arXiv subjects

M. A. Novotny

Publications and source records attributed to M. A. Novotny.

108 records · Page 6Linked to original sources

arXiv1997

Magnetization Switching in Single-Domain Ferromagnets

A model for single-domain uniaxial ferromagnetic particles with high anisotropy, the Ising model, is studied. Recent experimental observations have been made of the probability that the magnetization has not switched. Here an approach is described in which it is emphasized that a ferromagnetic particle in an unfavorable field is in fact a metastable system, and the switching is accomplished through the nucleation and subsequent growth of localized droplets. Nucleation theory is applied to finite systems to determine the coercivity as a function of particle size and to calculate the probability of not switching. Both of these quantities are modified by different boundary conditions, magnetostatic interactions, and quenched disorder.

cond-mat.mtrl-sci↗

arXiv1997

Kinetic Ising System in an Oscillating External Field: Stochastic Resonance and Residence-Time Distributions

Experimental, analytical, and numerical results suggest that the mechanism by which a uniaxial single-domain ferromagnet switches after sudden field reversal depends on the field magnitude and the system size. Here we report new results on how these distinct decay mechanisms influence hysteresis in a two-dimensional nearest-neighbor kinetic Ising model. We present theoretical predictions supported by numerical simulations for the frequency dependence of the probability distributions for the hysteresis-loop area and the period-averaged magnetization, and for the residence-time distributions. The latter suggest evidence of stochastic resonance for small systems in moderately weak oscillating fields.

cond-mat↗

arXiv1997

Monte Carlo Simulation of Magnetization Reversal in Fe Sesquilayers on W(110)

Iron sesquilayers grown at room temperature on W(110) exhibit a pronounced coercivity maximum near a coverage of 1.5 atomic monolayers. On lattices which faithfully reproduce the morphology of the real films, a kinetic Ising model is utilized to simulate the domain-wall motion. Simulations reveal that the dynamics is dominated by the second-layer islands, which act as pinning centers. The simulated dependencies of the coercivity on the film coverage, as well as on the temperature and the frequency of the applied field, are very similar to those measured in experiments. Unlike previous micromagnetic models, the presented approach provides insight into the dynamics of the domain-wall motion and clearly reveals the role of thermal fluctuations.

cond-mat↗

arXiv1997

Extrapolation-CAM Theory for Critical Exponents

By intentionally underestimating the rate of convergence of exact-diagonalization values for the mass or energy gaps of finite systems, we form families of sequences of gap estimates. The gap estimates cross zero with generically nonzero linear terms in their Taylor expansions, so that $ν= 1$ for each member of these sequences of estimates. Thus, the Coherent Anomaly Method can be used to determine $ν$. Our freedom in deciding exactly how to underestimate the convergence allows us to choose the sequence that displays the clearest coherent anomaly. We demonstrate this approach on the two-dimensional ferromagnetic Ising model, for which $ν= 1$. We also use it on the three-dimensional ferromagnetic Ising model, finding $ν\approx 0.629$, in good agreement with other estimates.

cond-mat.stat-mech↗

arXiv1997

Nucleation Theory of Magnetization Switching in Nanoscale Ferromagnets

A nucleation picture of magnetization switching in single-domain ferromagnetic nanoparticles with high local anisotropy is discussed. Relevant aspects of nucleation theory are presented, stressing the effects of the particle size on the switching dynamics. The theory is illustrated by Monte Carlo simulations and compared with experiments on single particles.

cond-mat.mtrl-sci↗

arXiv1997

Equilibrium and nonequilibrium applications of lattice-gas models in electrochemistry

We discuss applications of statistical-mechanical lattice-gas models to study static and dynamic aspects of electrochemical adsorption. The strategy developed to describe specific systems includes microscopic model formulation, calculation of zero-temperature phase diagrams, numerical simulation of thermodynamic and structural quantities at nonzero temperatures, and estimation of effective, lateral interactions. We briefly review earlier work, including studies by Monte Carlo simulation of the adsorption of urea on Pt(100). As an illustrative example, we discuss in some detail recent applications to the underpotential deposition of Cu with sulfate on Au(111). Experimental and numerical results are included for equilibrium coverages and voltammetric currents at slow potential sweep rates, and new results from dynamic Monte Carlo simulations are presented. In particular, we present simulated results for current transients far from equilibrium, following sudden changes in the electrode potential.

cond-mat↗

arXiv1997

Projected dynamics for metastable decay in Ising models

The magnetization switching dynamics in the kinetic Ising model is projected onto a one-dimensional absorbing Markov chain. The resulting projected dynamics reproduces the direct simulation results with great accuracy. A scheme is proposed to utilize simulation data for small systems to obtain the metastable lifetime for large systems and/or for very weak magnetic fields, for which direct simulation is not feasible.

