Magnetoresistance and non-Ohmic conductivity of thin platinum films at low temperatures

The electrical conductivity of thin Pt films is measured as a function of temperature $T$, magnetic field $B$, and electric field $E$. A logarithmic temperature dependence is observed. The magnetoresistance is positive and anisotropic, increasing as $\frac{B^2}{T}$ in small perpendicular fields and logarithmically in high $B_{\perp }$. The electric field causes the resistance to drop proportional to $E^2$ at low $E$ and logarithmically at high $E$, in agreement with localization theory. Our data on the magnetoresistance, however, disagree with theory.