Double-exchange model for noninteracting electron spins coupled to a lattice of classical spins: Phase diagram at zero temperature

The analytical zero-temperature phase diagram of the double exchange model for classical background spins as a function of the carrier density and Hund's coupling in the entire range of these parameters is presented. By constructing a continuum field theory we explore the possibility of a continuous phase transition from ferromagnetic state to a gently varying textured state. We find such a transition in and below two dimensions and show that the emerging stable state is a spin-spiral which survives the tendency towards phase separation into commonly considered phases, and is also energetically favored to the canted state, for low carrier density.