Analytical Description Of The Topological Interaction Between Magnetic Domain Walls In Nanowires

Magnetic domain walls in nanowires behave as particles interacting through the exchange field. As topological objects, their interaction is determined by their chirality or topological charge. We investigate analytically the topological repulsion between magnetic domain walls with the same topological charge in nanostripes (with easy-plane magnetization) and show that it decays algebraically as r(-2), being part of a larger class of interactions that produce topological long-range order in two dimensions. We compare the topological repulsion between the walls with other types of fundamental interactions with exponential spatial decay, such as the Yukawa-Reid potential, and with micromagnetic simulations. We determine that trains of such walls can be well described analytically and can be displaced regularly in nanowires leading to practical applications.