Localization and electron-interaction contributions to the magnetoresistance in three-dimensional metallic granular aluminum

Magnetoresistance measurements have been made on three-dimensional granular aluminum specimens with room-temperature resistivities ρRT between 300 and 6000 {μ} {Ω} cm. Four contributions, from localization and electron-interaction effects, including superconducting fluctuations, have been separated. This leads to values of the inelastic and spin-orbit scattering times τᵢₙ(T) and τₛₒ. The dependences of τᵢₙ on T and ρRT are in qualitative agreement with the theory of Schmid based on electron-electron interactions, but there are discrepancies in the quantitative details. The values of τᵢₙ and τₛₒ are of the same order of magnitude as those obtained from measurements on two-dimensional specimens.