Weak localization (WL) in three-dimensional anisotropic systems has been investigated by measuring the magnetoresistance (MR) of decagonal quasicrystal ${\mathrm{Al}}_{65}$${\mathrm{Cu}}_{15}$${\mathrm{Co}}_{20}$. Both transverse and longitudinal MR measurements have been made for temperatures between 2 and 35 K in fields up to 5 T on single crystals with transport anisotropic ratio $\delta =\frac{D_z}{D_{\mathrm{qc}}}\sim 8$ at 300 K, where $D_z$ and $D_{\mathrm{qc}}$ are diffusion constants along the periodical direction and the quasicrystal plane, respectively. The data can be well described by WL theory, with spin-orbit scattering time ${\tau }_{\mathrm{so}}=1.75\mathrm{}\times {10}^{-12\mathrm{}}$ s and inelastic scattering time ${\tau }_{\mathrm{ie}}=6.3\mathrm{}\times {10}^{-10\mathrm{}}{T}^{-1.7\mathrm{}}$ s, which are comparable to those of $i$-phase quasicrystals such as AlCuFe and AlCuRu. Furthermore, the scaling between transverse and longitudinal MR provides verification of the WL theory for anisotropic systems proposed by Al'tshuler et al.

• Received 2 April 1996

DOI:https://doi.org/10.1103/PhysRevB.54.6046