Magnetically induced ferroelectricity in TbMnO3: inverse Goodenough-Kanamori interaction

Improper ferroelectricity in magnets, as induced by non-centrosymmetric spin-, charge- or orbital-ordering, is a branch of the field of multiferroics having fascinating physics and a potentially important technological outcome. We focus here on ferroelectricity in orthorhombic TbMnO3, where the magnetic field along the a-axis produces a polar collinear spin- arrangement with a rather large in-plane electric polarization. The mechanism, similar to that occurring in orthorhombic HoMnO3 in the AFM-E phase, is efficiently driven by a large modification of the structural properties (such as MnO bond-lengths and Mn-O-Mn bond-angles) to favor eg electron hopping between Mn with parallel spins. A similar mechanism where the t(2g) states are involved is examined through a hypothetical collinear spin-structure, resulting in a weaker out-of-plane ferroelectric polarization.