Hall resistivity in pure cadmium and dilute crystals ofCd-Ag andCd-In

Abstract

The Hall resistivity ${\ensuremath{\rho}}_{21}(H,T)$ ($\stackrel{\ensuremath{\rightarrow}}{H}\ensuremath{\parallel}[0001], \stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}[11\overline{2}0]$) has been measured on pure cadmium single crystals and crystals alloyed with In and Ag in the temperature range 1.4-30 K and for field strengths from 1.7 to 24 kG. The residual resistance ratios of the pure samples varied from 16 000 to greater than 30 000; those of the alloys from 62 to approximately 20 000 [corresponding to controlled impurity concentrations from 500 to 1 part per million by weight (ppmw)]. In the pure samples, ${\ensuremath{\rho}}_{21}(H,T)$ reversed sign for $Tl5$ K, in agreement with previously published results on pure cadmium and a number of Cd-Zn crystal alloys, in which the behavior of ${\ensuremath{\rho}}_{21}(H,T)$ for $1.4 \mathrm{K}\ensuremath{\le}T\ensuremath{\le}10 \mathrm{K}$ was semiquantitatively described in terms of intersheet scattering. In the present alloys, at the lowest temperatures and highest fields, ${\ensuremath{\rho}}_{21}$ approaches a positive, constant value even for concentrations of Ag or In as low as 1 ppmw. It is shown that intersheet scattering cannot consistently account for this new behavior. A two-band model, based on published measurements of the temperature dependences of hole and electron mean free paths in cadmium, is found to be only qualitatively successful in describing ${\ensuremath{\rho}}_{21}(H,T\ensuremath{\le}10 \mathrm{K})$ in the alloys for which ${\ensuremath{\rho}}_{21}$ remains positive. It is suggested that combinations of orbital scattering times $\ensuremath{\tau}(T)$, with various temperature ranges of dominance must be considered for an accurate description of the Hall resistivity in these alloys.