Magnetic Phase Diagram of a Thin Film with a Reorientation Transition

We study the magnetic state of a thin film undergoing a reorientation transition, in the plane defined by the temperature T and the thickness N . In going beyond free spin wave theory, three distinct regions are found: one with perpendicular magnetization; one with in-plane magnetization and a third (high T )-region with no magnetization. We are able to determine the boundaries between these regions and the resulting phase diagram agrees with the existing experimental data. A possible maximum in the reorientation transition T R ( N ) is predicted. Further experimental work is necessary to check this possibility.