Orbital degree of freedom and phase separation in ferromagnetic manganitesat finite temperatures

The spin and orbital phase diagram for perovskite manganites is investigate d as a function of temperature and hole concentration. The superexchange an d double exchange interactions dominate the ferromagnetic phases in the lig htly and moderately doped regions of holes, respectively. The two interacti ons favor different orbital states. Between the phases, two interactions co mpete with each other and the phase separation appears in the wide range of temperature and hole concentration. The anisotropy of the orbital space ca uses discontinuous changes of the orbital state and promotes the phase sepa ration.