Cu-doped Pb10β(PO4β)6βO, and V doped SrTiO3β -- a tutorial on
electron-crystal lattice coupling in insulating materials with transition
metal dopants
We provide two pedagogical examples to understand the mechanisms at play in
stabilizing an insulating state, and an impurity level in the bandgap in two
insulators using DFT+U: Cu-doped Pb10β(PO4β)6βO and V-doped SrTiO3β
transition metal-doped insulators. We find both to be insulating, with isolated
impurity (flat) bands, regardless of doping location. In both cases, the
electron degeneracy and crystal lattice symmetry are broken, leading to an
insulating state, and a magnetically and orbitally polarized impurity state
within the gap, clearly separated from the valence and conduction bands. We
also resolve previously noticed inconsistencies between DFT and experiment
regarding doping site energetics, crystal structure, and transparency in
Cu-doped phosphate lead apatite 'LK-99'. Doping one of each type of site in the
same unit cell (20% doping) also simply leads to two spin-polarized
impurity bands in the material's gap. The local transition metal ion sites may
behave like color centers (or f-centers), possibly giving color at low
temperatures to what we predict to be a transparent, insulating material in the
recently synthesized LK-99. Weak ferromagnetism may be possible due to the
relatively delocalized unpaired spins in the valence band. Further work should
take into account the possibility of further changes in stoichiometry,
different doping locations, supercell effects, and quantification of magnetic
exchange interactions