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We report on measurements of the hyperfine $A, B$ and $C$-constants of the$3d4s^2 ~^2D_{5/2}$ and $3d4s^2 ~^2D_{3/2}$ atomic states in $^{45}$Sc.High-precision atomic calculations of the hyperfine fields of these states andsecond-order corrections are performed, and are used to extract$C_{5/2}=-0.06(6)$ kHz and $C_{3/2}=+0.04(3)$ kHz from the data. These resultsare one order of magnitude more precise than the available literature. From thecombined analysis of both atomic states, we infer the nuclear magnetic octupolemoment $\Omega = -0.07(53) \mu_N b$, including experimental and atomicstructure-related uncertainties. With a single valence proton outside of amagic calcium core, scandium is ideally suited to test a variety of nuclearmodels, and to investigate in-depth the many intriguing nuclear structurephenomena observed within the neighboring isotopes of calcium. We performnuclear shell-model calculations of $\Omega$, and furthermore explore the useof Density Functional Theory for evaluating $\Omega$. From this, mutuallyconsistent theoretical values of $\Omega$ are obtained, which are in agreementwith the experimental value. This confirms atomic structure calculationspossess the accuracy and precision required for magnetic octupole momentmeasurements, and shows that modern nuclear theory is capable of providingmeaningful insight into this largely unexplored observable.

Precision measurement of the magnetic octupole moment in $^{45}$Sc as a test for state-of-the-art atomic- and nuclear-structure theory