Spin waves and local magnetizations on the Penrose tiling

Abstract

We consider a Heisenberg antiferromagnet on the Penrose tiling, a quasiperiodic system having an inhomogeneous Neel-ordered ground state. Spin wave energies and wavefunctions are studied in the linear spin wave approximation. A linear dispersion law is found at low energies, as in other bipartite antiferromagnets, with an effective spin wave velocity lower than in the square lattice. Spatial properties of eigenmodes are characterized in several different ways. At low energies, eigenstates are relatively extended, and show multifractal scaling. At higher energies, states are more localized, and, depending on the energy, confined to sites of a specified coordination number. The ground state energy of this antiferromagnet, and local staggered magnetizations are calculated. Perpendicular space projections are presented in order to show the underlying simplicity of this "complex" ground state. A simple analytical model, the two-tier Heisenberg star, is presented to explain the staggered magnetization distribution in this antiferromagnetic system.

14 pages, 21 figures

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Cited by in corpus (22)

• Antiferromagnetic order in the Hubbard Model on the Penrose Lattice
• Strictly localized states in the octagonal Ammann-Beenker quasicrystal
• Hubbard Models for Quasicrystalline Potentials
• Mean-field study of the Bose-Hubbard model in Penrose lattice
• Spin waves in planar quasicrystal of Penrose tiling
• Perpendicular space accounting of localized states in a quasicrystal
• Quasiperiodic pairing in graphene quasicrystals
• A phason disordered two dimensional quantum antiferromagnet
• Quasiperiodic Heisenberg antiferromagnets in two dimensions
• Electronic structure and transport in approximants of the Penrose tiling
• Sub-diffusive electronic states in octagonal tiling
• Magnetic Field Controlled Surface Localization of Spin-Wave Ferromagnetic Resonance Modes in 3D Nanostructures
• Optical observation of quasiperiodic Heisenberg antiferromagnets in two dimensions
• Geometry fluctuations in a two-dimensional quantum antiferromagnet
• Electronic structure and transport in materials with flat bands: 2D materials and quasicrystals
• Approximations of symbolic substitution systems in one dimension
• Magnon Confinement on the Two-Dimensional Penrose Lattice: Perpendicular-Space Analysis of the Dynamic Structure Factor
• Polarized Raman Response of Two-Dimensional Quasiperiodic Antiferromagnets: Configuration-Interaction versus Green's Function Approaches
• Raman Characterization of Two-Dimensional Quasiperiodic Antiferromagnets on Various Lattices: Spin-Orbit Mechanism
• Phason Disorder Effects in the Penrose Tiling Antiferromagnet
• Weakening of antiferromagnetism due to frustration on inhomogeneous 2D lattices
• Ground states of a family of frustrated spin models for quasicrystals and their approximants