We study the spin-1 Blume-Emery-Griffiths model with bilinear and biquadratic exchange interactions and single-ion crystal field, using the mean field theory. In addition to the four usual phases: The disordered phase D, the ferromagnetic phase F, the staggered quadrupolar phase SQ and The ferrimagnetic phase I, we found two new phases, in the case of a thin magnetic film, namely: the sublattice (A or B) non magnetic phase NM and the global non magnetic phase G. These phases are studied, for each layer of the film in the temperature-crystal field plane (T/J,delta/J) for different film thicknesses. It is found that the ferrimagnetic and sublattice phases are absent for a monolayer film. Whereas, these phases appear for increasing film thicknessses N > 2. On the other hand, the thermal behaviour of the layer quadrupolar moments qA, qB and layer magnetisations mA, mB are investigated for negative values of the biquadratic coupling and crystal field. It is also shown that for fixed values of the biquadratic coupling, the temperature and the crystal field, each layer of the film can belong to a different phase. To illustrate this situation, an example is given for d/J = -1.5, delta/J = -3.0 and T/J = 1.3.
Two-sublattice BEG model; Thin films; Staggered quadrupolar phase; Phase diagrams; Multicritical behaviour
