Out-of-surface vortices in spherical shells

Abstract. We develop an approach to treat magnetic energy of a ferromagnet for arbitrary curved wires and shells on the assumption that the anisotropy contribution much exceeds the dipolar and other weak interactions. We show that the curvature induces two effective magnetic interactions: effective magnetic anisotropy and effective Dzyaloshinskii-like interaction. We derive an equation of magnetisation dynamics and propose a general static solution for the limit case of strong anisotropy. To illustrate our approach we consider the magnetisation structure in a ring wire and a cone surface: ground states in both systems essentially depend on the curvature excluding strictly tangential solutions even in the case of strong anisotropy. We derive also the spectrum of spin waves in such systems.

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“…Examples are magnetic vortices in easy-surface spherical shells [6], magnetic domains in Möbius rings with easy-normal anisotropy [12,13].…”

Section: Introductionmentioning

confidence: 99%

Curvature effects in statics and dynamics of low dimensional magnets

Sheka

Kravchuk

Gaididei

2015

J. Phys. A: Math. Theor.

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“…[14,15]. The expressions for E for an arbitrary three-dimensional magnetization distribution have already been obtained only for cylindrical [16,17] and spherical [18] geometries. Here we propose a general approach that can be used for an arbitrary curvilinear surface and an arbitrary magnetization vector field.…”

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confidence: 99%

Curvature Effects in Thin Magnetic Shells

2014

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A magnetic energy functional is derived for an arbitrary curved thin shell on the assumption that the magnetostatic effects can be reduced to an effective easy-surface anisotropy; it can be used for solving both static and dynamic problems. General static solutions are obtained in the limit of a strong anisotropy of both signs (easy-surface and easy-normal cases). It is shown that the effect of the curvature can be treated as the appearance of an effective magnetic field, which is aligned along the surface normal for the case of easy-surface anisotropy and is tangential to the surface for the case of easy-normal anisotropy. In general, the existence of such a field excludes the solutions that are strictly tangential or strictly normal to the surface. As an example, we consider static equilibrium solutions for a cone surface magnetization.

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“…Vortices in curved superfluid films 19) and magnetic thin films 20) are typical examples of such topological defects. When interacting constituents on a curved surface have orientational degrees of freedom, they can no longer show perfect orientational order.…”

Section: Curvature-induced Frustrationmentioning

confidence: 99%

Geometry-Property Relations in Physics on Curved Surfaces

Shima

2013

Journal of The Surface Science Society of Japan

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Geometric curvature of a low-dimensional host material often leads to drastic changes in physical properties of the system living upon it. In this article, I give a bird's-eye review on the theoretical progresses on the geometry-property relations, i.e., intriguing correlation between geometric curvature and physical property of the material considered. Some differential-geometry-based approaches that are aimed at quantitative description of physical systems confined to curved surfaces are presented.KEYWORDS : Gaussian curvature, quantum transport, liquid crystal, phase transition, foam coarsening 1．Introduction Mathematical notions of "geometry" and "curvature" are becoming commonplace in diverse classes of physics including surface sciences. Profound effects of geometric curvature have manifested not only in Einstein's gravity theory, but also in various lowdimensional materials such as nanocarbon layers, 1,2) liquid crystal films, 3) and cell membranes. 4) In all the systems abovementioned, the underlying geometric curvature is found to affect dominantly the physical properties of the systems.From a theoretical perspective, the body of research has relied on differential geometry, the mathematical discipline that gives a quantitative description of geometry-property relations in physics. In fact, differential geometry allows us to formulate explicitly the effective Hamiltonian of quantum excitations in curved nanomaterials. It also enables us to appreciate beautiful interplay between surface curvature and topological defect configuration in orientationally ordered systems in two dimensions. In particular, geometry-property relations become salient in soft matters that are mechanically deformable ; liquid crystal membranes and monolayered aqueous foam are the cases in point.In this article, I review the up-to-date findings on the geometry-property relations in low-dimensional materials endowed with nonzero surface curvature.Special focus is placed on the following three issues : (ⅰ) anomalous quantum transport in curved nanocarbons, (ⅱ) liquid crystal membranes with curved shape, and (ⅲ) time-evolution of aqueous foam confined within the gap of two curves substrates. Throughout the discussions, we will see that geometric curvature causes a drastic alteration in the nature of the systems, which imply the development of curved-shaped functional materials based on geometry-property relations. 2．Quantum Mechanics on Curved Surfaces 1 Curvature-induced potentialRapid advances in nanotechnology have made it possible to manufacture quasi one-and twodimensional nanostructures with non-flat geometries.5∼8) These experimental achievements arouse renewed interest in the effect of structural geometry on the quantum-mechanical properties.Surprisingly, the quantum mechanics of a particle whose motion is constrained to curved surfaces has been an old but new problem of theoretical physics for more than 50 years. The difficulty arises from operator-ordering ambiguities, 9) which permit multiple consistent quantizations for a ...

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Out-of-surface vortices in spherical shells

Cited by 71 publications

References 35 publications

Curvature effects in statics and dynamics of low dimensional magnets

Curvature effects in statics and dynamics of low dimensional magnets

Curvature Effects in Thin Magnetic Shells

Geometry-Property Relations in Physics on Curved Surfaces

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