It is well-established that measuring the magnetic resonance spectrum of nuclei in solids gives access to several quantities relevant to nuclear physics. The nuclear magnetic moment is obtained by the Zeeman interaction with an applied magnetic field. The nuclear electric quadrupole moment can also be estimated by measuring the quadrupolar interaction and estimating the electric field gradient imposed by the surrounding atoms. In principle, higher-order nuclear moments should be observable as well by NMR, but this requires a spectral resolution better than what can be reached by conventional NMR. We have developed a new method to measure the NMR spectrum of individual nuclear spins with high spectral resolution, by coupling them to a neighboring paramagnetic impurity itself detected by microwave photon counting at 10mK. We have applied it to a single 93Nb impurity atom in a CaWO4 crystal, which has spin 9/2. Thanks to the high spectral resolution reached (10mHz), we show that the spin Hamiltonian must include a hexadecapolar term [1]. This interaction term may arise from the interaction of the third derivative of the electric field with the 93Nb hexadecapolar moment, which would be probed for the first time. More generally, our results indicate that high moments of the charge distribution in stable nuclei can be probed by NMR spectroscopy.
[1] J. Travesedo et al., arXiv:2605.02857
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