Nuclear spin relaxation in quasicrystals via hierarchically variable-range electron hopping

A model of NMR spin-lattice relaxation in quasicrystals is presented, which takes into account two important quasicrystals-specific features: (i) the critical nature of the electronic states and (ii) the phonon-assisted hopping nature of electronic conduction within the self-similar quasiperiodic structure of hierarchical clusters. The model is derived for highly resistive quasicrystals that undergo a metal-to-insulator transition in the T --> 0 limit. The applicability of the model was tested by Al-27 NMR spin-lattice relaxation experiment on several samples including structurally perfect icosahedral Al70.5Pd21Re8.5 and Al62Cu25.5Fe12.5 and less perfect icosahedral Al63Cu23Fe12 quasicrystals, as well as on the metallic Al32.2Cu56.6Fe11.2. The results show that the model applies well to the structurally perfect samples with high-electrical resistivity, whereas it does not apply to the less perfect samples with an increased metallic character. However, the NMR relaxation data show a precursor of the electron hopping conduction also in less perfect samples, suggesting that this phenomenon may not be restricted to high-quality quasicrystals only.