Mixed-Conduction Model for Charge Transport inn-Type CdCr2Se4

A model consisting of a conduction band and a subsidiary hole band is presented and applied to explain recently published transport data on Cd${\mathrm{Cr}}_2$ ${\mathrm{Se}}_4$ — a chalcogenide spinel semiconductor which becomes ferromagnetic below $T_C\approx 130$°K. The crucial feature of the data, which describe the behavior of $\rho$, $R_0$, and $Q$ from 300 to 4.2°K, is the coincidence of maxima in $\rho$ and in $\left|R_0\right|$ with a minimum in $\mathrm{}\left|Q\right|\mathrm{}$, at 150°K. The data cannot be explained in terms of a single conduction band, even if the spin splitting of the band and the effect of spin-disorder scattering are included, nor in terms of two-electron conduction bands. The present twoband model, wherein one band is the $n$-type conduction band and the other is a subsidiary hole band in the band gap, is the simplest one which can account for the data in a consistent manner. As $T$ is lowered from 300 to 150°K, electrons freeze out onto the donors while the hole concentration increases; below 150°K the hole concentration decreases while the electron concentration increases rapidly, because of the reduction of the donor ionization energy. These effects are due to temperature-dependent changes of the above interband energies associated with the assumed relative motions of the bands as the temperature is lowered below 186°K - an effect due to intra-atomic exchange. Evidence for localized transport at very low temperatures is discussed briefly.