Renormalization Group Approach for the Double Exchange Ferromagnets

The discovery of the colossal magnetoresistance (CMR) in the manganese oxides with perovskite structures $T_1 - x DMnO_3$ (T = La, Pr, Nd; D=Sr, Ca, Ba, Pb) and its potential technological application motivated theoretical and experimental researchers to study the itinerant ferromagnetism. A first theoretical description of this phenomenon in terms of the double-exchange mechanism was given a long time ago by Zener. In this model, the spin orientation of adjacent Mn-moments is associated with kinetic exchange of conduction $e_g$ electrons. Consequently, alignment of the core Mn-spins by an external magnetic field causes higher conductivity. The Mn ions are considered as localized forming a spin of S = 3/2 and they are coupled to the itinerant electrons by a strong ferromagnetic Hund coupling, $J_H$ > 0. We apply the flow equation technique (nonperturbative method, based on continuous canonical transformation) to the double-exchange model for ferromagnetism described by the Kondo type Hamiltonian. We want to eliminate the interaction term responsible for non-conservation of magnon number and to take into account fermion and magnon degrees of freedom. We express the spin operators of Mn ions via the magnon operators (the Holstein-Primakoff transformation) and investigate the magnon excitation spectrum determined by Green's function.