Abstract

In the study of ultrathin magnetic films, one of the most simple and widely studied model is the two-dimensional Ising model with short-range ferromagnetic exchange and long-range antiferromagnetic dipolar interactions (ILRA model). In substrates with periodic boundary conditions, it is well known that the ground state of this system, depending on the strength parameter \(\delta \), is given by the antiferromagnetic, the irregular checkerboard and the striped states. In this work, we study the border effects on the ground state. We develop a systematic study on square substrates of size \(L\times L\) with open boundary conditions focusing our attention on the range \(0.35\leqslant \delta \leqslant 0.75\). Our results show that, at intermediate values of \(\delta \), none of the configurations present on substrates with periodic boundary conditions correspond to the ground state of the system. Specifically, we find three new kinds of ground states for \( L \le 8 \), which are also our best candidates to be ground state in systems of sizes up to \( L = 100\). Also, by means of the same systematic study on a similar short-range model, we analyze which of these ground states is a consequence of the long-range character of the dipolar interactions in the ILRA model.

Graphical Abstract

Ground states for \(8 \times 8\) lattice in the range of the strength parameter \(0.35\leqslant \delta \leqslant 0.75\)

中文翻译：

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超薄磁膜模型基态的边界效应

摘要

在超薄磁性薄膜的研究中，最简单、研究最广泛的模型之一是具有短程铁磁交换和长程反铁磁偶极相互作用的二维伊辛模型（ILRA模型）。在具有周期性边界条件的基底中，众所周知，该系统的基态取决于强度参数\(\delta \) ，由反铁磁、不规则棋盘态和条纹态给出。在这项工作中，我们研究了基态的边界效应。我们对具有开放边界条件的尺寸为\(L\times L\)的方形基板进行了系统研究，重点关注范围\(0.35\leqslant \delta \leqslant 0.75\)。我们的结果表明，在\(\delta \)的中间值下，具有周期性边界条件的基底上存在的构型均不对应于系统的基态。具体来说，我们发现了\( L \le 8 \)的三种新基态，这也是我们在大小高达\( L = 100\)的系统中成为基态的最佳候选。此外，通过对类似的短程模型进行相同的系统研究，我们分析了哪些基态是 ILRA 模型中偶极相互作用的长程特征的结果。

图形概要

在强度参数\(0.35\leqslant \delta \leqslant 0.75\)范围内\(8 \times 8\)晶格的基态