Resistivity, transverse magnetoresistance and Hall effect induced by electron-surface scattering on thin gold films deposited onto preheated mica substrates under high vacuum

We report measurements of the resistivity $\rho $, transverse magnetoresistance $\Delta \rho $/$\rho $ and Hall effect carried out on 4 gold films (thickness of 69, 93, 150 and 185 nm) evaporated onto mica substrates under high vacuum, where the signal is primarily determined by electron-surface scattering. The experiments were performed at low temperatures T (4K $\le $ T $\le $ 50K) under high magnetic field strengths \textbf{B} (1.5 T $\le $ B $\le $ 9 T). $\rho $, $\Delta \rho $/$\rho $ and the Hall tangent tan($\theta )$ = E$_{H}$/E$_{x}$ (E$_{H}$ stands for the transverse Hall field, E$_{x}$ for the longitudinal field) depend on film thickness. Sondheimer's theory predicts $\rho $ and tan($\theta )$, but leads to $\Delta \rho $/$\rho $ \textit{one order of magnitude smaller than observed}. Calecki's model predicts $\rho $ and tan($\theta )$, but leads to $\Delta \rho $/$\rho $ \textit{several orders of magnitude smaller than observed}. The failure of current theories to predict all 3 transport coefficients is the first compelling evidence pointing to the need of a new, fresh theory to describe size effects arising from electron-surface scattering in metallic films in the presence of a magnetic field. Work funded by FONDECYT 1040723.