We performed periodic spin-polarized DFT structure optimizations for Co atoms on MgO(001). The Mg(001) surface model was constructed by cleaving a DFT-optimized bulk cell along the (001) plane, using a lattice parameter of a = 2.119 Å, as determined in Ref. 67. For the surface models, we employed a 2 × 2 supercell of dimensions 8.48 × 8.48 × 25 Å, consisting of four layers of Mg 2+ and O 2-ions, with an 18 Å vacuum in the z direction.