Magnetic localization in mixed-valence manganites

The metal-insulator transition is mixed-valence manganites of the (La0.7{Ca}0.3$)${MnO}₃$ type is ascribed to a modification of the spin-dependent potential ${J}Hs·S associated with the onset of magnetic order at{T}C$. Here ${J}H$ is the on-site Hund's-rule exchange coupling of an ${e}g$ electron with s=1/2 to the ${t}2g$ ion core with S=3/2. Above ${T}C$, the ${e}gelectrons are localized by the random spin-dependent potential and conduction is by variable-range hopping. Over the whole temperature range, the resistivity varies as ln(ρ/{{{ρ}}}_{{{∞}}}$)=[${T}₀1-(M/{M}S)²}/T]1/4, where M/MS 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.