In spite of the high-density and strongly correlated nature of the atomic nucleus, experimental and theoretical evidence suggests that around particular ‘magic’ numbers of nucleons, nuclear properties are governed by a single unpaired nucleon1,2. A microscopic understanding of the extent of this behaviour and its evolution in neutron-rich nuclei remains an open question in nuclear physics3,4,5. The indium isotopes are considered a textbook example of this phenomenon6, in which the constancy of their electromagnetic properties indicated that a single unpaired proton hole can provide the identity of a complex many-nucleon system6,7. Here we present precision laser spectroscopy measurements performed to investigate the validity of this simple single-particle picture. Observation of an abrupt change in the dipole moment at N = 82 indicates that, whereas the single-particle picture indeed dominates at neutron magic number N = 82 (refs. 2,8), it does not for previously studied isotopes. To investigate the microscopic origin of these observations, our work provides a combined effort with developments in two complementary nuclear many-body methods: ab initio valence-space in-medium similarity renormalization group and density functional theory (DFT). We find that the inclusion of time-symmetry-breaking mean fields is essential for a correct description of nuclear magnetic properties, which were previously poorly constrained. These experimental and theoretical findings are key to understanding how seemingly simple single-particle phenomena naturally emerge from complex interactions among protons and neutrons.