Lack of a threefold rotation axis in α-Fe₂O₃ and α-Cr₂O₃ crystals.

Abstract

The crystal structure of α-Fe2O3 and α-Cr2O3 is usually described with the corundum-type trigonal crystal structure based on the space group R3¯c. There are, however, some observations of the magnetic ordering of both α-Fe2O3 and α-Cr2O3 that are incompatible with the trigonal symmetry. We show experimental evidence based on X-ray powder diffraction and supported by transmission electron microscopy that the symmetry of the crystal structure of both α-Fe2O3 and α-Cr2O3 is monoclinic and it is described with the space group C2/c (derived from R3¯c by removing the threefold rotation axis). The magnetic orderings of α-Fe2O3 and α-Cr2O3 are compatible with the magnetic space groups C2/c and C2/c', respectively. These findings are in agreement with the idea from Curie [(1894), J. Phys. 3, 393-415] that the dissymmetry of the magnetic ordering should be associated with a dissymmetry of the crystal structure.