Simulation study on the magnetic order in the phason space in quasilttices of antiferromagnetic interactions

采用模拟退火方法，在Ruderman-Kittel-Kasuya-Yosida类振荡相互作用下，对二十面体Zn-Mg-Ho准晶结构模型的Ising自旋磁序进行了模拟计算.在磁衍射计算中，通过锐斑确定了长程磁序。在第一和第三近邻的反铁磁相互作用以及第二和第四近邻的铁磁相互作用的情况下，发现了长程反铁磁有序。远于第二近邻的相互作用是实现整个系统尺寸上的反铁磁序所必需的。发现长程反铁磁序是一种新的自旋畴在相子空间中的细分序，这在通常的周期晶体中是不可能实现的，并对二维Penrose晶格中的反铁磁序进行了类似的研究.两种情况下的相互作用参数的反铁磁秩序被发现。这两种顺序被发现符合本地匹配规则的箭头设置原来的晶格。这些阶数被解释为自旋畴在相子空间中的细分阶数。在真实的空间中对相互作用的连通性进行了分析，发现在整个系统尺度上与长程有序相一致。在相子空间中，相互作用的连通性的一致性得到了最充分的把握。相关准晶的结构和磁性也进行了实验研究。

Simulation calculations were performed for the investigation of the magnetic orders of Ising spins on a structure model of the icosahedral Zn-Mg-Ho quasicrystal assuming oscillating Ruderman-Kittel-Kasuya-Yosida-like interactions by the use of the simulated annealing method. Long-range magnetic orders were identified by sharp spots in magnetic diffraction calculations. A long-range antiferromagnetic order was found in the case of antiferromagnetic Interactions for the first and third nearest neighbors and ferromagnetic interactions for the second and fourth nearest neighbors. Interactions farther than the second nearest neighbors were necessary for the realization of the antiferromagnetic order extending over the whole system size. The long-range antiferromagnetic order was found to be a new type of order of subdivisions of the spin domains in the phason space, which does not realize in usual periodic crystals.A similar investigation was carried out on antiferromagnetic orders in a 2-dimensional Penrose lattice. Two kinds of antiferromagnetic orders were found in two cases of the interaction parameters. Both orders are found to conform to the local matching rule of arrows set originally on the lattice. The orders are interpreted as the orders of subdivisions of the spin domains in the phason space. The connectivity of the interactions were analyzed in the real space, and is found to be consistent with the long range orders over the whole system size. The consistency of the connectivity of the interactions is most adequately grasped in the phason space.Experimental studies were also performed on the structural and magnetic properties of related quasicrystals.