cond-mat↗

arXiv1996

Effects of boundary conditions on magnetization switching in kinetic Ising models of nanoscale ferromagnets

Magnetization switching in highly anisotropic single-domain ferromagnets has been previously shown to be qualitatively described by the droplet theory of metastable decay and simulations of two-dimensional kinetic Ising systems with periodic boundary conditions. In this article we consider the effects of boundary conditions on the switching phenomena. A rich range of behaviors is predicted by droplet theory: the specific mechanism by which switching occurs depends on the structure of the boundary, the particle size, the temperature, and the strength of the applied field. The theory predicts the existence of a peak in the switching field as a function of system size in both systems with periodic boundary conditions and in systems with boundaries. The size of the peak is strongly dependent on the boundary effects. It is generally reduced by open boundary conditions, and in some cases it disappears if the boundaries are too favorable towards nucleation. However, we also demonstrate conditions under which the peak remains discernible. This peak arises as a purely dynamic effect and is not related to the possible existence of multiple domains. We illustrate the predictions of droplet theory by Monte Carlo simulations of two-dimensional Ising systems with various system shapes and boundary conditions.

cond-mat↗

arXiv1996

Magnetization switching in nanoscale ferromagnetic grains: simulations with heterogeneous nucleation

We present results obtained with various types of heterogeneous nucleation in a kinetic Ising model of magnetization switching in single-domain ferromagnetic nanoparticles. We investigate the effect of the presence of the system boundary and make comparison with simulations on periodic lattices. We also study systems with bulk disorder and compare how two different types of disorder influence the switching behavior.

cond-mat↗

arXiv1995

Numerical Study of a Mixed Ising Ferrimagnetic System

We present a study of a classical ferrimagnetic model on a square lattice in which the two interpenetrating square sublattices have spins one-half and one. This model is relevant for understanding bimetallic molecular ferrimagnets that are currently being synthesized by several experimental groups. We perform exact ground-state calculations for the model and employ Monte Carlo and numerical transfer-matrix techniques to obtain the finite-temperature phase diagram for both the transition and compensation temperatures. When only nearest-neighbor interactions are included, our nonperturbative results indicate no compensation point or tricritical point at finite temperature, which contradicts earlier results obtained with mean-field analysis.

cond-mat↗

arXiv1995

Response of Kinetic Ising System to Oscillating External Fields: Amplitude and Frequency Dependence

The S=1/2, nearest-neighbor, kinetic Ising model has been used to model magnetization switching in nanoscale ferromagnets. For this model, earlier work based on the droplet theory of the decay of metastable phases and Monte Carlo simulations has shown the existence of a size dependent spinodal field which separates deterministic and stochastic decay regimes. We extend the above work to study the effects of an oscillating field on the magnetization response of the kinetic Ising model. We compute the power spectral density of the time-dependent magnetization for different values of the amplitude and frequency of the external field, using Monte Carlo simulation data. We also investigate the amplitude and frequency dependence of the probability distributions for the hysteresis loop area and the period-averaged magnetization. The time-dependent response of the system is classified by analyzing the behavior of these quantities within the framework of the distinct deterministic and stochastic decay modes mentioned above.

cond-mat↗

arXiv1995

Monte Carlo with Absorbing Markov Chains: Fast Local Algorithms for Slow Dynamics

A class of Monte Carlo algorithms which incorporate absorbing Markov chains is presented. In a particular limit, the lowest-order of these algorithms reduces to the $n$-fold way algorithm. These algorithms are applied to study the escape from the metastable state in the two-dimensional square-lattice nearest-neighbor Ising ferromagnet in an unfavorable applied field, and the agreement with theoretical predictions is very good. It is demonstrated that the higher-order algorithms can be many orders of magnitude faster than either the traditional Monte Carlo or $n$-fold way algorithms.

cond-mat↗

arXiv1995

A Method to Study Relaxation of Metastable Phases: Macroscopic Mean-Field Dynamics

We propose two different macroscopic dynamics to describe the decay of metastable phases in many-particle systems with local interactions. These dynamics depend on the macroscopic order parameter $m$ through the restricted free energy $F(m)$ and are designed to give the correct equilibrium distribution for $m$. The connection between macroscopic dynamics and the underlying microscopic dynamic are considered in the context of a projection- operator formalism. Application to the square-lattice nearest-neighbor Ising ferromagnet gives good agreement with droplet theory and Monte Carlo simulations of the underlying microscopic dynamic. This includes quantitative agreement for the exponential dependence of the lifetime on the inverse of the applied field $H$, and the observation of distinct field regions in which the derivative of the lifetime with respect to $1/H$ depends differently on $H$. In addition, at very low temperatures we observe oscillatory behavior of this derivative with respect to $H$, due to the discreteness of the lattice and in agreement with rigorous results. Similarities and differences between this work and earlier works on finite Ising models in the fixed-magnetization ensemble are discussed.

