The Curie temperature of thin ferromagnetic films

The thickness-dependent Curie temperature T(c)(d) of thin ferromagnetic films is calculated within the molecular field approximation ('Weiss mean field') of the Heisenberg model. Two higher mean field theories are applied to obtain a quantitative improvement of the results: the Oguchi cluster method and the 'constant coupling approximation' (CCA). Analytical expressions are derived from difference equations or eigenvalue problems with an unknown parameter which can be solved numerically. Explicit expressions for T(c)(d) can be given if the interaction is restricted to next neighbour monolayers only, for any value of the spin S within the Weiss mean field and for S = 1/2 within the CCA. Effects of an enhanced interaction within the surface layers are briefly investigated. Calculated values of T(c)(d) for EuO are presented within the three models.