Stochastic Dynamics in Quenched-in Disorder and Hysteresis

The conditions under which relaxation dynamics in the presence of quenched-in disorder lead to rate-independent hysteresis are discussed. The calculation of average hysteresis branches is reduced to the solution of the level-crossing problem for the stochastic field describing quenched-in disorder. Closed analytical solutions are derived for the case where the disorder is characterized by Wiener-Levy statistics. This case is shown to be equivalent to the Preisach model and the associated Preisach distribution is explicitly derived, as a function of the parameters describing the original dynamic problem.Comment: 7 pages, 3 figures, MMM Conference, to be published on J.Appl.Phy

Conservative effects in spin-transfer-driven magnetization dynamics

It is shown that under appropriate conditions spin-transfer-driven magnetization dynamics in a single-domain nanomagnet is conservative in nature and admits a specific integral of motion, which is reduced to the usual magnetic energy when the spin current goes to zero. The existence of this conservation law is connected to the symmetry properties of the dynamics under simultaneous inversion of magnetisation and time. When one applies an external magnetic field parallel to the spin polarization, the dynamics is transformed from conservative into dissipative. More precisely, it is demonstrated that there exists a state function such that the field induces a monotone relaxation of this function toward its minima or maxima, depending on the field orientation. These results hold in the absence of intrinsic damping effects. When intrinsic damping is included in the description, a competition arises between field-induced and damping-induced relaxations, which leads to the appearance of limit cycles, that is, of magnetization self-oscillations.Comment: 5 pages, 3 figure

Domain wall dynamics and Barkhausen effect in metallic ferromagnetic materials. II. Experiments

Barkhausen effect (BE) phenomenology in iron‐based ferromagnetic alloys is investigated by a proper experimental method, in which BE experiments are restricted to the central part of the hysteresis loop, and the amplitude probability distribution, P0(Φ), and power spectrum, F(ω), of the B flux rate Φ are measured under controlled values of the magnetization rate and differential permeability μ. It is found that all of the experimental data are approximately consistent with the law P0(Φ)∝Φ−1 exp(−Φ/〈Φ〉), where all dependencies on and μ are described by the single dimensionless parameter >0. Also the parameters describing the shape of F(ω) are found to obey remarkably simple and general laws of dependence on and μ. The experimental results are interpreted by means of the Langevin theory of domain‐wall dynamics proposed in a companion paper. The theory is in good agreement with experiments, and permits one to reduce the basic aspects of BE phenomenology to the behavior of two parameters describing the stochastic fluctuations of the local coercive field experienced by a moving domain wall

Domain wall dynamics and Barkhausen effect in metallic ferromagnetic materials. I. Theory

The Barkhausen effect (BE) in metallic ferromagnetic systems is theoretically investigated by a Langevin description of the stochastic motion of a domain wall in a randomly perturbed medium. BE statistical properties are calculated from approximate analytical solutions of the Fokker-Planck equation associated with the Langevin model, and from computer simulations of domain‐wall motion. It is predicted that the amplitude probability distribution P0(Φ) of the B flux rate Φ should obey the equation P0(Φ)∝Φ−1 exp(−Φ/〈Φ〉), with >0. This result implies scaling properties in the intermittent behavior of BE at low magnetization rates, which are described in terms of a fractal structure of fractal dimension D<1. Analytical expressions for the B power spectrum are also derived. Finally, the extension of the theory to the case where many domain walls participate in the magnetization process is discussed

Averaging Technique for Random Magnetization Dynamics Driven by a Jump Noise Process

An averaging technique is applied to random magnetization dynamics driven by a jump-noise process. This results in the reduction of this dynamics to stochastic magnetic energy dynamics on graphs. The latter eventually leads to a continuous master equation whose validity is not based on or limited by the Kramers-Brown approximation. An eigenvalue technique for solving this master equation is presented and illustrated by numerical examples