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

Interplay between Orbital Magnetic Moment and Crystal Field Symmetry: Fe atoms on MgO