Renormalization Group Approach for the Double Exchange Ferromagnets

Abstract

The discovery of the colossal magnetoresistance (CMR) in the manganese oxides with perovskite structures T1−xDMnO3 (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 rst 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 eg electrons. Consequently, alignment of the core Mn-spins by an external magnetic eld 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, JH > 0. We apply the ow 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 Primako transformation) and investigate the magnon excitation spectrum determined by Green's function.