Spatial structures of dipolar ferromagnetic liquids

We have determined the magnetization structure in a ferromagnetic dipolar fluid by performing a numerical minimization of a free energy density functional which is highly nonlocal due to the long range of the dipolar interactions. In a cubic sample a vortex structure is found which consists of four domains and four thick domain walls. Depending on sample size and temperature, near the vortex line we observe an ''escape'' of the planar magnetization into the normal direction or a reduction of its magnitude inside the vortex core. We describe the temperature dependence of the structure upon approaching the Curie point. If an external field is applied, a transition to a homogeneously magnetized state takes place at a critical field strength.