Ultraregular generalized functions

Algebras of ultradifferentiable generalized functions are introduced. We give a microlocal analysis within these algebras related to the regularity type and the ultradifferentiable property.Comment: This paper is the composition of our two recent paper

Giant perpendicular magnetic anisotropy energies in CoPt thin films: Impact of reduced dimensionality and imperfections

The impact of reduced dimensionality on the magnetic properties of the tetragonal L1$_{0}$ CoPt alloy is investigated from ab-initio considering several kinds of surface defects. By exploring the dependence of the magnetocrystalline anisotropy energy (MAE) on the thickness of CoPt thin films, we demonstrate the crucial role of the chemical nature of the surface. For instance, Pt-terminated thin films exhibit huge MAEs which can be 1000% larger than those of Co-terminated films. Besides the perfect thin films, we scrutinize the effect of defective surfaces such as stacking faults or anti-sites on the surface layers. Both types of defects reduce considerably the MAE with respect to the one obtained for Pt-terminated thin films. A detailed analysis of the electronic structure of the thin films is provided with a careful comparison to the CoPt bulk case. The behavior of the MAEs is then related to the location of the different virtual bound states utilising second order perturbation theory.Comment: 10 pages, 7 figures, accepted in Journal of Physics: Condensed Matte

Toroidal membrane vesicles in spherical confinement

We investigate the morphology of a toroidal fluid membrane vesicle confined inside a spherical container. The equilibrium shapes are assembled in a geometrical phase diagram as a function of scaled area and reduced volume of the membrane. For small area the vesicle can adopt its free form. When increasing the area, the membrane cannot avoid contact and touches the confining sphere along a circular contact line, which extends to a zone of contact for higher area. The elastic energies of the equilibrium shapes are compared to those of their confined counterparts of spherical topology to predict under which conditions a topology change is favored energetically.Comment: 16 pages, 7 figure

Impact of single atomic defects and vacancies on the magnetic anisotropy energy of CoPt thin films

The impact of surface vacancies and single adatoms on the magnetic properties of tetragonal {\bf{L1}$_{0}$} CoPt thin films is investigated from first principles. We consider Co and Fe single adatoms deposited on a Pt-terminated thin film while a Pt adatom is assumed to be supported by a Co-terminated film. The vacancy is injected in the top-surface layer of the films with both types of termination. After finding the most stable location of the defects, we discuss their magnetic properties tight to those of the substrate and investigate the magnetic crystalline anisotropy energy (MAE). Previous simulations [Brahimi et al. J. Phys.: Condens. Matter. \textbf{28}, 496002 (2016)] predicted a large out-of-plane surface MAE for the Pt-terminated CoPt films (4 meV per f.u.) in contrast to in-plane surface MAE for Co-terminated films (-1 meV per f.u.). Here, we find that the surface MAE is significantly modified upon the presence of the atomic defects. All investigated defects induce an in-plane MAE, which is large enough for Fe adatom and Pt vacancy to switch the surface MAE from out-of-plane to in-plane for the Pt-terminated films. Interestingly, among the investigated defects Pt vacancy has the largest effect on the MAE in contrast to Co vacancy, which induced the smallest but still significant effect. This behavior is explained in terms of the orbital moment anisotropy of the thin films