Electronic and magnetic properties of multiferroic ScFeO₃ available from diffraction experiments

Electronic and magnetic properties of ferric ions (3d ⁵) in multiferroic ScFeO₃ are puzzling, in part because they are different from the only other multiferroic known to possess the same polar chemical structure, BiFeO₃. Open questions about ScFeO₃ can be addressed by confronting observations with results for G-type antiferromagnetism allowed by the lithium niobate (LiNbO₃)-like parent R3c structure. Calculated structure factors for resonant x-ray diffraction include all charge-like quadrupoles allowed by symmetry, and if experimental results for ScFeO₃ subsequently imply they are different from zero then ferric ions cannot be in the high-spin ⁶S state. The same type of experiment can reveal the moment direction in the G-type antiferromagnetism, according to our calculations, and thereby contribute to understanding magnetic anisotropy. Furthermore, structure factors for magnetic neutron diffraction by ScFeO₃ include Dirac multipoles that are time-odd and parity-odd, e.g. dipoles that are often called anapoles or toroidal moments. Apart from Dirac multipoles, the conventional approach to the interpretation of neutron Bragg diffraction data will be inadequate if ferric ions (Fe³⁺) are not in the high-spin ⁶S state, because the scattering amplitude includes more than simple dipole moments in the general case.