Interrogating the composition and distribution of nuclear magnetization via the hyperfine anomaly: experiment meets nuclear and atomic theory for short-lived $^{47}$K
To date, the magnetic structure of nuclei has been poorly constrained, with limited information on its spatial distribution. In this work, we address the composition and distribution of nuclear magnetization in a precision study of short-lived $^{47}$K. We measure the Larmor frequency with part-per-million precision using liquid-state $\beta$-detected nuclear magnetic resonance at CERN-ISOLDE, improving determination of the experimental differential hyperfine anomaly relative to $^{39}$K by more than an order of magnitude. By combining these experimental results with relativistic all-orders atomic calculations and nuclear density functional theory, we obtain the relative spin and orbital contributions to the nuclear magnetic moments. Our analysis reveals an overestimation of the spin contribution predicted by nuclear theory, that persists even after considering two-body currents. Conversely, we show that the measured hyperfine anomaly is reproduced when adopting the spatial distribution of nuclear magnetization provided by density functional theory. The methodology introduced in this work establishes a means to probe the detailed magnetic structure of the nucleus. This is critical for benchmarking nuclear structure theory and calculations of symmetry-violating nuclear moments relevant to searches for physics beyond the Standard Model in atoms and molecules.