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

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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.