The true low field Hall coefficient of pure aluminium at low temperatures

A study has been made of the true low field Hall coefficient, R_H, of four samples of pure aluminium between 4.2 and 77K. All samples exhibited a low-temperature maximum in the temperature range 7-10K and the three purest samples possessed a minimum between 25 and 30K. An analysis of the low-temperature results is given using a three group model. It is found that, despite the dominance of impurity scattering, the low-temperature maximum may be explained if the mean free paths due to phonon scattering of second-zone holes and third-zone electrons have different temperature dependences. The experimental results on the four samples are found to obey the theoretical prediction that a single function exists when ((R_H-R_H(T=0))/(R_H^max-R_H(T=0))) is plotted against (T/T_max). The theory also enables the anisotropy of mean free paths for phonon scattering of the second-zone free electrons and the third-zone electrons to be deduced from the Hall results and is found to agree with that deduced from radio frequency size effect and surface Landau level experiments.