Dimensionality crossover in magnetism: from domain walls (2D) to vortices (1D).

Dimensionality crossover is a classical topic in physics. Surprisingly, it has not been searched in micromagnetism, which deals with objects such as domain walls (2D) and vortices (1D). We predict by simulation a second-order transition between these two objects, with the wall length as the Landau parameter. This was confirmed experimentally based on micron-sized flux-closure dots.