Ising Spin Orders Conforming to Local Matching Rule and Long-Range Regularity of Interactions in Penrose Lattice

Abstract

A simple arithmetic rule is proposed to correlate the matching rule in Penrose lattice with long-range Ising spin orders with the aim of clarifying the energetic mechanism of the orders under Ruderman–Kittel–Kasuya–Yoshida-like (RKKY) alternating interactions. Three different types of antiferromagnetic orders were found to be compatible with the rule. The orders showed sharp magnetic diffraction spots with the same peak widths as the ordinary lattice diffraction, which were consistent with the long-range orders enforced by the matching rule. The three types of the orders were most adequately interpreted as the orders in the occupation domain in the phason space. The RKKY interactions resulted in two of the orders in simulated annealing calculations. The results indicate the importance in the energetic mechanism of the consistency of the connectivity of the interaction signs inherent in the quasiperiodic structure.