Fragile magnetic order in metallic quasicrystals

Abstract

Inspired by recent experimental studies of local magnetic moments interacting with a metallic quasicrystal, we study the low-temperature fate of spins placed in two-dimensional tilings. In the diluted local moment limit, we calculate the spin relaxation rate $1/T_1$, as measured by electron spin resonance, and show that it displays a marked dependence on the system size $N$ and the filing $n$ of the electronic bath. For a finite concentration of spins, we integrate out the conduction electrons and generate an effective magnetic coupling between the local moments, which we treat as Ising spins. Despite the strongly frustrating nature of the magnetic couplings and the lack of periodicity in the problem, we find long-range orders for finite $N$ in our large-scale Monte Carlo simulations. However, the resulting magnetically state is fragile, as clusters of essentially free spins fluctuate down to very low temperatures.

13 pages, 16 figures. Published version

References in corpus (25)

• The Kernel Polynomial Method
• Quantum critical state in a magnetic quasicrystal
• Superconductivity and strong interactions in a tunable moiré quasiperiodic crystal
• Real-space calculation of the conductivity tensor for disordered topological matter
• Superconductivity on a Quasiperiodic Lattice: Extended-to-Localized Crossover of Cooper Pairs
• Antiferromagnetic order in the Hubbard Model on the Penrose Lattice
• Conventional superconductivity in quasicrystals
• Non-Fermi-Liquid Behavior in Metallic Quasicrystals with Local Magnetic Moments
• Kohn-Luttinger mechanism driven exotic topological superconductivity on the Penrose lattice
• Valence Fluctuations and Electric Reconstruction in the Extended Anderson Model on the Two-Dimensional Penrose Lattice
• Magnetic and transport properties of i-$R$-Cd icosahedral quasicrystals ($R$ = Y, Gd-Tm)
• Magnetic orders induced by RKKY interaction in Tsai-type quasicrystalline approximant Au-Al-Gd
• Magnetism in Rare Earth Quasicrystals: RKKY Interactions and Ordering
• Anderson-Kitaev spin liquid
• Mean-field study of the Bose-Hubbard model in Penrose lattice
• Energy levels and their correlations in quasicrystals
• Partial lifting of degeneracy in the $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice
• Superconducting proximity effect and order parameter fluctuations in disordered and quasiperiodic systems
• Quasicrystalline Weyl points and dense Fermi-Bragg arcs
• The phase diagram of a frustrated Heisenberg model: from disorder to order and back again
• Properties of the Ammann-Beenker tiling and its square approximants
• Stripe order, impurities, and symmetry breaking in a diluted frustrated magnet
• The Aubry-Andre Anderson model: Magnetic impurities coupled to a fractal spectrum
• Partial magnetic order in kagome spin ice
• Universality in the 2d quasi-periodic Ising model and Harris-Luck irrelevance

Cited by in corpus (1)

• Stripe order in quasicrystals