Skyrmions, dipolar interaction and anomalous Hall effect.

Skyrmions are topologically protected states which are at the focus of considerable theoretical and experimental efforts in recent years. Being originally proposed in the context of particle physics, skyrmions now play a major role in almost every field in physics from condensed matter to cosmology.  Particularly they are related to quantum Hall effect and fractional quantum Hall effect, liquid crystals, Bose-Einstein condensates, magnetism and even superconductivity.

We show that dipolar interaction in quasi two dimensional ferromagnetic materials breaks the symmetry between different topological excitations. Being sensitive to long range order the interaction prefers the skyrmion topology with positive winding number over the anti-skyrmion topology with negative winding number. We show that the broken symmetry leads to the occurrence of giant anomalous Hall effect (AHE) due to real-space Berry phase.