Multipolar interactions and complex phases in ferromagnetic ultrathin films

We present a model to describe complex phases observed at mesoscopic scales in ultrathin magnetic films. The model is based on the interaction between dipolar as well as quadrupolar magnetic moments. In the special case of strong perpendicular crystal anisotropy, we show that quadrupolar degrees of freedom associated with orientation of domain walls are essential in order to correctly describe the observed phenomenology of domain formation. A nematic phase characterized by orientational order of domain walls (stripe-like) but without translational order is predicted. This isotropic-nematic transition belongs to the Kosterlitz-Thouless type in the thermodynamic limit. However, we found that in actual experimental scales, the fluctuations of the nematic order parameter are regularized by the sample size, and orientational long range order, as predicted by mean field, should be observable. The transition may be completely characterized experimentally from measurements of the magnetic structure factor as well as from the non-linear in-plane magnetic susceptibility.