Magnon Confinement on the Two-Dimensional Penrose Lattice: Perpendicular-Space Analysis of the Dynamic Structure Factor
arXiv:2407.19369 · doi:10.3390/cryst14080702
Abstract
Employing the spin-wave formalism within and beyond the harmonic-oscillator approximation, we study the dynamic structure factors of spin- nearest-neighbor quantum Heisenberg antiferromagnets on two-dimensional quasiperiodic lattices with particular emphasis on a magnetic analog to the well-known confined states of a hopping Hamiltonian for independent electrons on a two-dimensional Penrose lattice. We present comprehensive calculations on the Penrose tiling in comparison with the Ammann-Beenker tiling, revealing their decagonal and octagonal antiferromagnetic microstructures. Their dynamic spin structure factors both exhibit linear soft modes emergent at magnetic Bragg wavevectors and have nearly or fairly flat scattering bands, signifying magnetic excitations localized in some way, at several different energies in a self-similar manner. In particular, the lowest-lying highly flat mode is distinctive of the Penrose lattice, which is mediated by its unique antiferromagnons confined within tricoordinated sites only, unlike their itinerant electron counterparts involving pentacoordinated as well as tricoordinated sites. Bringing harmonic antiferromagnons into higher-order quantum interaction splits the lowest-lying nearly flat scattering band in two, each mediated by further confined antiferromagnons, which is fully demonstrated and throughly visualized in the perpendicular as well as real spaces. We disclose superconfined antiferromagnons on the two-dimensional Penrose lattice.
26 pages including 15 figures and 3 tables
References in corpus (29)
- Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
- Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
- Matter-wave diffraction from a quasicrystalline optical lattice
- Bose-Einstein Condensates in Optical Quasicrystal Lattices
- Observing localisation in a 2D quasicrystalline optical lattice
- Quantum Antiferromagnetism in Quasicrystals
- A Schwinger-boson approach to the kagome with Dzyaloshinskii-Moriya interactions: phase diagram and dynamical structure factors
- Low Temperature Properties of Quantum Antiferromagnetic Chains with Alternating Spins S=1 and 1/2
- Thermodynamic Properties of Heisenberg Ferrimagnetic Spin Chains: Ferromagnetic-Antiferromagnetic Crossover
- Antiferromagnetic order in the Hubbard Model on the Penrose Lattice
- What is a crystal?
- Quantum Fluctuations and Excitations in Antiferromagnetic Quasicrystals
- Order and excitations in large- kagomé-lattice antiferromagnets
- Penrose Quantum Antiferromagnet
- Bosonic representation of one-dimensional Heisenberg ferrimagnets
- Superlattice structure in the antiferromagnetically ordered state in the Hubbard model on the Ammann-Beenker tiling
- Combination of Ferromagnetic and Antiferromagnetic Features in Heisenberg Ferrimagnets
- Ferromagnetism of cold fermions loaded into a decorated square lattice
- The eight-fold way for optical quasicrystals
- Spectrum of short-wavelength magnons in two-dimensional quantum Heisenberg antiferromagnet on a square lattice: third order expansion in 1/S
- Spin waves and local magnetizations on the Penrose tiling
- Mean-field study of the Bose-Hubbard model in Penrose lattice
- Hyperuniform electron distributions controlled by electron interactions in quasicrystal
- Spin-wave thermodynamics of square-lattice antiferromagnets revisited
- Neutron scattering study on spin correlations and fluctuations in the transition-metal-based magnetic quasicrystal Zn-Fe-Sc
- Self-similarity under inflation and level statistics: a study in two dimensions
- Optical observation of quasiperiodic Heisenberg antiferromagnets in two dimensions
- Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: A message from spin waves
- Polarized Raman Response of Two-Dimensional Quasiperiodic Antiferromagnets: Configuration-Interaction versus Green's Function Approaches