Howard L. Richards

Computational lattice-gas modeling of the electrosorption of small molecules and ions

Abstract We present two recent applications of lattice-gas modeling techniques to electrochemical adsorption on catalytically active metal substrates: urea on Pt(100) and (bi)sulfate on Rh(111). Both systems involve the specific adsorption of small molecules or ions on single-crystal electrodes, and they are characterized by a particularly good fit between the adsorbate geometry and the substrate structure. The close geometric fit facilitates the formation of ordered submonolayer adsorbate phases in a range of electrode potential positive of the range in which an adsorbed monolayer of hydrogen is stable. In both systems the ordered-phase region is separated from the adsorbed-hydrogen region by a phase transition, signalled in cyclic voltammograms by a sharp current peak. Based on data from in situ radiochemical surface concentration measurements, cyclic voltammetry, and scanning tunneling microscopy, and ex situ Auger electron spectroscopy and low-energy electron diffraction, we have developed specific lattice-gas models for the two systems. These models were studied by group-theoretical ground-state calculations and numerical Monte Carlo simulations, and effective lattice-gas interaction parameters were determined so as to provide agreement with the experimental results.

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.

ANALYTICAL AND COMPUTATIONAL STUDY OF MAGNETIZATION SWITCHING IN KINETIC ISING SYSTEMS WITH DEMAGNETIZING FIELDS

An important aspect of real ferromagnetic particles is the demagnetizing field resulting from magnetostatic dipole-dipole interactions, which causes large particles to break up into equilibrium domains. Sufficiently small particles, however, remain single domain in equilibrium. This makes them particularly promising as materials for high-density magnetic recording media. In this paper we use analytic arguments and Monte Carlo simulations to quantitatively study the effects of the demagnetizing field on the dynamics of magnetization switching in two-dimensional, single-domain, kinetic Ising systems. For systems in the weak-field {open_quote}{open_quote}stochastic region,{close_quote}{close_quote} where magnetization switching is on average effected by the nucleation and growth of a single droplet, the simulation results can be explained by a simple model in which the free energy is a function only of magnetization. In the intermediate-field {open_quote}{open_quote}multidroplet region,{close_quote}{close_quote} a generalization of Avrami{close_quote}s law involving a magnetization-dependent effective magnetic field gives good agreement with the simulations. The effects of the demagnetizing field do not qualitatively change the droplet-theoretical picture of magnetization switching in highly anisotropic, single-domain ferromagnetic grains, which we recently proposed [J. Magn. Magn. Mater. {bold 150}, 37 (1995)]. {copyright} {ital 1996 The American Physical Society.}

KINETIC ISING SYSTEMS AS MODELS OF MAGNETIZATION SWITCHING IN SUBMICRON FERROMAGNETS

Experimental techniques, such as magnetic force microscopy (MFM), have recently enabled the magnetic state of individual submicron particles to be resolved. Motivated by these experimental developments, we use Monte Carlo simulations of two‐dimensional kinetic Ising ferromagnets to study the magnetic relaxation in a negative applied field of a grain with an initial magnetization m0=+1. The magnetostatic dipole–dipole interactions are treated to lowest order by adding to the Hamiltonian a term proportional to the square of the magnetization. We use droplet theory to predict the functional forms for some quantities, which can be observed by MFM. One such quantity is the probability that the magnetization is positive, which is a function of time, field, grain size, and grain dimensionality. The relaxation is characterized by the number of droplets larger than a field‐dependent critical size, which form during the switching process. Our simulations of the kinetic Ising model are in excellent agreement with dr...

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.

Nucleations 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.

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 \ensuremath{\tau}(T), the surface stiffness coefficient \ensuremath{\kappa}(T), and the step free energy s(T) for Ising ferromagnets with (\ensuremath{\infty}\ifmmode\times\else\texttimes\fi{}L) square-lattice and (\ensuremath{\infty}\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}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 for either rough or smooth interfaces. The finite-size scaling behavior of the interfacial correlation length provides the means of investigating \ensuremath{\tau}(T), \ensuremath{\kappa}(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.

Phase Separation on a Hyperbolic Lattice

Abstract We report a preliminary numerical study by kinetic Monte Carlo simulation of the dynamics of phase separation following a quench from high to low temperature in a system with a single, conserved, scalar order parameter (a kinetic Ising ferromagnet) confined to a hyperbolic lattice. The results are compared with simulations of the same system on two different, Euclidean lattices, in which cases we observe power-law domain growth with an exponent near the theoretically known value of 1/3. For the hyperbolic lattice we observe much slower domain growth, consistent to within our current accuracy with power-law growth with a much smaller exponent near 0.13. The paper also includes a brief introduction to non-Euclidean lattices and their mapping to the Euclidean plane.

Extrapolation-CAM theory for critical exponents

We propose and test a new method for generating canonical sequences for analysis by the coherent anomaly method (CAM) from non-mean-field approximations. 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 for each member of these sequences of estimates. Thus, the CAM can be used to determine . 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 . We also use it on the three-dimensional ferromagnetic Ising model, finding , in good agreement with other estimates. Finally, we apply it to an antiferromagnetic spin-1 Heisenberg chain, finding at the phase transition between the Haldane phase and the dimerized phase, in agreement with the field-theoretic prediction . Although the specific systems used to test the extrapolation-CAM procedure involve finite system sizes, the method could be applied to other finite approximations, such as systematic variational approximations.