cond-mat↗

arXiv1994

Magnetization switching in nanoscale ferromagnetic grains: description by a kinetic Ising model

The magnetic relaxation of ferromagnetic powders has been studied for many years, largely due to its importance to recording technologies. However, only recently have experiments been performed that resolve the magnetic state of individual sub-micron particles. Motivated by these experimental developments, we use droplet theory and Monte Carlo simulations to study the time and field dependence of some quantities that can be observed by magnetic force microscopy. Particular emphasis is placed on the effects of finite particle size. The qualitative agreement between experiments on switching and our simulations in individual single-domain ferromagnets suggests that the switching mechanism in such particles may involve local nucleation and subsequent growth of droplets of the stable phase.

cond-mat↗

arXiv1994

Application of a constrained-transfer-matrix method to metastability in the $d$$=$$2$ Ising ferromagnet

Applying a numerical transfer-matrix formalism, we obtain complex-valued constrained free energies for the two-dimensional square-lattice nearest-neighbor Ising ferromagnet below its critical temperature and in an external magnetic field. In particular, we study the imaginary part of the constrained free-energy branch that corresponds to the metastable phase. Although droplets are not introduced explicitly, the metastable free energy is obtained in excellent agreement with field-theoretical droplet-model predictions. The finite-size scaling properties are different in the weak-field and intermediate-field regimes, and we identify the corresponding different critical-droplet shapes. For intermediate fields, we show that the surface free energy of the critical droplet is given by a Wulff construction with the equilibrium surface tension. We also find a prefactor exponent in complete agreement with the field-theoretical droplet model. Our results extend the region of validity for known results of this field-theoretical droplet model, and they indicate that this transfer-matrix approach provides a nonperturbative numerical continuation of the equilibrium free energy into the metastable phase.

cond-mat↗

arXiv1994

Finite-range-scaling analysis of metastability in an Ising model with long-range interactions

We apply both a scalar field theory and a recently developed transfer-matrix method to study the stationary properties of metastability in a two-state model with weak, long-range interactions: the $N$$\times$$\infty$ quasi-one-dimensional Ising model. Using the field theory, we find the analytic continuation $\tilde f$ of the free energy across the first-order transition, assuming that the system escapes the metastable state by nucleation of noninteracting droplets. We find that corrections to the field-dependence are substantial, and by solving the Euler-Lagrange equation for the model numerically, we have verified the form of the free-energy cost of nucleation, including the first correction. In the transfer-matrix method we associate with subdominant eigenvectors of the transfer matrix a complex-valued ``constrained'' free-energy density $f_α$ computed directly from the matrix. For the eigenvector with an associated magnetization most strongly opposed to the applied magnetic field, $f_α$ exhibits finite-range scaling behavior in agreement with $\tilde f$ over a wide range of temperatures and fields, extending nearly to the classical spinodal. Some implications of these results for numerical studies of metastability are discussed.

cond-mat↗

arXiv1993

Numerical Transfer-Matrix Study of Metastability in the d=2 Ising Model

We apply a generalized numerical transfer-matrix method to the 2-d Ising ferro- magnet in a nonzero field to obtain complex constrained free energies. Below $T_c$ certain eigenstates of the transfer matrix are identified as representing a metastable phase. The imaginary parts of the metastable constrained free energies are found to agree with a field-theoretic droplet model for a wide range of fields, allowing us to numerically estimate the average free-energy cost of a critical cluster. We find excellent agreement with the equilibrium cluster free energy obtained by a Wulff construction with the exact, aniso- tropic zero-field surface tension, and we present strong evidence for Gold- stone modes on the critical cluster surface. Our results are also fully con- sistent with average metastable lifetimes from previous Monte-Carlo simula- tions. The study indicates that our constrained-transfer-matrix technique pro- vides a nonperturbative numerical method to obtain an analytic continuation of the free energy around the essential singularity at the first-order transition.

cond-mat↗

arXiv1993

A Numerical Transfer-Matrix Study of Surface-Tension Anisotropy in Ising Models on Square and Cubic Lattices

We compute by numerical transfer-matrix methods the surface free energy $τ(T),$ the surface stiffness coefficient $κ(T),$ and the single-step free energy $s(T)$ for Ising ferromagnets with $(\infty \times L)$ square-lattice and $(\infty \times L \times M)$ cubic-lattice geometries, into which an interface is introduced by imposing antiperiodic or plus/minus boundary conditions in one transverse direction. These quantities occur in expansions of the angle-dependent surface tension, either for rough or for smooth interfaces. The finite-size scaling behavior of the interfacial correlation length provides the means of investigating $κ(T)$ and $s(T).$ The resulting transfer-matrix estimates are fully consistent with previous series and Monte Carlo studies, although current computational technology does not permit transfer-matrix studies of sufficiently large systems to show quantitative improvement over the previous estimates.

cond-mat↗