Hall coefficient in amorphous alloys: critical behavior and quantitative test of quantum corrections due to weak localization and electron-electron interactions

Here, we present the measurements of $R_H$ in a series of $Ti_xSi_{100-x}$ amorphous reaching the critical concentration, $x_c\approx9-9.5$. For $x\geq17$, the Hall coefficient displays the behavior predicted by the perturbation theory, $R_H^{-1}\left(T\right)=R_H^{-1}\left(0\right)+bT^{1/2}$, which extends up to the temperature 150 K. The temperature dependence gets stronger in alloys with lower $x$; $R_H\left(0\right)$ diverges at $x_c$ displaying critical behavior. We used the combined conductivity and Hall coefficient data for alloys with high Ti content to test the theories of quantum corrections to conductivity. We found that the correction due to weak localization is dominated by the electron-phonon scattering with the rate varying with temperature as $\tau_{ep}^{-1}=A_{ep}T^2$. The extracted parameter $A_{ep}$ is in good agreement with the theory that considers the incomplete drag of impurities by lattice vibrations. The spin-orbit scattering time extracted from the weak localization correction was found to be two orders of magnitude larger than the time given by the standard estimate $\tau_{so}\approx\tau\left(\hbar c/e^2Z\right)^4$. The theory of the EEI quantum correction was tested using the Hall coefficient and specific heat data for Ti-Si and $\left(Ag_{0.5}Cu_{0.5}\right)_{100-x}Ge_x$ amorphous alloys, which allowed us to estimate all microscopic parameters needed by the theory. We found that, within the accuracy of our measurements, the EEI theory works exactly for alloys that follow the free electron model [$\left(Ag_{0.5}Cu_{0.5}\right)_{100-x}Ge_x$ with $x\le50$.] The deviation from the theory observed in all Ti-Si alloys and in Ag-Cu-Ge alloys with $x\geq60$ can be qualitatively explained by weakening of the electron screening in the systems.