Re-orientation Transition in Molecular Thin Films: Potts Model with Dipolar Interaction

TL;DR

This paper investigates the phase transition and re-orientation phenomena in molecular thin films modeled by a Potts system with dipolar interactions, revealing how surface effects and interaction ratios influence ordering.

Contribution

It introduces a Monte Carlo simulation study of a Potts model with dipolar interactions, highlighting the dependence of ground states and phase transitions on interaction ratios and film thickness.

Findings

Re-orientation transition occurs near a critical dipolar strength D_c.

Surface phase transition can occur below or above the bulk transition.

Ground state depends on the ratio D/A and cutoff distance r_c.

Abstract

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 3-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 $r_c$ (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 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. 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.