  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 that 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.
