Symmetry of Magnetic Structures: Magnetic Structure of Chalcopyrite

Abstract

The transformation properties of magnetic moments under symmetry and antisymmetry operations lead to 1421 possible space groups for ferromagnetic and antiferromagnetic crystal structures. A systematic procedure for magnetic structure determination is proposed, which takes into account the restrictions imposed on spin directions by space groups. This method is applied to chalcopyrite, CuFe${\mathrm{S}}_2$, which is found to be antiferromagnetic at room temperature: the chemical structure is that proposed by Pauling and Brockway, the space group $I\overline{4}2d$ holds for the magnetic structure, in which the two iron (and possibly also the two copper) atoms tetrahedrally bonded to a common sulfur atom have antiparallel spins directed along the $c$ axis. A value of 3.85 μB is found for the iron moment (0±0.20 μB for copper). The possible existence of a second chalcopyrite modification in nature, suggested by conflicting results on material of Japanese origin, is ruled out, as specimens from both Ugo, Japan and Joplin, Missouri are found to have the same structure.