Towards a comprehensive DFT theory of the anti-ferromagnetic and paramagnetic phases of the classic Mott insulators MnO, FeO, CoO, and NiO

The insulating character of the antiferromagnetic (AFM) and paramagnetic (PM) phases of the classic NaCl-structure Mott insulators MnO, FeO, CoO, and NiO is traditionally explained as a manifestation of strong correlation. Within this view, the gap originates from electrons moving in the lattice and forming states with doubly occupied d orbitals on certain metal sites and empty d orbitals on others, even without spatial symmetry breaking. The need for a correlated picture is usually justified, at least in part, by the failure of band theory to predict a gap for the PM phases when modeled by a non-magnetic NaCl structure, where all transition metal (TM) sites are symmetry equivalent (a monomorphous description). Here, we seek to understand the minimum theoretical description needed to capture the gapping and moment formation in these classic Mott systems. As noted by previous authors, band theory predicts a gap for the spin-ordered AFM phases. For the spin-disordered PM phases, we use large NaCl-type supercells where each TM site can have different spin directions and local bonding environments with zero total magnetization. Such a polymorphous description accommodates symmetry-breaking lattice distortions and in open-shell systems allows for full occupation of just some of the components of a degenerate level rather than partial occupation of all of them. In such supercells the degeneracy of the d orbitals can be lifted, thus allowing for on-site magnetic moments to develop. For this polymorphous description we use special quasi-random structures (SQSs), supercells defined so as to provide the best approximations of average properties of random configurations (not individual snapshots). Single determinant band theory (based on DFT+U) applied to the SQS models predicts significant (1-3 eV) band gaps and large local moments in the PM phases of MnO, FeO, CoO, and NiO, in agreement with experiment.