The electronic and magnetic behavior of the iron sulphide mineral greigite $\left({\text{Fe}}_3{\text{S}}_4\right)$ is studied using ab initio density-functional theory in the generalized gradient approximation (GGA) with the on-site Hubbard ${\text{U}}_{\text{eff}}$ parameter ($\text{GGA}+\text{U}$). The effect of the Hubbard correction is investigated and is found to be a necessary requirement for the accurate description of both the unit cell structure and the magnetic moment. A ferrimagnetic normal-spinel structure is found when ${\text{U}}_{\text{eff}}=0\text{eV}$, while for all values of ${\text{U}}_{\text{eff}}>0\text{eV}$ an inverse spinel structure is predicted, in agreement with experiment. For low values of ${\text{U}}_{\text{eff}}$ $\left(0<{\text{U}}_{\text{eff}}<4\text{eV}\right)$ the predicted electronic structure corresponds to that of a semimetal, with semimetallicity arising from electron hopping between ferric and ferrous Fe on octahedral sites. For values of ${\text{U}}_{\text{eff}}\ge 4\text{eV}$ the S atoms are found to oxidize the ferrous octahedral sites Fe to the ferric state. To determine whether $\text{GGA}+\text{U}$ predicts a stable monoclinic form of greigite arising from a Verwey-type low-temperature transition, analogous to that seen in magnetite, a monoclinic form of greigite is postulated. It is found that such a phase is stable, with an electronic band-gap opening up for values of ${\text{U}}_{\text{eff}}\ge 2\text{eV}$, but is energetically unfavorable when compared with the spinel phase for all ${\text{U}}_{\text{eff}}$ values tested. It is argued that an accurate description of all the properties of greigite requires a ${\text{U}}_{\text{eff}}$ value of approximately 1 eV.

• Received 10 February 2009

DOI:https://doi.org/10.1103/PhysRevB.79.195126