Magnetic structure and exchange interactions in pyrrhotite end member minerals: Hexagonal FeS and monoclinic Fe₇S₈

Iron mono-sulphides, or pyrrhotites, are minerals present in the Earth's crust and mantle as well as major magnetic constituents of several classes of meteorites, thus are of interest to a wide range of disciplines including geology, geophysics, geochemistry, and material science. Despite displaying diverse magnetic properties as a result of iron vacancy ordering, the underlying exchange mechanism has not been quantified. This study presents an examination of the electronic and magnetic properties for the two pyrrhotite group end members, hexagonal FeS and monoclinic Fe7S8 (4C superstructure) by means of density functional theory coupled with a Heisenberg magnetic model. The easy magnetization axes of FeS and Fe7S8 are found to be positioned along the crystallographic c-direction and at an angle of 56 to the c-direction, respectively. The magnetic anisotropy energy in Fe7S8 is greatly increased as a consequence of the vacancy framework when compared to FeS. The main magnetic interaction, in both compounds, is found to be the isotropic exchange interaction favouring antiferromagnetic alignment between nearest-neighbouring spins. The origin of the exchange interaction is elucidated further following the Goodenough-Kanamori-Anderson rules. The antisymmetric spin exchange is found to have a minor effect in both compounds. The theoretical findings presented in this work thus help to further resolve some of the ambiguities in the magnetic features of pyrrhotites.