Fast and Robust Algorithm for the Energy Minimization of Spin Systems Applied in an Analysis of High Temperature Spin Configurations in Terms of Skyrmion Density

An algorithm for the minimization of the energy of magnetic systems is presented and applied to the analysis of thermal configurations of a ferromagnet to identify inherent structures, i.e. the nearest local energy minima, as a function of temperature. Over a rather narrow temperature interval, skyrmions appear and reach a high temperature limit for the skyrmion density. In addition, the performance of the algorithm is further demonstrated in a self-consistent field calculation of a skyrmion in an itinerant magnet. The algorithm is based on a geometric approach in which the curvature of the spherical domain is taken into account and as a result the length of the magnetic moments is preserved in every iteration. In the limit of infinitesimal rotations, the minimization path coincides with that obtained using damped spin dynamics while the use of limited-memory quasi-newton minimization algorithms, such as the limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm, significantly accelerates the convergence

Long-timescale simulations of H2_2O admolecule diffusion on Ice Ih(0001) surfaces

Long-timescale simulations of the diffusion of a H$_2$O admolecule on the (0001) basal plane of ice Ih were carried out over a temperature range of 100 to 200 K using the adaptive kinetic Monte Carlo method and TIP4P/2005f interaction potential function. The arrangement of dangling H atoms was varied from the proton-disordered surface to the perfectly ordered Fletcher surface. A large variety of sites was found leading to a broad distribution in adsorption energy at both types of surfaces. Up to 4 % of the sites on the proton-disordered surface have an adsorption energy exceeding the cohesive energy of ice Ih. The mean squared displacement of a simulated trajectory at 175 K for the proton-disordered surface gave a diffusion constant of 6$\cdot$10$^{-10}$ cm$^2$/s, consistent with an upper bound previously reported from experimental measurements. During the simulation, dangling H atoms were found to rearrange so as to reduce clustering, thereby approaching a linear Fletcher type arrangement. Diffusion on the perfectly ordered Fletcher surface was estimated to be significantly faster, especially in the direction along the rows of dangling hydrogen atoms. From simulations over the range in temperature, an effective activation energy of diffusion was estimated to be 0.16 eV and 0.22 eV for diffusion parallel and perpendicular to the rows, respectively. Even a slight disruption of the rows of the Fletcher surface made the diffusion isotropic.Comment: 24 pages, 8 figures, 1 tabl

Electonic transport properties of nitrate-doped carbon nanotube networks

The conductivity of carbon nanotube (CNT) networks can be improved markedly by doping with nitric acid. In the present work, CNTs and junctions of CNTs functionalized with NO$_3$ molecules are investigated to understand the microscopic mechanism of nitric acid doping. According to our density functional theory band structure calculations, there is charge transfer from the CNT to adsorbed molecules indicating p-type doping. The average doping efficiency of the NO$_3$ molecules is higher if the NO$_3$ molecules form complexes with water molecules. In addition to electron transport along individual CNTs, we have also studied electron transport between different types (metallic, semiconducting) of CNTs. Reflecting the differences in the electronic structures of semiconducting and metallic CNTs, we have found that besides turning semiconducting CNTs metallic, doping further increases electron transport most efficiently along semiconducting CNTs as well as through a junction between them.Comment: 13 pages, 12 figure

The effect of confinement and defects on the thermal stability of skyrmions

The stability of magnetic skyrmions against thermal fluctuations and external perturbations is investigated within the framework of harmonic transition state theory for magnetic degrees of freedom. The influence of confined geometry and atomic scale non-magnetic defects on the skyrmion lifetime is estimated. It is shown that a skyrmion on a track has lower activation energy for annihilation and higher energy for nucleation if the size of the skyrmion is comparable with the width of the track. Two mechanisms of skyrmion annihilation are considered: inside the track and escape through the boundary. For both mechanisms, the dependence of activation energy on the track width is calculated. Non-magnetic defects are found to localize skyrmions in their neighborhood and strongly decrease the activation energy for creation and annihilation. This is in agreement with experimental measurements that have found nucleation of skyrmions in presence of spin-polarized current preferably occurring near structural defects

