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We study a variational model from micromagnetics involving a nonlocalGinzburg-Landau type energy for S^1-valued vector fields. These vector fieldsform domain walls, called Neel walls, that correspond to one-dimensionaltransitions between two directions within the unit circle S^1. Due to thenonlocality of the energy, a Neel wall is a two length scale object, comprisinga core and two logarithmically decaying tails. Our aim is to determine theenergy differences leading to repulsion or attraction between Neel walls. Incontrast to the usual Ginzburg-Landau vortices, we obtain a renormalised energyfor Neel walls that shows both a tail-tail interaction and a core-tailinteraction. This is a novel feature for Ginzburg-Landau type energies thatentails attraction between Neel walls of the same sign and repulsion betweenNeel walls of opposite signs.

Interaction energy of domain walls in a nonlocal Ginzburg-Landau type model from micromagnetics