Orbital degree of freedom and phase separation in ferromagnetic manganites at finite temperatures

The spin and orbital phase diagram for perovskite manganites is investigated as a function of temperature and hole concentration. The superexchange and double exchange interactions dominate the ferromagnetic phases in the lightly and moderately doped regions of holes, respectively. The two interactions favor different orbital states. Between the phases, two interactions compete with each other and the phase separation appears in the wide range of temperature and hole concentration. The anisotropy of the orbital space causes discontinuous changes of the orbital state and promotes the phase separation.