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We argue that the homogeneous distribution of spins in the spin-spiral stateof orthorhombic manganites is deformed by the relativistic spin-orbitinteraction. The thus induced spin-spiral inhomogeneity gives rise to theferroelectric response of the purely electronic origin in even-periodicmagnetic structures. The mechanism is generic and explains the appearance offerroelectricity in the twofold periodic structure of HoMnO3 as well as thefourfold periodic structure of TbMnO3. Nevertheless, odd-periodic magneticstructures preserve the inversion symmetry and thus are not ferroelectric. Ouranalysis is based on the low-energy model derived from the first-principleselectronic structure calculations and the Berry-phase formalism for theelectronic polarization.

Spin-spiral inhomogeneity as the origin of ferroelectricity in orthorhombic manganites