  We investigate the origin of the coplanar helicoidal magnetic structure and
the ferroelectric polarization in Cu3Nb2O8 by combining first-principles
calculations and our spin-induced ferroelectric polarization model. The
coplanar helicoidal spin state comes from the competition between the isotropic
exchange interactions, and the ferroelectric polarization from the symmetric
exchange striction with slight spin canting. However, the direction of the
polarization is not determined by the orientation of the spin rotation plane.
