Hierarchical structure of domain walls in magnetic layers

Abstract

I discuss thin magnetic layers in the context of a two-dimensional ferromagnetic Heisenberg spin system. In the low energy regime it is shown that the system follows a Belavin-Polyakov type of equation. It is argued that unlike in traditional systems where these equations occur only under uniform boundary conditions, the boundary conditions in this case are less restrictive, allowing for a new family of solutions. These solutions consist of magnetic domains of spins that are oriented at relative opposite directions. The boundaries between regions are sharp on the continuous scale but within a domain wall the magnetization changes orientation continuously from one ground state to another. All the magnetic energy in the system is shown to concentrate along the domain walls. It is therefore argued that most favorable for the walls is to rearrange in a hierarchical or fractal fashion because such an arrangement lowers the overall energy density. It is suggested that this hierarchical structure of magnetic domain boundaries should be observable by magnetic force microscopy. Recent results suggest that such configurations may also dominate the structure of domain walls in magnetostrictive materials and magnetic nanotubes.