Micromagnetic simulations of the magnetization precession induced by a spin polarized current in a point contact geometry

This paper is devoted to numerical simulations of the magnetization dynamics driven by a spin-polarized current in extended ferromagnetic multilayers when a point-contact setup is used. We present (i) detailed analysis of methodological problems arising by such simulations and (ii) physical results obtained on a system similar to that studied in Rippard et al., Phys. Rev. Lett., v. 92, 027201 (2004). We demonstrate that the usage of a standard Slonczewski formalism for the phenomenological treatment of a spin-induced torque leads to a qualitative disagreement between simulation results and experimental observations and discuss possible reasons for this discrepancy.Comment: Invited paper on MMM2005 (San Jose); accepted for publication in J. Applied Physic

Magnetization precession due to a spin polarized current in a thin nanoelement: numerical simulation study

In this paper a detailed numerical study (in frames of the Slonczewski formalism) of magnetization oscillations driven by a spin-polarized current through a thin elliptical nanoelement is presented. We show that a sophisticated micromagnetic model, where a polycrystalline structure of a nanoelement is taken into account, can explain qualitatively all most important features of the magnetization oscillation spectra recently observed experimentally (S.I. Kiselev et al., Nature, vol. 425, p. 380 (2003), namely: existence of several equidistant spectral bands, sharp onset and abrupt disappearance of magnetization oscillations with increasing current, absence of the out-of-plane regime predicted by a macrospin model and the relation between frequencies of so called small-angle and quasichaotic oscillations. However, a quantitative agreement with experimental results (especially concerning the frequency of quasichaotic oscillations) could not be achieved in the region of reasonable parameter values, indicating that further model refinement is necessary for a complete understanding of the spin-driven magnetization precession even in this relatively simple experimental situation.Comment: Submitted to Phys. Rev. B; In this revised version figure positions on the page have been changed to ensure correct placements of the figure caption

Extinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach

The extinction of a single species due to demographic stochasticity is analyzed. The discrete nature of the individual agents and the Poissonian noise related to the birth-death processes result in local extinction of a metastable population, as the system hits the absorbing state. The Fokker-Planck formulation of that problem fails to capture the statistics of large deviations from the metastable state, while approximations appropriate close to the absorbing state become, in general, invalid as the population becomes large. To connect these two regimes, a master equation based on a real space WKB method is presented, and is shown to yield an excellent approximation for the decay rate and the extreme events statistics all the way down to the absorbing state. The details of the underlying microscopic process, smeared out in a mean field treatment, are shown to be crucial for an exact determination of the extinction exponent. This general scheme is shown to reproduce the known results in the field, to yield new corollaries and to fit quite precisely the numerical solutions. Moreover it allows for systematic improvement via a series expansion where the small parameter is the inverse of the number of individuals in the metastable state

Coulomb Drag between One-Dimensional Wigner Crystal Rings

We consider the Coulomb drag between two metal rings in which the long range Coulomb interaction leads to the formation of a Wigner crystal. The first ring is threaded by an Ahranov Bohm flux creating a persistent current J_0. The second ring is brought in close proximity to the second and due to the Coulomb interaction between the two rings a drag current J_D is produced in the second. We investigate this system at zero temperature for perfect rings as well as the effects of impurities. We show that the Wigner crystal state can in principle lead to a higher ratio of drag current to drive current J_D/J_0 than in weakly interacting electron systems.Comment: 12 pages, 10 figure

Crossover from Rate-Equation to Diffusion-Controlled Kinetics in Two-Particle Coagulation

We develop an analytical diffusion-equation-type approximation scheme for the one-dimensional coagulation reaction A+A->A with partial reaction probability on particle encounters which are otherwise hard-core. The new approximation describes the crossover from the mean-field rate-equation behavior at short times to the universal, fluctuation-dominated behavior at large times. The approximation becomes quantitatively accurate when the system is initially close to the continuum behavior, i.e., for small initial density and fast reaction. For large initial density and slow reaction, lattice effects are nonnegligible for an extended initial time interval. In such cases our approximation provides the correct description of the initial mean-field as well as the asymptotic large-time, fluctuation-dominated behavior. However, the intermediate-time crossover between the two regimes is described only semiquantitatively.Comment: 21 pages, plain Te

Diffusion-Limited Aggregation Processes with 3-Particle Elementary Reactions

A diffusion-limited aggregation process, in which clusters coalesce by means of 3-particle reaction, A+A+A->A, is investigated. In one dimension we give a heuristic argument that predicts logarithmic corrections to the mean-field asymptotic behavior for the concentration of clusters of mass $m$ at time $t$, $c(m,t)~m^{-1/2}(log(t)/t)^{3/4}$, for $1 << m << \sqrt{t/log(t)}$. The total concentration of clusters, $c(t)$, decays as $c(t)~\sqrt{log(t)/t}$ at $t --> \infty$. We also investigate the problem with a localized steady source of monomers and find that the steady-state concentration $c(r)$ scales as $r^{-1}(log(r))^{1/2}$, $r^{-1}$, and $r^{-1}(log(r))^{-1/2}$, respectively, for the spatial dimension $d$ equal to 1, 2, and 3. The total number of clusters, $N(t)$, grows with time as $(log(t))^{3/2}$, $t^{1/2}$, and $t(log(t))^{-1/2}$ for $d$ = 1, 2, and 3. Furthermore, in three dimensions we obtain an asymptotic solution for the steady state cluster-mass distribution: $c(m,r) \sim r^{-1}(log(r))^{-1}\Phi(z)$, with the scaling function $\Phi(z)=z^{-1/2}\exp(-z)$ and the scaling variable $z ~ m/\sqrt{log(r)}$.Comment: 12 pages, plain Te

Subdiffusion-limited reactions

We consider the coagulation dynamics A+A -> A and A+A A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems, each of which leads to interesting dynamics separately and to even more interesting dynamics in combination. Our analysis is based on the fractional diffusion equation

A Method of Intervals for the Study of Diffusion-Limited Annihilation, A + A --> 0

We introduce a method of intervals for the analysis of diffusion-limited annihilation, A+A -> 0, on the line. The method leads to manageable diffusion equations whose interpretation is intuitively clear. As an example, we treat the following cases: (a) annihilation in the infinite line and in infinite (discrete) chains; (b) annihilation with input of single particles, adjacent particle pairs, and particle pairs separated by a given distance; (c) annihilation, A+A -> 0, along with the birth reaction A -> 3A, on finite rings, with and without diffusion.Comment: RevTeX, 13 pages, 4 figures, 1 table. References Added, and some other minor changes, to conform with final for

On Matrix Product Ground States for Reaction-Diffusion Models

We discuss a new mechanism leading to a matrix product form for the stationary state of one-dimensional stochastic models. The corresponding algebra is quadratic and involves four different matrices. For the example of a coagulation-decoagulation model explicit four-dimensional representations are given and exact expressions for various physical quantities are recovered. We also find the general structure of $n$-point correlation functions at the phase transition.Comment: LaTeX source, 7 pages, no figure

Multiparticle Reactions with Spatial Anisotropy

We study the effect of anisotropic diffusion on the one-dimensional annihilation reaction kA->inert with partial reaction probabilities when hard-core particles meet in groups of k nearest neighbors. Based on scaling arguments, mean field approaches and random walk considerations we argue that the spatial anisotropy introduces no appreciable changes as compared to the isotropic case. Our conjectures are supported by numerical simulations for slow reaction rates, for k=2 and 4.Comment: nine pages, plain Te