Strategy for achieving multiferroic E-type magnetic order in orthorhombic manganites RMnO₃ (R = La-Lu)

Based on first-principles calculations, multiferroic properties of orthorhombic manganites (RMnO₃, R = La-Lu) with E-type ground state have been achieved by lanthanide contraction (chemical pressure) and/or external strain. Our research demonstrates that a smaller R radius within the octahedral voids in RMnO₃ results in the increase in the tilts of the octahedra but only a gentle change in the Jahn-Teller (JT) distortion. The reduction of the intraplane octahedral rotation angle and the narrowed e_g states and lifting t_2g band edge are mainly responsible for the intraplane magnetic transition from ferromagnetic (La-Gd) to zigzag-like spin arrangement (Ho-Lu). In turn, the center-broken E-type RMnO₃ bulk characterizes the dominated electronic polarization behavior, benefiting from their distortion response to small R substitution, which gives rise to the strong magnetoelectricity. Subsequently, we have figured out the strain strategy for obtaining an E-type transition in light rare-earth manganites (La-Gd) by imposing a series of hypothetical strains, where the small intraplane rotation angle (Θ) and large JT distortion favor the small aspect ratios of a/b and c/b, respectively. The strained LaMnO₃ and GdMnO₃ achieve E-type transitions successfully by imposing a modest compressive strain along the a- and c-axes and remaining free along the b-direction. Simultaneously, their polarization behaviors were comparatively studied. It was found that the size of the A-site rare-earth ions has a great influence on the external strain response, in addition to its effect on the magnetic phase transition.