Related papers: Curved thin-film limits of chiral Dirichlet energi…
We investigate the behavior of minimizers of perturbed Dirichlet energies supported on a wire generated by a regular simple curve $\gamma$ and defined in the space of $\mathbb{S}^2$-valued functions. The perturbation $K$ is represented by a…
We present a variational treatment of confined magnetic skyrmions in a minimal micromagnetic model of ultrathin ferromagnetic films with interfacial Dzylashinksii-Moriya interaction (DMI) in competition with the exchange energy, with a…
Recently a significant interest in ferromagnetic curved thin films has appeared. In particular, thin spherical shells are currently of great interest due to their capability to support skyrmion solutions which can be stabilized by curvature…
In this paper, we study the thin-film limit of the micromagnetic energy functional in the presence of bulk Dzyaloshinskii-Moriya interaction (DMI). Our analysis includes both a stationary $\Gamma$-convergence result for the micromagnetic…
We characterize skyrmions in ultrathin ferromagnetic films as local minimizers of a reduced micromagnetic energy appropriate for quasi two-dimensional materials with perpendicular magnetic anisotropy and interfacial Dzyaloshinskii-Moriya…
We derive four reduced two-dimensional models that describe, at different spatial scales, the micromagnetics of ultrathin ferromagnetic materials of finite spatial extent featuring perpendicular magnetic anisotropy and interfacial…
Periodical equilibrium states of magnetization exist in chiral ferromagnetic films, if the constant of antisymmetric exchange (Dzyaloshinskii-Moriya interaction) exceeds some critical value. Here, we demonstrate that this critical value can…
We consider electrostatic interactions in two classes of nanostructures embedded in a three dimensional space: (1) helical nanotubes, and (2) thin films with uniform bending (i.e., constant mean curvature). Starting from the atomic scale…
Under the correct conditions, Dzyaloshinskii-Moriya interactions (DMI) can lead to topologically protected spin textures such as skyrmions. The application of DMI for spin-based computation and memory technologies is promising and requires…
We consider the problem of modeling of interaction of thin material films with fields of quantum electrodynamics. Taking into account the basic principles of quantum electrodynamics (locality, gauge invariance, renormalizability) we…
It is well known that boundary conditions on quantum fields produce divergences in the renormalized energy-momentum tensor near the boundaries. Although irrelevant for the computation of Casimir forces between different bodies, the…
Current quadratic smoothness energies for curved surfaces either exhibit distortions near the boundary due to zero Neumann boundary conditions, or they do not correctly account for intrinsic curvature, which leads to unnatural-looking…
We show that if $\{M_t\}_{t\in \Delta}$ is a polarized family of compact K\"ahler manifolds over the open unit disk $\Delta$, if $N$ is a Riemannian manifold of nonpositive complexified sectional curvature, and if $\{\phi_t:M_t\to N\}_{t\in…
The magnetic properties of ferromagnetic thin films down to the nanoscale are ruled by the exchange stiffness, anisotropies and the effects of magnetic fields. As surfaces break inversion symmetry, an additional effective chiral exchange is…
A combined approach using first-principles calculations and spin dynamics simulations is applied to study Ni/Ir$_{n}$/Pt(111) ($n=0,1,2$) films. The lowest-energy states are predicted to be spin-spirals but with a minute (of the order of a…
We study the Dirichlet Casimir effect for a complex scalar field on two noncommutative spatial coordinates plus a commutative time. To that end, we introduce Dirichlet-like boundary conditions on a curve contained in the spatial plane, in…
The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional in the class of $\mathbb{S}^2$-valued maps defined in cylindrical surfaces. The model naturally arises as a curved thin-film limit in the theories of…
We consider an energy functional that arises in micromagnetic and liquid crystal theory on thin films. In particular, our energy comprises a non-convex term that models anti-symmetric exchange as well as an anisotropy term. We devise an…
We study the vacuum polarization (Casimir) energy in renormalizable, continuum quantum field theory in the presence of a background field, designed to impose Dirichlet boundary conditions on the fluctuating quantum field. In two and three…
We consider the three-dimensional micromagnetic model with Dzyaloshinskii-Moriya interaction in a thin-film regime. We prove the Gamma-convergence of the micromagnetic energy in the considered regime, for which the Gamma-limit energy is…