Spin-spiral inhomogeneity as the origin of ferroelectric activity in orthorhombic manganites

We argue that the homogeneous distribution of spins in the spin-spiral state of orthorhombic manganites is strongly 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 the even-periodic magnetic structures. The mechanism is generic and takes place in the twofold-periodic HoMnO₃ as well as in the fourfold-periodic TbMnO₃. Thus, we expect that the magnetic structure of these two characteristic improper multiferroics with the orthorhombic Pbnm structure is neither E-type antiferromagnetic nor the homogeneous spin spiral, but a new type of noncollinear magnetic state, which breaks the inversion symmetry and leads to the ferroelectric activity of a similar origin both in HoMnO₃ and in TbMnO₃. Furthermore, we predict that odd-periodic magnetic structures preserve the inversion symmetry and thus should not be ferroelectric. We discuss available experimental data in the light of these new arguments. Our theoretical 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.