Four-spin ring interaction as a source of unconventional magnetic orders in orthorhombic perovskite manganites

We use ab initio electronic structure calculations and Monte Carlo simulations to investigate the magnetic and ferroelectric properties of bulk orthorhombic HoMnO₃ and ErMnO₃. Our goals are to explain the inconsistencies in the measured magnetic properties of the orthorhombic perovskite manganites (o-RMnO₃) with small rare-earth (R) cations or Y, as well as the contradictions between the directions and amplitudes of the electric polarizations reported by different experimental groups. We find that several unconventional magnetic orders (so-called w-spiral, H-AFM and I-AFM) can be stabilized in these materials due to strong four-spin ring exchange interactions. We show that the presence of these orders resolves the contradictions in the measured magnetic and ferroelectric properties of o-RMnO₃.