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

采用模拟退火方法对二十面体Zn-Mg-Ho准晶结构模型上的Ising自旋磁序进行了模拟计算，并假设了ruderman - kittel - kasuyya - yosida -like相互作用的振荡。在磁衍射计算中，用尖点来识别长程磁阶。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，发现了一个远程反铁磁序。要实现在整个系统尺度上扩展的反铁磁有序，需要比第二近邻更远的相互作用。在相位空间中发现了一种新的自旋域细分顺序，这是在通常的周期晶体中不存在的。对二维彭罗斯晶格中的反铁磁序进行了类似的研究。在两种相互作用参数下发现了两种反铁磁序。发现这两个阶都符合原先在格上的箭头的局部匹配规则。这些阶数被解释为相空间中自旋域的细分阶数。在实际空间中分析了相互作用的连通性，发现在整个系统尺寸上，相互作用的连通性与长范围阶数一致。相互作用的连通性的一致性在相空间中得到了最充分的把握。实验研究了相关准晶的结构和磁性能。

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.