Chiral properties of the two phases - collinear motif (below Morin transition temperature, TM=250 K) and canted motif (above TM) - of magnetically ordered hematite ({alpha}-Fe2O3) have been identified in single crystal resonant x-ray Bragg diffractio
n, using circular polarized incident x-rays tuned near the iron K-edge. Magneto-electric multipoles, including an anapole, fully characterize the high-temperature canted phase, whereas the low-temperature collinear phase supports both parity-odd and parity-even multipoles that are time-odd. Orbital angular momentum accompanies the collinear motif, while it is conspicuously absent with the canted motif. Intensities have been successfully confronted with analytic expressions derived from an atomic model fully compliant with chemical and magnetic structures. Values of Fe atomic multipoles previously derived from independent experimental data, are shown to be completely trustworthy.
Collinear and canted magnetic motifs in haematite were investigated by Kokubun et al. (2008) using x-ray Bragg diffraction magnified at the iron K-edge, and analyses of observations led to various potentially interesting conclusions. We demonstrate t
hat the reported analyses for both non-resonant and resonant magnetic diffraction at low energies near the absorption K-edge are not appropriate. In its place, we apply a radically different formulation, thoroughly tried and tested, that incorporates all magnetic contributions to resonant x-ray diffraction allowed by the established chemical and magnetic structures. Essential to a correct formulation of diffraction by a magnetic crystal with resonant ions at sites that are not centres of inversion symmetry are parity-odd atomic multipoles, time-even (polar) and time-odd (magneto-electric), that arise from enhancement by the electric-dipole (E1) - electric-quadrupole (E2) event. Analyses of azimuthal-angle scans on two space-group forbidden reflections, hexagonal (0, 0, 3)h and (0, 0, 9)h, collected by Kokubun et al. above and below the Morin temperature (TM = 250K), allow us to obtain good estimates of contributing polar and magneto-electric multipoles, including the iron anapole. We show, beyond reasonable doubt, that available data are inconsistent with parity-even events only (E1-E1 and E2- E2). For future experiments, we show that chiral states of haematite couple to circular polarization and differentiate E1-E2 and E2-E2 events, while the collinear motif supports magnetic charges.
