Re-orientation transition in molecular thin films: Potts model with dipolar interaction

We study the low-temperature behavior and the phase transition of a thin film by Monte Carlo simulation. The thin film has a simple cubic lattice structure where each site is occupied by a Potts parameter which indicates the molecular orientation of the site. We take only three molecular orientations in this paper, which correspond to the three-state Potts model. The Hamiltonian of the system includes (i) the exchange interaction J(ij) between nearest-neighbor sites i and j, (ii) the long-range dipolar interaction of amplitude D truncated at a cutoff distance r(c), and (iii) a single-ion perpendicular anisotropy of amplitude A. We allow J(ij) = J(s) between surface spins, and J(ij) = J otherwise. We show that the ground state depends on the ratio D/A and r(c). For a single layer, for a given A, there is a critical value D(c) below (above) which the ground-state (GS) configuration of molecular axes is perpendicular (parallel) to the film surface. When the temperature T is increased, a re-orientation transition occurs near D(c): the low-T in-plane ordering undergoes a transition to the perpendicular ordering at a finite T, below the transition to the paramagnetic phase. The same phenomenon is observed in the case of a film with a thickness. Comparison with the Fe/Gd experiment is given. We show that the surface phase transition can occur below or above the bulk transition depending on the ratio J(s)/J. Surface and bulk order parameters as well as other physical quantities are shown and discussed.