Topological theory of magnetism in nanostructured ferromagnets

It is postulated that in nanostructured ferromagnets, e.g., Ni, Fe, and Co, exchange and magnetostatic energy dominate crystalline anisotropy energy and therefore the usual domain structure imposed via anisotropy is replaced by a structure consisting of topological defects. The defects are nonlinear solutions of the classical Heisenberg Hamiltonian of spins modified by magnetostatic energy, have the topological properties of disclinations, and are partly classified by the Hopf index. Coercive force is a consequence of entanglements of disclinations, pinning, and mutual obstruction during crossing processes correlated to local (spin) conductivity. Domain boundaries at surfaces are replaced by topological point defects of opposite topological charge generated pairwise.