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perturbation of H$_{DM}$ : 

where | 0 〉 , the ground state, has a component ( V/ε$_{dp}$ ) | ψ$_{p}$ 〉 . If we take E$_{0}$$_{M}$ to be the exchange energy J , then eq. (25) and eq. (30) are equivalent in view of eqs. (26) and (28-30). 

Now we can see more clearly what the origin of internal electric field E$_{k}$ is. From eq. (30), we found 

where the factor m$_{e}$c 2 will be cancelled by its inverse in λ . The small factor J/t arises because of the cancellation between different band. See also eqs. (14) and (16). The electric field originates from the perturbation of spin-orbit interaction. The spin-orbit interaction changes the angular dependence of the d-orbital wave functions and hence, the electron density, via the hybridization of d-and p- orbitals. This effect can be interpreted as the result of an internal electric field. However, the electric field thus created does not necessarily give rise to net electric polarization. Certain environments are more advantageous than others. As one can see from eqs. (20), (25) and (28), the helical spin configuration is apt to provide spin current, net electric polarization and multiferroics. 

The magnitude of polarization is also important. If there are odd number of filled bands then the polarization is of the order − → P − q / Ω where Ω ∼ 250 ˚ A 3 is the volume of a unit cell and eq. (14) is used. If we take | ε$_{p}$ − ε$_{d}$ | ∼ 2 eV , Δ E$_{cf}$ ∼ 2 . 0 eV , V $_{= (}$√$_{3}$$_{/}$$_{2) sin(}$$_{α}$ − β ) sin( α/ 2) V ( pdσ ) ∼ 0 . 2 eV , λ ∼ 0 . 05 eV and sin β ∼ 0 . 1 then P ∼ 10 µC/m 2 for ρ ∼ 0 . 1 ˚ A . The bond-bending activated hybridization V is in general greater than V ( pdπ ). and ρ sin β/I where I is 

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