Origin of the Hall-coefficient anisotropy in the Y–Al–Ni–Co periodic approximant to the decagonal phase

We present an experimental and theoretical study of the anisotropic Hall coefficient R H of the Y–Al–Ni–Co periodic approximant to the decagonal phase with composition Al76Co22Ni2. Performing ab-initio calculation of R H for the original Y–Al–Ni–Co structural model [B. Zhang, V. Gramlich, W. Steurer, Z. Kristallogr. 210 (1995) 498] and its relaxed version, we reproduced the experimentally observed anisotropy for all combinations of crystalline directions of the electric current and magnetic field, where the relaxed model yielded better quantitative matching to the experiment. The origin of the anisotropic Hall coefficient is the anisotropic Fermi surface, the anisotropy of which originates from the specific stacked-layer structure of the Y–Al–Ni–Co compound and the chemical decoration of the lattice. Due to the structural similarity of Y–Al–Ni–Co to the d -Al–Ni–Co-type decagonal quasicrystals, the same physical picture explains the universal R H anisotropy of this family of quasicrystals, where R H changes sign along different crystalline directions.