  We study theoretically the electric polarization induced by noncollinear spin
configurations in the limit of strong Hund coupling. We employ a model of two
magnetic ions sandwitching an oxygen ion. It is shown that there appears a
longitudinal polarization P_x along the bond, which is roughly proportional to
(m_r^x)^2-(m_l^x)^2 where m_{r(l)}^x is the x-component of the spin orientation
vector at right (left) magnetic ion. A numerical study of the model Hamiltonian
yields both longitudinal and transverse electric dipole moments. The transverse
polarization is shown to have a non-uniform as well as a uniform component,
with the latter being consistent with the previous theory. The longitudinal
polarization is non-uniform and oscillating with the period half that of the
spin order, but the local magnitude is typically much larger than the uniform
transverse polarization and may be detected by X-ray/neutron scattering
experiments.
