  The dielectric constant of the incipient ferroelectric EuTiO$_3$ exhibits a
sharp decrease at about 5.5K, at which temperature antiferromagnetic ordering
of the Eu spins simultaneously appears, indicating coupling between the
magnetism and dielectric properties. This may be attributed to the modification
of the soft-phonon mode, $T_{1\mu}$, which is the main contribution to the
large dielectric constant, by the Eu spins(7$\mu_B$ per Eu). By adding the
coupling term between the magnetic and electrical subsystems as $
-g\sum\limits_l {\sum\limits_{< {i,j}} {q_l^2}} \overrightarrow {S_i} \cdot
\overrightarrow {S_j} $ we show that the variation of the frequency of
soft-phonon mode depends on the spin correlation between the nearest neighbors
Eu spins and is substantially changed under a magnetic field.
