Olga Petrova

Dynamics of magnetic charges in artificial spin ice.

Artificial spin ice has been recently implemented in two-dimensional arrays of mesoscopic magnetic wires. We propose a theoretical model of magnetization dynamics in artificial spin ice under the action of an applied magnetic field. Magnetization reversal is mediated by domain walls carrying two units of magnetic charge. They are emitted by lattice junctions when the local field exceeds a critical value Hc required to pull apart magnetic charges of opposite sign. Positive feedback from Coulomb interactions between magnetic charges induces avalanches in magnetization reversal.

Reducing Disorder in Artificial Kagome Ice

Artificial spin ice has become a valuable tool for understanding magnetic interactions on a microscopic level. The strength in the approach lies in the ability of a synthetic array of nanoscale magnets to mimic crystalline materials, composed of atomic magnetic moments. Unfortunately, these nanoscale magnets, patterned from metal alloys, can show substantial variation in relevant quantities such as the coercive field, with deviations up to 16%. By carefully studying the reversal process of artificial kagome ice, we can directly measure the distribution of coercivities, and, by switching from disconnected islands to a connected structure, we find that the coercivity distribution can achieve a deviation of only 3.3%. These narrow deviations should allow the observation of behavior that mimics canonical spin-ice materials more closely.

Spin waves in a skyrmion crystal

We derive the spectrum of low-frequency spin waves in skyrmion crystals observed recently in noncentrosymmetric ferromagnets. We treat the skyrmion crystal as a superposition of three helices whose wavevectors form an equilateral triangle. The low-frequency spin waves are Goldstone modes associated with displacements of skyrmions. Their dispersion is determined by the elastic properties of the skyrmion crystal and by the kinetic terms of the effective Lagrangian, which include both kinetic energy and a Berry-phase term reflecting a nontrivial topology of magnetization. The Berry-phase term acts like an effective magnetic field, mixing longitudinal and transverse vibrations into a gapped cyclotron mode and a twist wave with a quadratic dispersion.

A Simple Anisotropic Three-dimensional Quantum Spin Liquid with Fracton Topological Order

We present a three-dimensional cubic lattice spin model, anisotropic in the z direction, that exhibits fractonlike order. This order can be thought of as the result of interplay between two-dimensional Z2 topological order and spontaneous symmetry breaking along the z direction. Fracton order is a novel type of topological order characterized by the presence of immobile pointlike excitations, named fractons, residing at the corners of an operator with two-dimensional support. As other recent fracton models, ours exhibits a subextensive ground-state degeneracy: On an Lx×Ly×Lz three-torus, it has a 22Lz topological degeneracy and an additional symmetry-breaking nontopological degeneracy equal to 2LxLy−2. The fractons can be combined into composite excitations that move either in a straight line along the z direction or freely in the xy plane at a given height z. While our model draws inspiration from the toric code, we demonstrate that it cannot be adiabatically connected to a layered toric code construction. Additionally, we investigate the effects of imposing open boundary conditions on our system. We find zero energy modes on the surfaces perpendicular to either the x or y directions and their absence on the surfaces normal to z. This result can be explained using the properties of the two kinds of composite two-fracton mobile excitations.

Dynamics of artificial spin ice: a continuous honeycomb network

We model the dynamics of magnetization in an artificial analogue of spin ice specializing to the case of a honeycomb network of connected magnetic nanowires. The inherently dissipative dynamics is mediated by the emission and absorption of domain walls in the sites of the lattice, and their propagation in its links. These domain walls carry two natural units of magnetic charge, whereas sites of the lattice contain a unit magnetic charge. Magnetostatic Coulomb forces between these charges play a major role in the physics of the system, as does quenched disorder caused by imperfections of the lattice. We identify and describe different regimes of magnetization reversal in an applied magnetic field determined by the orientation of the applied field with respect to the initial magnetization. One of the regimes is characterized by magnetic avalanches with a 1/n distribution of lengths.

Coulomb potentialV(r)=1/rproblem on the Bethe lattice

We study the problem of a particle hopping on the Bethe lattice in the presence of a Coulomb potential. We obtain an exact solution to the particles Greens function along with the full energy spectrum. In addition, we present a mapping of a generalized radial potential problem defined on the Bethe lattice to an infinite number of one-dimensional problems that are easily accessible numerically. The latter method is particularly useful when the problem admits no analytical solution.