Bond electronic polarization induced by spin

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.