Magnetic domain wall computer

This thesis develops a 'magnetic domain wall computer' concept in which information is encoded by the presence or absence of a domain wall propagating through nanoscale ferromagnetic thin-film nanowires. It establishes a theoretical framework that reduces the Landau'Lifshitz'Gilbert description of magnetisation dynamics to an effective sine-Gordon model, allowing domain walls to be treated as robust soliton excitations whose timing and synchronisation can be analysed and engineered. Building on this, the thesis introduces geometry as an active control knob: by incorporating spatially varying film width into the sine-Gordon Lagrangian, it shows how tailored width profiles can inject kinetic energy and modulate domain-wall velocity under an otherwise constant driving field, enabling controlled traversal of junction barriers. The proposed mechanisms are validated through numerical simulations in specially designed T- and Y-junction architectures, demonstrating feasible routes to domain-wall pinning, merging/cloning, and the realisation of logic-gate functionality within thin-film devices.