Functional Integration Approach to Hysteresis

A general formulation of scalar hysteresis is proposed. This formulation is based on two steps. First, a generating function g(x) is associated with an individual system, and a hysteresis evolution operator is defined by an appropriate envelope construction applied to g(x), inspired by the overdamped dynamics of systems evolving in multistable free energy landscapes. Second, the average hysteresis response of an ensemble of such systems is expressed as a functional integral over the space G of all admissible generating functions, under the assumption that an appropriate measure m has been introduced in G. The consequences of the formulation are analyzed in detail in the case where the measure m is generated by a continuous, Markovian stochastic process. The calculation of the hysteresis properties of the ensemble is reduced to the solution of the level-crossing problem for the stochastic process. In particular, it is shown that, when the process is translationally invariant (homogeneous), the ensuing hysteresis properties can be exactly described by the Preisach model of hysteresis, and the associated Preisach distribution is expressed in closed analytic form in terms of the drift and diffusion parameters of the Markovian process. Possible applications of the formulation are suggested, concerning the interpretation of magnetic hysteresis due to domain wall motion in quenched-in disorder, and the interpretation of critical state models of superconducting hysteresis.Comment: 36 pages, 9 figures, to be published on Phys. Rev.

Spin-wave instabilities in spin-transfer-driven magnetization dynamics

We study the stability of magnetization precessions induced in spin-transfer devices by the injection of spin-polarized electric currents. Instability conditions are derived by introducing a generalized, far-from-equilibrium interpretation of spin-waves. It is shown that instabilities are generated by distinct groups of magnetostatically coupled spin-waves. Stability diagrams are constructed as a function of external magnetic field and injected spin-polarized current. These diagrams show that applying larger fields and currents has a stabilizing effect on magnetization precessions. Analytical results are compared with numerical simulations of spin-transfer-driven magnetization dynamics.Comment: 4 pages, 2 figure

Efficient adaptive pseudo-symplectic numerical integration techniques for Landau-Lifshitz dynamics

Numerical time integration schemes for Landau-Lifshitz magnetization dynamics are considered. Such dynamics preserves the magnetization amplitude and, in the absence of dissipation, also implies the conservation of the free energy. This property is generally lost when time discretization is performed for the numerical solution. In this work, explicit numerical schemes based on Runge-Kutta methods are introduced. The schemes are termed pseudo-symplectic in that they are accurate to order p, but preserve magnetization amplitude and free energy to order q > p. An effective strategy for adaptive time-stepping control is discussed for schemes of this class. Numerical tests against analytical solutions for the simulation of fast precessional dynamics are performed in order to point out the effectiveness of the proposed methods

Concave Plasmonic Particles: Broad-Band Geometrical Tunability in the Near Infra-Red

Optical resonances spanning the Near and Short Infra-Red spectral regime were exhibited experimentally by arrays of plasmonic nano-particles with concave cross-section. The concavity of the particle was shown to be the key ingredient for enabling the broad band tunability of the resonance frequency, even for particles with dimensional aspect ratios of order unity. The atypical flexibility of setting the resonance wavelength is shown to stem from a unique interplay of local geometry with surface charge distributions

Magnetoelastic effects in Jahn-Teller distorted CrF2_2 and CuF2_2 studied by neutron powder diffraction

We have studied the temperature dependence of crystal and magnetic structures of the Jahn-Teller distorted transition metal difluorides CrF$_2$ and CuF$_2$ by neutron powder diffraction in the temperature range 2-280 K. The lattice parameters and the unit cell volume show magnetoelastic effects below the N\'eel temperature. The lattice strain due to the magnetostriction effect couples with the square of the order parameter of the antiferromagnetic phase transition. We also investigated the temperature dependence of the Jahn-Teller distortion which does not show any significant effect at the antiferromagnetic phase transition but increases linearly with increasing temperature for CrF$_2$ and remains almost independent of temperature in CuF$_2$. The magnitude of magnetovolume effect seems to increase with the low temperature saturated magnetic moment of the transition metal ions but the correlation is not at all perfect

Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations

We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche fluctuations. There is a critical value of disorder at which a jump in the magnetization (corresponding to an infinite avalanche) first occurs. We study the universal behavior at this critical point using mean-field theory, and also present preliminary results of numerical simulations in three dimensions.Comment: 12 pages plus 2 appended figures, plain TeX, CU-MSC-747

Stochastic Hysteresis and Resonance in a Kinetic Ising System

We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on small systems and weak field amplitudes at a temperature below $T_{c}$. For these restricted parameters, the magnetization switches through random nucleation of a single droplet of spins aligned with the applied field. We analyze the stochastic hysteresis observed in this parameter regime, using time-dependent nucleation theory and the theory of variable-rate Markov processes. The theory enables us to accurately predict the results of extensive Monte Carlo simulations, without the use of any adjustable parameters. The stochastic response is qualitatively different from what is observed, either in mean-field models or in simulations of larger spatially extended systems. We consider the frequency dependence of the probability density for the hysteresis-loop area and show that its average slowly crosses over to a logarithmic decay with frequency and amplitude for asymptotically low frequencies. Both the average loop area and the residence-time distributions for the magnetization show evidence of stochastic resonance. We also demonstrate a connection between the residence-time distributions and the power spectral densities of the magnetization time series. In addition to their significance for the interpretation of recent experiments in condensed-matter physics, including studies of switching in ferromagnetic and ferroelectric nanoparticles and ultrathin films, our results are relevant to the general theory of periodically driven arrays of coupled, bistable systems with stochastic noise.Comment: 35 pages. Submitted to Phys. Rev. E Minor revisions to the text and updated reference