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 sandwiching an oxygen ion. It is shown that there appears a longitudinal polarization $P_x$ along the bond, which is roughly proportional to ${\left(m_r^x\right)}^2-{\left(m_l^x\right)}^2$ where $m_{r\left(l\right)}^x$ 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 nonuniform as well as a uniform component, with the latter being consistent with the previous theory. The longitudinal polarization is nonuniform 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.