Double-exchange mechanism in rare-earth compounds

We show that double-exchange mechanism is responsible for ferromagnetism in low dimensional rare-earth compounds. We use the bosonized version of the one-dimensional Anderson lattice model in Toulouse limit to characterize the properties of the emerging ferromagnetic phase. We give a comprehensive description of the ferromagnetic ordering of the correlated electrons which appears at intermediate couplings and doping. The obtained ferromagnetic phase transitions have been identified to be an order–disorder transition of the quantum random transverse-field Ising type.