The magnetoresistance of CdS samples doped with In has been measured. The samples had electron concentrations between 8.3×${10}^{17}$ and 1.2×${10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The data up to 8 kG were taken over a wide range of temperatures; however, the temperature was limited to the liquid-helium range for fields between 8 and 150 kG. It was found that the observed magnetoresistance is negative to much higher temperatures and fields than has been reported for any other semiconductor. The data are analyzed as the sum of a negative and a positive component. Although qualitative features of the negative component at low fields are consistent with the localized-magnetic-moment model of Toyozawa, we found that there exist quantitative disagreements with the calculations using the second-order perturbation expansion of the $s-d$ exchange Hamiltonian. Some evidence for inclusion of higher-order terms is provided by the logarithmic temperature dependence of the resistivity at zero field. The positive component, because of the magnetic field dependence of the Hall coefficient, is interpreted in terms of the magnetic freeze-out. A semiempirical expression, $\frac{\Delta \rho }{{\rho }_0}=-B_1\ln (1+B_2^2{H}^2)+\frac{B_3^2{H}^2}{(1+B_4^2{H}^2)}$, is suggested to describe the behavior of the observed magnetoresistance. Least-squares fits to this expression are provided along with the consistent and reasonable values of the calculated negative and the positive components.

• Received 25 June 1970

DOI:https://doi.org/10.1103/PhysRevB.2.4084