Symmetry, Geometry, Topology and Spin: Heisenberg spins in the continuum limit/magnetic vesicles

Abstract

In this thesis I present my research on the exotic configurations of antiferromagnetic systems characterised by a topological invariant. The research presented outlines the construction of novel local antiferromagnetic degrees of freedom for low dimensional antiferromagnetic lattices. This new construction reproduces the real division algebra hierarchy satisfied by the nonlinear sigma-model and reveals the presence of a novel local gauge field. I have also studied elastic magnetic vesicles of spherical and toric genus in the presence of a magnetic soliton. My studies reveal a global shrinking, with local swellings in the regions where the soliton presents a spin-flip. The geometrical origin of this novel phenomena led me to interpret the geometric frustration of magnetic vesicles as the competition between the two topological orders present. The microscopic mechanism and topological competition suggested above go beyond the scope of this thesis, providing a microscopic explanation for the Fermi-Bose transmutation and a way to deal with this type of exotic physics.