  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.
