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We consider the two-band double exchange model for manganites withJahn-Teller (JT) coupling and explore the suppression of the ferromagnetismbecause of the JT distortion. The localized spins of the $\emph{t}_{2g}$electrons are represented in terms of the Schwinger bosons, and twospin-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 isin a diagonal form and one accounts for it exactly. Integrating out thespin-singlet fermions, we derive an effective Heisenberg model for a vectorwhich describes the local orientations of the total magnetization. The exchangeconstants are different for different space directions and depend on thedensity $n$ of $\emph{e}_{g}$ electrons and JT energy. At zero temperature,with increasing the density of the $\emph{e}_{g}$ electrons the systemundergoes phase transition from ferromagnetic phase $(0<n<n_c)$ to A-typeantiferromagnetic phase $(n_c<n)$. The critical value $n_c$ decreases as JTenergy is increased. At finite temperature we calculate the Curie temperatureas a function of electron density for different JT energy. The results showthat JT coupling strongly suppresses the spin fluctuations and decreases theCurie temperature.

Effect of Jahn-Teller coupling on Curie temperature in the Double Exchange Model