  We argue that the homogeneous distribution of spins in the spin-spiral state
of orthorhombic manganites is deformed by the relativistic spin-orbit
interaction. The thus induced spin-spiral inhomogeneity gives rise to the
ferroelectric response of the purely electronic origin in even-periodic
magnetic structures. The mechanism is generic and explains the appearance of
ferroelectricity in the twofold periodic structure of HoMnO3 as well as the
fourfold periodic structure of TbMnO3. Nevertheless, odd-periodic magnetic
structures preserve the inversion symmetry and thus are not ferroelectric. Our
analysis is based on the low-energy model derived from the first-principles
electronic structure calculations and the Berry-phase formalism for the
electronic polarization.
