Nematic versus ferromagnetic shells: new insights in curvature-induced effects
arXiv:2102.13497 · doi:10.1039/D1SM00719J
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 disclinations of charge located at the vertices of a square inscribed in a great circle on larger particles.
References in corpus (19)
- Towards a Tetravalent Chemistry of Colloids
- Nematic textures in spherical shells
- Topological Defects in Spherical Nematics
- Curvature effects in statics and dynamics of low dimensional magnets
- Orientability and energy minimization in liquid crystal models
- Topologically stable magnetization states on a spherical shell: curvature stabilized skyrmions
- Micromagnetic Theory of Curvilinear Ferromagnetic Shells
- Surface free energies for nematic shells
- Out-of-surface vortices in spherical shells
- Comparing skyrmions and merons in chiral liquid crystals and magnets
- Topological defects in cholesteric liquid crystal shells
- Curvilinear one-dimensional antiferromagnets
- Skyrmion Spin Ice in Liquid Crystals
- Geometry induced phase transitions in magnetic spherical shell
- Temperature-driven anchoring transitions at liquid crystal / water interfaces
- Nematic liquid crystals on curved surfaces - a thin film limit
- Magnetization ground states and phase diagrams for a nano-sized Co hollow sphere : an onion-type magnetization state
- Alignment induced re-configurable walls for patterning and assembly of liquid crystal skyrmions
- Cooling a spherical nematic shell