Localization and negative magnetoresistance in thin copper films

The electrical properties of thin Cu films with resistance per square in the range 1 to 100 $\frac{\ensuremath{\Omega}}{\ensuremath{\square}}$ have been studied. For temperatures below 10 K, the resistance of the films increases logarithmically with decreasing temperature and the magnitude of the rise becomes larger as the resistance per square is increased. The results are in good agreement with the predictions of Abrahams et al. for localization in two dimensions. The effect of a magnetic field has also been investigated. The negative magnetoresistance observed in a perpendicular field is in good agreement with the recent theory of Altshuler et al.: At low fields ($Hl{10}^{\ensuremath{-}2}$ T), no magnetoresistance is observed; for ${10}^{\ensuremath{-}2}\mathrm{T}lHl1$ T the magnetoresistance changes logarithmically with the magnetic field. For very high fields ($H\ensuremath{\gtrsim}5$ T), localization is destroyed, as predicted by theory. In a field parallel to the film plane no negative magnetoresistance is observed. A detailed analysis of the results indicates that spin-orbit effects (of moderate strength) must be taken into account.