Longitudinal Magnetoresistance of Pure Aluminum Wires

Abstract

The longitudinal magnetoresistance has been investigated for aluminum wires having purity sufficient to make boundary scattering observable. Measurements were made at 4.2°K using fields up to 13 kOe. Wire diameters were in the range 0.005-0.05 cm. As expected, the magnetoresistance becomes increasingly negative at smaller diameters. In order to analyze the data, the normal positive magnetoresistance was taken into account by means of a modified Kohler's rule suggested by Olsen. By use of the free-electron theory of Chambers the mean free path $l$, electron momentum $p$, and the product of mean free path by resistivity $l_{\rho }$, were obtained for each wire. The average $\frac{p}{\hslash }$ was found to be 1.0±0.2×${10}^8$ ${\mathrm{cm}}^{-1\mathrm{}}$. This result was compared with wave numbers expected for central orbits of the approximate second-zone Fermi surface. It was found to correspond most closely to the (111) orbit, consistent with the preferred grain orientation in the wires. The $l_{\rho }$ result, interpreted according to the free-electron relation, gives a surface area about $\frac{2}{3}$ that predicted for the second-zone surface.