Phase Transition in Perovskite Manganites with Orbital Degree of Freedom

Roles of orbital degree of freedom of Mn ions in phase transition as a function of temperature and hole concentration in perovskite manganites are studied. It is shown that the orbital order-disorder transition is of the first order in the wide region of hole concentration and the N$\rm \acute{e}$el temperature for the anisotropic spin ordering, such as the layer-type antiferromagnetic one, is lower than the orbital ordering temperature due to the anisotropy in the orbital space. The calculated results of the temperature dependence of the spin and orbital order parameters explain a variety of the experiments observed in manganites.