Parity-odd multipoles, magnetic charges and chirality in haematite (alfa-Fe2O3)

TL;DR

This paper revises the analysis of magnetic diffraction in haematite, emphasizing the importance of parity-odd multipoles and demonstrating the presence of chiral states and magnetic charges through resonant x-ray diffraction.

Contribution

It introduces a new formulation for analyzing magnetic x-ray diffraction that incorporates parity-odd multipoles, challenging previous analyses and providing clearer insights into haematite's magnetic structure.

Findings

Parity-odd multipoles are essential for accurate diffraction analysis.

Data indicate the presence of chiral states and magnetic charges in haematite.

Analysis shows inconsistency with only parity-even events in previous models.

Abstract

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.