First order phase transition in thin anisotropic films linear chain approximation for a spin-one Ising model

Abstract

The theory of a thin magnetic film is developed, introducing higher spins into the Valenta model to which the perpendicular linear chain approach is applied. The free energy of the thin film is derived using the transfer matrix method and mean field approximation. The phase diagrams, as well as temperature dependencies of magnetization curves, for different sets of anisotropic exchange interactions, are calculated. The existence of first and second order phase transitions that can occur in the case of spin-1 thin films with a sufficiently large single-ion anisotropy is discussed. The equations describing the location of the tricritical points that account for the anisotropy of exchange interaction parallel and perpendicular to the film surface are also given. Both the critical and tricritical temperatures are functions of film thickness. The method is tested for spin- 1 2 systems and the results are compared with those previously published.