I will give a description of topological and non-topological solitons in condensed matter systems such as magnetic materials and Bose-Einstein condensates of atoms or of exciton-polaritons in semiconductors. The main focus will be on vortices in films, that is, swirling configurations which are stable localised structures with particle-like properties. Vortices appear not only in fluids but also in superfluids (quantised vortices), in magnetic materials (magnetic vortices) and indeed across condensed matter.
Magnetic vortices are structures of the magnetisation of the atomic crystal and they have sizes down to 10nm. Their stability and robustness is often due to their topological properties. Static vortices can be used for the storing of information (e.g., in magnetic media). Their dynamics can be used to produce oscillators at the nanoscopic scale, to transfer information, or construct logic gates.
In the last decade it was realised that a class of magnetic materials with a crystal structure which lacks certain symmetries, can support so-called skyrmions (a type of vortices) and these may even form the ground state of the system. We study a model for such materials and give a description of their unusual dynamical properties, that is, their motion under the influence of an external field or an electrical current.