Magnetically induced ferroelectricity in orthorhombic manganites:: Microscopic origin and chemical trends

The microscopic origin of the magnetically driven ferroelectricity in collinear E-type antiferromagnetic (AFM-E) orthorhombic manganites is explained by means of first-principles Wannier functions. We show that the polarization is mainly determined by the asymmetric electron hopping of orbitally polarized e(g) states, implicit in the peculiar in-plane zigzag spin arrangement in the AFM-E configuration. In ortho-HoMnO3, Wannier-function centers are largely displaced with respect to corresponding ionic positions, implying that the final polarization is strongly affected by a purely electronic contribution, at variance with standard ferroelectrics where the ionic displacement is dominant. However, the final value of the polarization is the result of competing effects, as shown by the opposite signs of the contributions to the polarization coming from the Mn e(g) and t(2g) states. Furthermore, a systematic analysis of the link between ferroelectricity and the spin, orbital, and lattice degrees of freedom in the manganite series has been carried out, in the aim of ascertaining chemical trends as a function of the rare-earth ion. Our results show that the Mn-O-Mn angle is the key quantity in determining the exchange coupling: upon decreasing the Mn-O-Mn angle, the first- (second-) nearest-neighbor ferromagnetic (antiferromagnetic) interaction decreases (remains constant), in turn stabilizing either the A-type antiferromagnetic or the AFM-E spin configuration for weakly or strongly distorted manganites, respectively. The Mn e(g) contribution to the polarization dramatically increases with the Mn-O-Mn angle and decreases with the long Mn-O bond length, whereas the Mn t(2g) contribution decreases with the short Mn-O bond length, partially canceling the former term.