On a broader level, this work also reveals a striking parallel between Co/MgO(001) and a linear, twofold-coordinate Co(II) molecular magnet, both of which exhibit an axial ligand field. In both systems, the ground state is a non-aufbau quartet state with maximal orbital angular momentum and strong spin-orbit coupling, resulting in a record-high spin-inversion barrier. Also, both systems have a comparable temperature dependence of the susceptibility.