  By performing density functional calculations, we investigate the origin of
the skyrmion state and ferroelectricity in Cu2OSeO3. We find that the
Dzyaloshinskii-Moriya interactions between the two different kinds of Cu ions
are extremely strong and induce the helical ground state and the skyrmion state
in the absence and presence of magnetic field, respectively. On the basis of
the general model for the spin-order induced polarization, we propose that the
ferroelectric polarization of Cu2OSeO3 in the collinear ferrimagnetic state
arises from an unusual mechanism, i.e., the single-spin-site contribution due
to the spin-orbit coupling.
