Double Exchange Model at Low Densities: Magnetic Polarons and Coulomb   Suppressed Phase Separation
  We consider the double exchange model at very low densities. The conditions for the formation of self-trapped magnetic polarons are analyzed using an independent polaron model. The issue of phase separation in the low density region of the temperature-density phase diagram is discussed. We show how electrostatic and localization effects can lead to the substantial suppression of the phase separated regime. By examining connections between the resulting phase and the polaronic phase, we conclude that they reflect essentially the same physical situation of a ferromagnetic droplet containing one single electron. In the ultra diluted regime, we explore the possible stabilization of a Wigner crystal of magnetic polarons. Our results are compared with the experimental evidence for a polaronic phase in europium hexaboride, and we are able to reproduce the experimental region of stability of the polaronic phase. We further demonstrate that phase-separation is a general feature expected in metallic ferromagnets whose bandwidth depends on the magnetization. 
Vitor M. Pereira, J. M. B. Lopes dos Santos, Antonio H. Castro Neto