Alberto Verga

Nonlinear evolution of a morphological instability in a strained epitaxial film

A strained epitaxial film deposited on a deformable substrate undergoes a morphological instability relaxing the elastic energy by surface diffusion. The nonlinear dynamical equation of such films with wetting interactions are derived and solved numerically in two and three dimensions. Nonlocal nonlinearities together with wetting effects are crucial to regularize the instability leading to an island morphology. The island chemical potential decreases with its volume and the system consistently experiences a non-interrupted coarsening evolution described by power laws with a marked dimension dependence.

Magnetization structure of a Bloch point singularity

Abstract Switching of magnetic vortex cores involves a topological transition characterized by the presence of a magnetization singularity, a point where the magnetization vanishes (Bloch point). We analytically derive the shape of the Bloch point that is an extremum of the free energy with exchange, dipolar and Landau terms. From a one parameter family of solutions, two types of singularities are distinguished, a radial one (hedgehog) corresponding to a local energy maximum, and a twisted one corresponding to a local energy minimum. Micromagnetic simulations show that the hedgehog magnetization naturally evolves to a twisted one if the size of the ferromagnet is much larger than the exchange length.

HAMILTONIAN DYNAMICS AND THE PHASE TRANSITION OF THE XY MODEL

A Hamiltonian dynamics is defined for the

Topological changes of two-dimensional magnetic textures

\mathrm{XY}

Dynamical approach to the microcanonical ensemble.

model by adding a kinetic energy term. Thermodynamical properties (total energy, magnetization, vorticity) derived from microcanonical simulations of this model are found to be in agreement with canonical Monte Carlo results in the explored temperature region. The behavior of the magnetization and energy as functions of the temperature are thoroughly investigated, taking into account finite size effects. By representing the spin field as a superposition of random phased waves, we derive a nonlinear dispersion relation whose solutions allow the computation of thermodynamical quantities, which agree quantitatively with those obtained in numerical experiments, up to temperatures close to the transition. At low temperatures the propagation of phonons is the dominant phenomenon, while above the phase transition the system splits into ordered domains separated by interfaces populated by topological defects. In the high temperature phase, spins rotate, and an analogy with an Ising-like system can be established, leading to a theoretical prediction of the critical temperature

Anomalous quantum Hall effect induced by disorder in topological insulators

{T}_{\mathrm{KT}}\ensuremath{\approx}0.855.

Skyrmion to ferromagnetic state transition: A description of the topological change as a finite-time singularity in the skyrmion dynamics

We investigate the interaction of magnetic vortices and skyrmions with a spin-polarized current. In a square lattice, fixed classical spins and quantum itinerant electrons evolve according to the coupled Landau-Lifshitz and Schrodinger equations. Changes in the topology occur at microscopic time and length scales and are shown to be triggered by the nucleation of a nontrivial electron-spin structure at the vortex core.

Anisotropic dynamics of a vicinal surface under the meandering step instability

An analytical method to compute thermodynamic properties of a given Hamiltonian system is proposed. This method combines ideas of both dynamical systems and ensemble approaches to thermodynamics, providing de facto a possible alternative to traditional ensemble methods. Thermodynamic properties are extracted from effective motion equations. These equations are obtained by introducing a general variational principle applied to an action averaged over a statistical ensemble of paths defined on the constant energy surface. The method is applied first to the one-dimensional beta-Fermi-Pasta-Ulam chain and to the two-dimensional lattice straight phi(4) model. In both cases, the method gives a good insight of some of their statistical and dynamical properties.

Dynamics of vortices and drift waves: a point vortex model

We investigate a transition between a two-dimensional topological insulator conduction state, characterized by a conductance G = 2 (in fundamental units e 2 /h) and a Chern insulator with G = 1, induced by polarized magnetic impurities. Two kinds of coupling, ferromagnetic and antiferromagnetic, are considered with the electron and hole subbands. We demonstrate that for strong disorder, a phase G = 1 exists even for ferromagnetic order, in contrast with the prediction of the mean field approximation. This result is supported by direct numerical computations using Landauer transport formula, and by analytical calculations of the chemical potential and mass renormalization as a function of the disorder strength, in the self-consistent Born approximation. The transition is related to the suppression of one of the spin conduction channels, for strong enough disorder, by selective spin scattering and localization.