Influence of exchange correlation on the symmetry and properties of siderite according to density-functional theory

Density-functional theory (DFT) without spin-orbit coupling (SOC), as implemented in CASTEP, yields structural, energetic, and elastic properties of siderite $({\text{FeCO}}_{3})$ in good agreement with available data from the literature. The electronic ground state is however found ferromagnetic (FM) with a nonzero density of states at the Fermi level, whereas real siderite is antiferromagnetic (AFM) and insulating. We show in both cases how the paradox can be removed. Concerning the metallic/insulating character, a symmetry analysis of the electronic structure performed with the help of ISOTROPY shows that the absence of gap is due to an essential degeneracy of monoelectronic wave functions in the experimental $R\overline{3}c$ symmetry. The small dispersion of individual bands establishes a clear difference with the case of a real metal. Complemented by $\text{DFT}+\text{SOC}$ computations performed using ABINIT this shows the consistency of the DFT description with crystal-field theory data taken from the literature. Thus for DFT the electronic structure of siderite is characterized by correlation, but of exchange origin, as opposed to electrostatic origin. The AFM nature of the ground state is also restored by SOC. Without SOC the total energies of the FM and AFM states are very close. After introducing some modifications in a classical model of superexchange we obtain a satisfactory interpretation of our DFT results in terms of spin polarization in the iron-carbonate bonds, spin-coupling mechanisms between neighboring iron ions and finally of the observed FM over AFM stability. Hence, siderite emerges as an original model system among transition-metal compounds for the application of DFT to open-shell electronic structures.