Manganites near a metal-insulator transition — double-exchange and phase competition
Double-Exchange (Zener 1951): in mixed-valence manganites (Mn³⁺/Mn⁴⁺), an e_g electron hops Mn³⁺→O→Mn⁴⁺ only when the core t₂g spins are parallel (Hund's rule). Thus ferromagnetism and metallicity are tied together. Near T_C, thermal spin disorder blocks hopping → insulator. A magnetic field aligns spins → dramatic resistance drop. CMR ratio can reach 10⁶ in thin films near T_C (La₀.₇Ca₀.₃MnO₃). Competing with charge-ordered (CO) insulating phase at x≈0.5 makes the transition exceptionally sharp.