Long-range interactions in magnetic bilayer above the critical temperature.

In this paper we have studied the stabilization of the long-range order in ( z ; x ) -plane of two isotropic Heisenberg ferromagnetic monolayers coupled by a short-range exchange interaction ( J ⊥ ), by a long range dipole-dipole interactions and a magnetic field. We have applied a magnetic field along of the z -direction to study the thermodynamic properties above the critical temperature. The dispersion relation ω and the magnetization are given as function of dipolar anisotropy parameter defined as E d = ( g μ ) 2 S / a 3 J ∥ and for other Hamiltonian parameters, and they are calculated by the double-time Zubarev-Tyablikov Green's functions in the random-phase approximation (RPA). The results show that the system is unstable for values of E d ≥ 0.012 with external magnetic field ranging between H / J ∥ = 0 and 1 0 − 3 . The instability appears for E d larger then E d c = 0.0158 with H / J ∥ = 1 0 − 5 , E d c = 0.02885 with H / J ∥ = 1 0 − 4 , and E d c = 0.115 with H / J ∥ = 1 0 − 3 , i.e., a small magnetic field is sufficient to maintain the magnetic order in a greater range of the dipolar interaction. [ABSTRACT FROM AUTHOR]