Mean Free Path of Electrons and Magnetomorphic Effects in Small Single Crystals of Gallium

Abstract

The variation of electrical resistivity of 99.9999%-pure gallium has been investigated as a function of size in oriented single crystals for current flow along the $C$ axis. The crystals were in the form of wires of square cross section and their dimensions varied from 1 to 0.1 mm. Analysis of the data based on the free-electron model, assuming diffuse scattering at the boundaries, yields a value of 8.11×${10}^{-11\mathrm{}}$ Ω-${\mathrm{cm}}^2$ for ${\left({\rho }_b{l}_b\right)}_{\mathrm{Caxis}}$ and indicates that at 0°K the mean free path of the charge carriers in the bulk metal is considerably in excess of 1 cm. The temperature dependence of the size effect seems to be in fair agreement with a theory due to Blatt and Satz. Within the accuracy of our measurements the ideal bulk resistivity at low temperatures varies as $T^2$, indicating that the electron-electron collisions may be contributing to the resistive processes. For low values of a longitudinal magnetic field, all the crystals showed a large decrease in resistance followed by an increase due to bulk magnetoresistance, both at 4.2° and at 1.2°K. For the same two temperatures these crystals also displayed a rather large magnetoresistance in transverse magnetic fields. Magnetomorphic effects for transverse fields were evidenced by the fact that the field dependence of magnetoresistance was less than quadratic for all crystals until the cyclotron radius of the charge carriers acquired a value much smaller than the cross-sectional dimensions of the specimens. The resistance of all the crystals was found to be a complicated function of the measuring current. Calculations based on certain simplifying assumptions show that for thin wires in which boundary scattering is predominant, the resistance decreases monotonically as a function of the current and is due to the trapping of the charge carriers in the magnetic field generated by the current. The details of the experimental curves can be reproduced reasonably well if the fall in resistance due to the trapped particles is superimposed on the magnetoresistance caused by the self field.