corresponding stochastic Langevin equation. In this way we establish a general framework, that allows both coarse-graining simulations and faster calculations beyond the truncation approximation used here.Comment: 5 pages LaTeX2e, 2 EPS figures; uses elsarticle.cls. Presented at HMM 2015, 10th International Symposium on Hysteresis Modeling and Micromagnetic

Colored-noise magnetization dynamics: from weakly to strongly correlated noise

Statistical averaging theorems allow us to derive a set of equations for the averaged magnetization dynamics in the presence of colored (non-Markovian) noise. The non-Markovian character of the noise is described by a finite auto-correlation time, tau, that can be identified with the finite response time of the thermal bath to the system of interest. Hitherto, this model was only tested for the case of weakly correlated noise (when tau is equivalent or smaller than the integration timestep). In order to probe its validity for a broader range of auto-correlation times, a non-Markovian integration model, based on the stochastic Landau-Lifshitz-Gilbert equation is presented. Comparisons between the two models are discussed, and these provide evidence that both formalisms remain equivalent, even for strongly correlated noise (i.e. tau much larger than the integration timestep).Comment: 4 pages LaTeX2e, 3 EPS figures; uses IEEEtran.cl

Frequency-dependent effective permeability tensor of unsaturated polycrystalline ferrites

Frequency-dependent permeability tensor for unsaturated polycrystalline ferrites is derived through an effective medium approximation that combines both domain-wall motion and rotation of domains in a single consistent scattering framework. Thus derived permeability tensor is averaged on a distribution function of the free energy that encodes paramagnetic states for anhysteretic loops. The initial permeability is computed and frequency spectra are given by varying macroscopic remanent field.Comment: 24 pages, 3 figure

Wave propagation and spatial dispersion in random media

4 pages, 2 figuresInternational audienceThe study of spatial dispersion in electromagnetic wave propagation in random media is approached via the quasi-crystalline approximation in the framework of multiple-scattering theory. Longitudinal and transverse permittivity kernels are obtained explicitly by using a simplified resonant model for the T-matrix of the scatterers. The transverse dispersion equation is solved numerically for all its frequency-dependent solutions in a given domain of the complex plane. The physical meaning of these solutions is discussed

The Off-Shell Electromagnetic T-matrix: momentum-dependent scattering from spherical inclusions with both dielectric and magnetic contrast

The momentum- and frequency-dependent T-matrix operator for the scattering of electromagnetic waves by a dielectric/conducting and para- or diamagnetic sphere is derived as a Mie-type series, and presented in a compact form emphasizing various symmetry properties, notably the unitarity identity. This result extends to magnetic properties one previously obtained for purely dielectric contrasts by other authors. Several situations useful to spatially-dispersive effective-medium approximations to one-body order are examined. Partial summation of the Mie series is achieved in the case of elastic scattering.Comment: 22 pages. Preprint of a paper to appear in `Waves in Complex And Random Media' ((c) Taylor and Francis, 2011

Thermostatting the atomic spin dynamics from controlled demons

International audienc