We consider the two-band double exchange model for manganites with Jahn-Teller (JT) coupling and explore the suppression of the ferromagnetism because of the JT distortion. The localized spins of the $\emph{ t}_{ 2g}$ electrons are represented in terms of the Schwinger bosons, and two spin-singlet Fermion operators are introduced instead of the $e_{ g}$ electrons' operators. In terms of the new Fermi fields the on-site Hund's interaction is in a diagonal form and one accounts for it exactly. Integrating out the spin-singlet fermions, we derive an effective Heisenberg model for a vector which describes the local orientations of the total magnetization. The exchange constants are different for different space directions and depend on the density $n$ of $\emph{ e}_{ g}$ electrons and JT energy. At zero temperature, with increasing the density of the $\emph{ e}_{ g}$ electrons the system undergoes phase transition from ferromagnetic phase $(0<n<n_c)$ to A-type antiferromagnetic phase $(n_c<n)$. The critical value $n_c$ decreases as JT energy is increased. At finite temperature we calculate the Curie temperature as a function of electron density for different JT energy. The results show that JT coupling strongly suppresses the spin fluctuations and decreases the Curie temperature.
Categories: cond-mat.str-el cond-mat.mtrl-sci