Relationship between ferroelectricity and Dzyaloshinskii-Moriya interaction in multiferroics and the effect of bond-bending

We studied the microscopic mechanism of multiferroics, in particular, with the spin current model [H. Katsura et al., Phys. Rev. Lett. 95, 057205 (2005)]. Starting from a system with helical spin configuration, we solved for the forms of the electron wave functions and analyzed their characteristics. The relation between ferroelectricity and Dzyaloshinskii-Moriya interaction [I. Dzyaloshinskii, J. Phys. Chem. Solids 4, 241 (1958) and T. Moriya, Phys. Rev. 120, 91 (1960)] is clearly established. There is also a simple relation between the electric polarization and the wave vector of magnetic orders. Finally, we show that the bond-bending existing in transition metal oxides can enhance ferroelectricity.