Nematic versus ferromagnetic shells: new insights in curvature-induced effects

TL;DR

This paper explores how curvature influences the behavior of ferromagnetic and nematic shells, revealing curvature-induced chirality effects and different defect textures depending on the order parameter type.

Contribution

It introduces a continuum theory framework linking curvature effects to order parameter textures in ferromagnetic and nematic shells, highlighting new curvature-induced phenomena.

Findings

Curvature combined with director out-of-plane component induces chirality effects.

Ground state configurations depend on shell size, with specific defect arrangements.

Extrinsic curvature determines defect positions on nematic spherical shells.

Abstract

Within the framework of continuum theory, we draw a parallel between ferromagnetic materials and nematic liquid crystals confined on curved surfaces, which are both characterized by local interaction and anchoring potentials. We show that the extrinsic curvature of the shell combined with the out-of-plane component of the director field gives rise to chirality effects. This interplay produces an effective energy term reminiscent of the chiral term in cholesteric liquid crystals, with the curvature tensor acting as a sort of anisotropic helicity. We discuss also how the different nature of the order parameter, a vector in ferromagnets and a tensor in nematics, yields different textures on surfaces with the same topology as the sphere. In particular, we show that the extrinsic curvature governs the ground state configuration on a nematic spherical shell, favouring two antipodal disclinations of charge +1 on small particles and four $+1/2$ disclinations of charge located at the vertices of a square inscribed in a great circle on larger particles.