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If the mass excess of neutron-deficient nuclei and their neutron-rich mirrorpartners are both known, it can be shown that deviations of the Isobaric MassMultiplet Equation (IMME) in the form of a cubic term can be probed. Such acubic term was probed by using the atomic mass of neutron-rich magnesiumisotopes measured using the TITAN Penning trap and the recently measuredproton-separation energies of $^{29}$Cl and $^{30}$Ar. The atomic mass of$^{27}$Mg was found to be within 1.6$\sigma$ of the value stated in the AtomicMass Evaluation. The atomic masses of $^{28,29}$Mg were measured to be bothwithin 1$\sigma$, while being 8 and 34 times more precise, respectively. Usingthe $^{29}$Mg mass excess and previous measurements of $^{29}$Cl we uncovered acubic coefficient of $d$ = 28(7) keV, which is the largest known cubiccoefficient of the IMME. This departure, however, could also be caused byexperimental data with unknown systematic errors. Hence there is a need toconfirm the mass excess of $^{28}$S and the one-neutron separation energy of$^{29}$Cl, which have both come from a single measurement. Finally, our resultswere compared to ab initio calculations from the valence-space in-mediumsimilarity renormalization group, resulting in a good agreement.

Precision mass measurements of magnesium isotopes and implications on the validity of the Isobaric Mass Multiplet Equation