Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, CNRS, UMR 8089 2, Avenue Adolphe Chauvin, F-95302 Cergy-Pontoise Cedex, France.
J Phys Condens Matter. 2013 Feb 6;25(5):056006. doi: 10.1088/0953-8984/25/5/056006. Epub 2013 Jan 3.
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.
我们通过蒙特卡罗模拟研究了薄膜的低温行为和相变。薄膜具有简单立方晶格结构，每个位置由一个表明位置分子取向的 Potts 参数占据。在本文中，我们仅考虑三种分子取向，它们对应于三态 Potts 模型。系统的哈密顿量包括（i）最近邻位置 i 和 j 之间的交换相互作用 J(ij)，（ii）幅度为 D 的长程偶极相互作用，截止距离为 r(c)，以及（iii）幅度为 A 的单离子垂直各向异性。我们允许 J(ij) = J(s) 之间的表面自旋，J(ij) = J 否则。我们表明，基态取决于 D/A 和 r(c)的比值。对于单层，对于给定的 A，存在一个临界值 D(c)，低于（高于）该值时，分子轴的基态（GS）构型垂直（平行）于膜表面。当温度 T 升高时，在 D(c)附近会发生重新取向转变：低温面内有序在有限 T 下转变为垂直有序，低于向顺磁相的转变。在具有厚度的薄膜的情况下也观察到了相同的现象。给出了与 Fe/Gd 实验的比较。我们表明，表面相转变可以在体相转变之上或之下发生，这取决于 J(s)/J 的比值。显示和讨论了表面和体相序参量以及其他物理量。
