Collective electron description of the conduction mechanism in $M_x{\mathrm{Fe}}_{3-x}{O}_4$, $M=\mathrm{Cd},\mathrm{Zn}$

For ${\mathrm{Cd}}_x{\mathrm{Fe}}_{3-x}{O}_4$ and ${\mathrm{Zn}}_x{\mathrm{Fe}}_{3-x}{O}_4$, the conduction-electron concentration has been varied over a wide range without the introduction of $B$-site impurities or defects. Analysis of the ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ Mössbauer-effect data in terms of the local configurations of ${\mathrm{Zn}}^{2+}$ or ${\mathrm{Cd}}^{2+}$ about a $B$-site Fe has permitted the influence of the conduction electrons on the electrostatic and magnetic hyperfine interactions to be monitored. For $x\le 0.3$, the area ratio of the $A$- and $B$-site patterns indicates that all $B$-site ions have nearly identical interactions with the conduction electrons. The isomer shift and magnetic hyperfine field for the local configuration corresponding to ${\mathrm{Fe}}_3$ ${\mathrm{O}}_4$ tend toward more ferriclike values in a regular fashion as the conduction-electron concentration decreases. Shielding effects at the $B$-site ${\mathrm{Fe}}^{3+}$ cores by the conduction electrons are manifested in the form of increasing charge and spin transfer from the neighboring ligands with decreasing conduction-electron concentration. Quadrupole splittings are found to be nearly independent of variation in the conduction electron concentration. All of these results, either individually or collectively, require a collective electron description of the conduction mechanism in ${\mathrm{Fe}}_3$ ${\mathrm{O}}_4$ and no tendency toward localized states at low dopant levels is observed if no defects or impurities are on the $B$ sites.