Néel Ordered Magnetic Phases in Bipartite Quasicrystals

Abstract

Magnetism is a fundamental research area in which the recently proposed altermagnetism (AM) has become an emergent frontier. Very recently, the quasicrystal (QC) was proposed as a possible platform to realize AM. However, the existence of AM in QCs still lacks vigorous evidence. In this work, we adopt the sign-problem-free projector quantum Monte Carlo (PQMC) algorithm to investigate the magnetic phases in the half-filled Hubbard models in various 2D bipartite QCs, and always obtain Néel ordered states. While the Néel states in bipartite crystals are usually antiferromagnetism (AFM), we find it common that those in bipartite QCs can also be AM or ferrimagnetism (FIM). Based on symmetry analysis, combined with our comprehensive PQMC results, we propose a general criterion for determining the magnetism classes of the Néel states in a bipartite QC: According to whether the two sublattices are related by inversion, a non-inversion point-group operation such as mirror or rotation, or no operation about the unique symmetry center, the corresponding Néel state is AFM, AM or FIM / geometry-enforced AM (G-AM), respectively. The G-AM is a special type of $s$-wave AM caused by the unique QC structure formed through projection from high-dimensional crystals to lower dimensions, which is rare in crystals. For example, our results yield symmetry-protected AM for the two $D_4$-symmetric Thue-Morse QCs and G-AM for the $D_5$-symmetric Penrose QC at half-filling. Our results provide a solid foundation for experimental investigations and potential applications of different classes of magnetism in QCs.

arXiv comment4.2 pages, 4 figures, with supplementary materials