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.

The effect of additive noise on dynamical hysteresis

We investigate the properties of hysteresis cycles produced by a one-dimensional, periodically forced Langevin equation. We show that depending on amplitude and frequency of the forcing and on noise intensity, there are three qualitatively different types of hysteresis cycles. Below a critical noise intensity, the random area enclosed by hysteresis cycles is concentrated near the deterministic area, which is different for small and large driving amplitude. Above this threshold, the area of typical hysteresis cycles depends, to leading order, only on the noise intensity. In all three regimes, we derive mathematically rigorous estimates for expectation, variance, and the probability of deviations of the hysteresis area from its typical value.Comment: 30 pages, 5 figure

Exact Solution of Return Hysteresis Loops in One Dimensional Random Field Ising Model at Zero Temperature

Minor hysteresis loops within the main loop are obtained analytically and exactly in the one-dimensional ferromagnetic random field Ising-model at zero temperature. Numerical simulations of the model show excellent agreement with the analytical results

Magnetization Reversal and Nanoscopic Magnetic Phase Separation in Doped La1-xSrxCoO3

The doped perovskite cobaltite La1-xSrxCoO3 (LSCO) has been advanced as a model system for studying intrinsic magnetic phase separation. We have employed a first-order reversal curve (FORC) method to probe the amount of irreversible switching in bulk polycrystalline LSCO as a function of Sr doping, field cooling procedure, and temperature. The value of the FORC distribution, rho, is used as a measure of the extent of irreversible switching. For x < 0.18, the small values of rho and its ridge-like distribution along local coercivity (Hc) and zero bias (Hb), are characteristic of non-interacting single domain particles. This is consistent with the formation of an array of isolated nanoscopic ferromagnetic clusters, as observed in previous work. For x >= 0.18, the much larger values of rho, the tilting of its distribution towards negative bias field, and the emergence of regions with negative rho, are consistent with increased long-range ferromagnetic ordering. The FORC distributions display little dependence on the cooling procedure. With increasing temperature, the fraction of irreversible switching determined from the FORC distribution follows closely the ferromagnetic phase fraction measured by La nuclear magnetic resonance. Our results furthermore demonstrate that the FORC method is a valuable first-pass characterization tool for magnetic phase separation.Comment: 30 pages, 8 figures, to appear in PR

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

Quantification of magnetic force microscopy images using combined electrostatic and magnetostatic imaging

A method for calibrating the force gradients and probe magnetic moment in phase-contrast magnetic force microscopy ~MFM! is introduced. It is based upon the combined electrostatic force microscopy EFM and MFM images of a conducting non magnetic metal strip. The behavior of the phase contrast in EFM is analyzed and modeled as a finite area capacitor. This model is used in conjunction with the imaging data to derive the proportionality constant between the phase and the force gradient. This calibration is further used to relate the measured MFM images with the field gradient from the same conducting strip to derive the effective magnetic moment of the probe. The knowledge of the phase-force gradient proportionality constant and the probe’s effective moment is essential to directly quantify field derivatives in MFM images

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