Transverse magnetoresistance and size effects of thin gold films: Experiment and theory.

We report new experimental data regarding the transverse magnetoresistance measured with the electric field \textbf{E} oriented perpendicular to the magnetic field \textbf{B}, both fields (\textbf{E}, \textbf{B}) contained within the plane of the film (the MacDonald configuration) performed in a family of gold films of different thickness. The signal at 4 K can be univocally attributed to electron-surface scattering. Transport measurements were performed at low temperatures T (4K $\le $ T $\le $ 50K) under magnetic field strengths B (1.5 T $\le $ B $\le $ 9 T). The magnetoresistance signal exhibits a marked thickness dependence, and its curvature as a function of magnetic field B varies with film thickness. We also present a new theoretical description based upon a solution of Boltzmann Transport Equation [MacDonald D. C. K. and Sarginson K., 1950 \textit{Proc. Roy. Soc. (London)} \textbf{A 203} 223], computed using the method of characteristics proposed by Chambers [Chambers R. G., 1950 \textit{Proc. Roy. Soc. (London)} \textbf{A 202} 378]. The theoretical description of the magnetic field dependence of the magnetoresistance requires a Hall field that varies with the thickness of the film; this Hall field is tuned to reproduce the experimental data.