Rotational Band Structure in $^{32}$Mg

There is significant evidence supporting the existence of deformed ground states within the neutron-rich N =20 neon, sodium, and magnesium isotopes that make up what is commonly called the "Island of Inversion". However, rotational band structures, a characteristic fingerprint of a rigid non-spherical shape, have yet to be observed. We report on a measurement and analysis of the yrast (lowest lying) rotational band in $^{32}$Mg up to spin $I$ = 6+, produced in a two-step projectile fragmentation reaction and observed using the state-of-the-art $\gamma$-ray tracking detector array, GRETINA. Large-scale shell model calculations using the SDPF-U-MIX effective interaction show excellent agreement with the new data. Moreover, a theoretical analysis of the spectrum of rotational states as a function of the pairing gap, together with cranked shell model calculations, provides intriguing evidence for a reduction in pairing correlations with increased angular momentum, also in line with the shell-model results.