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

We use ab initio electronic structure calculations in combination with Monte Carlo simulations to investigate the magnetic and ferroelectric properties of bulk orthorhombic HoMnO$_3$ and ErMnO$_3$. Our goals are to explain the inconsistencies in the measured magnetic properties of the orthorhombic perovskite manganites (o-$R$MnO$_3$) 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. Our computations stabilize several exotic magnetic orders (so-called w-spiral, H-AFM and I-AFM), whose presence resolve the contradictions in the measured magnetic and ferroelectric properties of o-$R$MnO$_3$. We show that these orders emerge due to strong four-spin ring exchange interactions.