Charge order in Magnetite. An LDA+U study

– The electronic structure of the monoclinic structure of Fe3O4 is studied using both the local density approximation (LDA) and the LDA+U . The LDA gives only a small charge disproportionation, thus excluding that the structural distortion should be sufficient to give a charge order. The LDA+U results in a charge disproportion along the c-axis in good agreement with the experiment. We also show how the effective U can be calculated within the augmented plane wave methods. Introduction. – Magnetite has received a lot of attention both for fundamental and technological reasons. Above the Verwey transition it is a half-metal and has the highest known Tc of 860 K. The crystal structure is the inverse spinel structure with the formal chemical composition Fe A [Fe Fe]BO 2− 4 . The two octahedrally coordinated B positions are symmetry equivalent and order antiferromagnetically with the tetrahedrally coordinated A site in the cubic Fd3̄m spacegroup. When cooled to the Verwey transition temperature, which lies around 122-125 K depending on sample, the conductivity of magnetite drops abruptly by two orders of magnitude. Originally the structure below the Verwey transition transition was thought to be have iron cations at the B sites order as Fe and Fe along the (001) planes. This turned out to be too simple a model and single crystal diffraction studies showed that the low temperature structure is monoclinic with a √ 2a × √ 2a × 2a supercell and a Cc space group symmetry. A recent NMR study resolved 8 tetrahedral and 16 octahedral environments thereby confirming the Cc space group. [1] However, the diffracted supercell peaks are extremely weak and even a recent synchrotron diffraction study could only resolve three supercell peaks. [2] The structure has therefore only been refined in a a/ √ 2×a/ √ 2×2a monoclinic subcell with an additional orthorhombic Pmca pseudo symmetry constraint (see refs. [2, 3] for a detailed description of the structure). It is generally agreed that the charge order model with alternating Fe/Fe layers below the Verwey transition is too simple but the full charge order is still not fully understood. A Mössbauer study fitted the spectrum with five components. [4] One corresponding to Fe A and four to Fe B and Fe 3+ B on two non-equivalent octahedral sites. [4] A resonant X-ray diffraction