Ideal, Defective, and Gold--Promoted Rutile TiO2(110) Surfaces: Structures, Energies, Dynamics, and Thermodynamics from PBE+U

Extensive first principles calculations are carried out to investigate gold-promoted TiO2(110) surfaces in terms of structure optimizations, electronic structure analyses, ab initio thermodynamics calculations of surface phase diagrams, and ab initio molecular dynamics simulations. All computations rely on density functional theory in the generalized gradient approximation (PBE) and account for on-site Coulomb interactions via inclusion of a Hubbard correction, PBE+U, where U is computed from linear response theory. This approach is validated by investigating the interaction between TiO2(110) surfaces and typical probe species (H, H2O, CO). Relaxed structures and binding energies are compared to both data from the literature and plain PBE results. The main focus of the study is on the properties of gold-promoted titania surfaces and their interactions with CO. Both PBE+U and PBE optimized structures of Au adatoms adsorbed on stoichiometric and reduced TiO2 surfaces are computed, along with their electronic structure. The charge rearrangement induced by the adsorbates at the metal/oxide contact are also analyzed and discussed. By performing PBE+U ab initio molecular dynamics simulations, it is demonstrated that the diffusion of Au adatoms on the stoichiometric surface is highly anisotropic. The metal atoms migrate either along the top of the bridging oxygen rows, or around the area between these rows, from one bridging position to the next along the [001] direction. Approximate ab initio thermodynamics predicts that under O-rich conditions, structures obtained by substituting a Ti5c atom with an Au atom are thermodynamically stable over a wide range of temperatures and pressures.Comment: 20 pages, 12 figures, accepted for publication in Phys. Rev.

A view of canonical extension

This is a short survey illustrating some of the essential aspects of the theory of canonical extensions. In addition some topological results about canonical extensions of lattices with additional operations in finitely generated varieties are given. In particular, they are doubly algebraic lattices and their interval topologies agree with their double Scott topologies and make them Priestley topological algebras.Comment: 24 pages, 2 figures. Presented at the Eighth International Tbilisi Symposium on Language, Logic and Computation Bakuriani, Georgia, September 21-25 200

Bayesian imaging of the 2000 Western Tottori (Japan) earthquake through fitting of strong motion and GPS data

We image the rupture process of the 2000 Western Tottori earthquake (Mw = 6.6) through fitting of strong motion and GPS data. We consider an observational network consisting of 18 strong motion and 16 GPS stations, located within three fault lengths from the epicentre. We assume a planar fault and compute Green's functions for a 1-D velocity model. The earthquake rupture is described as a shear dislocation parameterized in terms of peak slip velocity, rake angle, rupture time and rise time, defined on a regular grid of nodes on the fault surface and derived at inner points through bilinear interpolation. Our inversion procedure is based on a Bayesian approach. The solution of the inverse problem is stated in terms of a posterior probability density function (pdf), representing the conjunction of prior information with information contained in the data and in the physical law relating model parameters with data. Inferences on model parameters are thus expressed in terms of posterior marginal pdfs. Due to the non-linearity of the problem, we use a Markov Chain Monte Carlo (MCMC) method, based on the Metropolis algorithm, to compute posterior marginals. Except for a few cases posterior marginals do not show a Gaussian-like distribution. This prevents us from providing a mean model and from characterizing uncertainties in terms of standard deviations only. Resolution on each single parameter is analysed by looking at the difference between prior and posterior marginal pdfs. Posterior marginals indicate that the best resolved feature is a major slip patch (peak value of 311 ± 140 cm), located between the hypocentre and the top edge of the fault, centered at a depth of 4.5 km. This shallow slip patch is triggered about 3 s after the earthquake nucleated and required about 4 s to reach its final slip value. The presence of this shallow slip patch is common to all previous studies. In contrast to some previous studies, we do not identify any significant slip (>1 m) at the bottom of the fault. We also compare inferences from both strong motion and GPS data with inferences derived from strong motion data only. In both cases the shallow slip patch is identified. At other locations, the main effect of the GPS data is in reducing the probability associated with high values of slip. GPS data reduce the presence of spurious fault slip and therefore strongly influence the resulting final seismic momen