Universality of the Hall-effect anisotropy in decagonal quasicrystals

Careful studies on single decagonal quasicrystals show that the anisotropy of the Hall coefficient ${\mathit{R}}_{\mathit{H}}$ is quite universal for these structures. ${\mathit{R}}_{\mathit{H}}$ changes sign when the magnetic field rotates by 90° from the tenfold axis. In both cases, ${\mathit{R}}_{\mathit{H}}$ depends weakly on the temperature T between 80–330 K. All the single quasicrystals (Al-Ni-Co, Al-Cu-Co, and Al-Si-Cu-Co) have actual compositions which lead to a definite average valence-electron number, in spite of the nominal compositions, indicating the formation of the decagonal phase confined in a narrow composition range by the strong interaction of the Fermi surface with the quasi-Brillouin zone.