We combine density functional theory, x-ray magnetic circular dichroism, multiplet calculations, and scanning tunneling spectroscopy to assess the magnetic properties of Fe atoms adsorbed on a thin layer of MgO(100) on Ag(100). Despite the strong axi
al field due to the O ligand, the weak cubic field induced by the four-fold coordination to Mg atoms entirely quenches the first order orbital moment. This is in marked contrast to Co, which has an out-of-plane orbital moment of $L_z = pm 3$ that is protected from mixing in a cubic ligand field. The spin-orbit interaction restores a large fraction of the Fe orbital moment leading a zero-field splitting of $14.0 pm 0.3$~meV, the largest value reported for surface adsorbed Fe atoms.
