Disorder and density-of-states effects on the Hall constant in amorphous transition-metal alloys

The magnitude of the Hall coefficient $R_H$ of amorphous ${\mathrm{Cu}}_{\mathrm{x}}$ ${\mathrm{Ti}}_{100\mathrm{-}\mathrm{x}}$ and ${\mathrm{Cu}}_{\mathrm{x}}$ ${\mathrm{Zr}}_{100\mathrm{-}\mathrm{x}}$ alloys, prepared by rapid quenching from the melt as well as by sputtering, is found to decrease with increasing temperature. This temperature dependence and the positive sign of $R_H$ are discussed with respect to the presence of d electrons and disorder. Neglecting vertex corrections, we study the effects of a finite spread in the electron’s spectral function. Short-range order is included, and hybridization is taken into account in a two-band model. It is shown that under certain conditions lifetime broadening can lead to a positive Hall constant. Below about 25 K the temperature dependence can be described by a $T^{1/2}$ law for the most accurate measurements. This finding gives support to corrections due to electron-electron interaction that are consistent with the low-temperature conductivity and predictions from perturbation theories for coherence effects in disordered conductors.