Magnetic localization in mixed-valence manganites

The metal-insulator transition is mixed-valence manganites of the (${\mathrm{La}}_{0.7}$ ${\mathrm{Ca}}_{0.3}$)${\mathrm{MnO}}_3$ type is ascribed to a modification of the spin-dependent potential ${\mathrm{J}}_{\mathrm{H}}$ s⋅S associated with the onset of magnetic order at ${\mathrm{T}}_{\mathrm{C}}$. Here ${\mathrm{J}}_{\mathrm{H}}$ is the on-site Hund's-rule exchange coupling of an ${\mathrm{e}}_{\mathrm{g}}$ electron with s=1/2 to the ${\mathrm{t}}_{2\mathrm{g}}$ ion core with S=3/2. Above ${\mathrm{T}}_{\mathrm{C}}$, the ${\mathrm{e}}_{\mathrm{g}}$ electrons are localized by the random spin-dependent potential and conduction is by variable-range hopping. Over the whole temperature range, the resistivity varies as ln(ρ/${\mathrm{\rho }}_{\mathrm{\infty }}$)=[${\mathrm{T}}_0${1-(M/${\mathrm{M}}_{\mathrm{S}}$ ${)}^2$}/T${]}^{1\mathrm{/}4}$, where M/${\mathrm{M}}_{\mathrm{S}}$ is the reduced magnetization. The temperature and field dependence of the resistivity deduced from the molecular-field theory of the magnetization reproduces the experimental data over a wide range of temperature and field.