Temperature-dependent magnetoresistance of pure aluminum and dilute Al-Ga and Al-Mg alloys

We have measured the resistance of very pure polycrystalline aluminum wires (resistance ratio ∼2000) and dilute Al-Ga and Al-Mg alloys in zero field and transverse magnetic fields up to 50 kG for temperatures between 4.2 and 100 K. For all of our samples at low fields, the magnetoresistance, $\frac{\Delta \rho }{{\rho }_0}$, decreases monotonically with temperature and Kohler's rule is observed. At high fields, however, departures from Kohler's rule are observed. For the pure aluminum samples and with $H>\mathrm{}10\mathrm{}$ kG, $\frac{\Delta \rho }{{\rho }_0}$ first increases with temperature, reaches a maximum at 20-25 K, then deceases monotonically with temperature. The temperature at which the maximum in $\frac{\Delta \rho }{{\rho }_0}$ occurs increases with increasing field from about 20 K at $H=10$ kG to about 25 K at $H=50$ kG. Also, with increasing field the departures from Kohler's rule become more pronounced. Although greatly reduced, similar departures from Kohler's rule are also observed in Al-Ga samples, and to an even lesser extent in Al-Mg samples. We find that our results can be understood in terms of a simple "two-band" model assuming the resistivity of the ith band is of the form $a_i+b_i{T}^{x_i}$ and the total conductivity is the sum of the conductivities from each band.