Unconventional Altermagnetism in Quasicrystals: A Hyperspatial Projective Construction

TL;DR

This paper extends the concept of altermagnetism to quasicrystals using a hyperspatial projection approach, revealing unconventional spin splitting and magnetic phases unique to quasiperiodic systems.

Contribution

It introduces a hyperspatial construction method to realize altermagnetism in quasicrystals, expanding the understanding of magnetic phases beyond periodic crystals.

Findings

Interaction-induced Nél order leads to alternating spin-polarized spectral functions.

Unconventional $g$-wave and $h$-wave altermagnetism observed in quasicrystalline lattices.

Symmetry analysis shows compatibility of spin splitting with quasicrystalline rotational symmetry.

Abstract

Altermagnetism, a novel magnetic phase characterized by symmetry-protected, momentum-dependent spin splitting and collinear compensated magnetic moments, has thus far been explored primarily in periodic crystals. In this Letter, we extend the concept of altermagnetism to quasicrystals -- aperiodic systems with long-range order and noncrystallographic rotational symmetries. Using a hyperspatial projection framework, we construct decorated Ammann-Beenker and Penrose quasicrystalline lattices with inequivalent sublattices and investigate a Hubbard model with anisotropic hopping. We demonstrate that interaction-induced N\'eel order on such lattices gives rise to alternating spin-polarized spectral functions that reflect the underlying quasicrystalline symmetry, revealing the emergence of unconventional $g$-wave (octagonal) and $h$-wave (decagonal) altermagnetism. Our symmetry analysis and low-energy effective theory further reveal unconventional altermagnetic spin splitting, which is compatible with quasicrystalline rotational symmetry. Our work shows that quasicrystals provide a fertile ground for realizing unconventional altermagnetic phases beyond crystallographic constraints, offering a platform for novel magnetisms and transport phenomena unique to quasiperiodic systems.