Double-exchange theory of ferroelectric polarization in orthorhombic manganites with twofold periodic magnetic texture

We argue that many aspects of improper ferroelectric (FE) activity in orthorhombic manganites can be rationalized by considering the limit of infinite intra-atomic splitting between majority-and minority-spin states (or the double-exchange limit), which reduces the problem to the analysis of a spinless double-exchange (DE) Hamiltonian. We apply this strategy to the low-energy model, derived from the first-principles electronic-structure calculations, and combine it with the Berry-phase theory of electric polarization. We start with the analysis of the simplest two-orbital model, describing the behavior of the e(g) bands, and apply it to the E-type antiferromagnetic (AFM) phase, which in the DE limit effectively breaks up into one-dimensional zigzag chains. We derive an analytical expression for the electronic polarization (P-el) and explain how it depends on the orbital ordering and the energy splitting Delta between e(g) states. Then, we evaluate parameters of this model for the series of manganites. For these purposes, we start from a more general five-orbital model for all Mn 3d bands and construct a new downfolded model for the e(g) bands. From the analysis of these parameters, we conclude that the behavior of P-el in realistic manganites always corresponds to the limit of large Delta. This property holds for all considered compounds even in the local-density approximation, which typically underestimates Delta. We further utilize this property in order to derive an analytical expression for P-el in a general twofold periodic magnetic texture, based on the five-orbital model and the perturbation-theory expansion for the Wannier functions in the first order of 1/Delta. This expression explains the functional dependence of P-el on the relative directions of spins. Furthermore, it suggests that P-el is related to the asymmetry of transfer integrals, which should have simultaneously symmetric and antisymmetric components in the crystal-field representation. Themain contribution to this asymmetry comes from the antiferro-orbital ordering in the ab plane. Finally, we explain how the FE polarization can be switched between orthorhombic a and c directions by inverting the zigzag AFM texture in every second ab plane. We argue that this property is generic and can be realized even in the twofold periodic texture. DOI: 10.1103/PhysRevB.87.144424