Magnetic dipole ($M1$) moments in nuclei neighboring the doubly magic core are investigated by self-consistent mean-field (SCMF) approaches that allow for the breaking of time-reversal symmetry. By the SCMF calculations with the M3Y-P6 interaction, which keeps realistic spin-isospin and tensor channels, the $M1$ moments are well reproduced, particularly those in the nuclei adjacent to $jj$-closed magicity. The results are in better agreement with the data than those with the Gogny-D1S interaction, slightly better than those of UNEDF1 supplemented by a spin-isospin channel adjusted to the $M1$ moments themselves, and comparable to the shell-model results with the chiral effective-field-theory ($\chi \mathrm{EFT}$) interaction. Analyses via quadrupole moments, occupation numbers, and the lowest-order perturbation theory elucidate the cooperative effects of quadrupole deformation and spin correlation on the displacement from the Schmidt values, which has been known in terms of the quenching of the spin matrix elements. It is shown that a significant portion of the spin correlation is carried by the spin-isospin and tensor channels in the effective interaction. However, while agreement is remarkable at ${}^{131}\mathrm{Sn}^m, {}^{133}\mathrm{Sn}$, and ${}^{209}\mathrm{Pb}$, discrepancies remain at the $Z=\mathrm{odd}$ nuclei ${}^{133}\mathrm{Sb}, {}^{207}\mathrm{Ti}$, and ${}^{209}\mathrm{Bi}$, as in the $\chi \mathrm{EFT}$-based shell-model results.

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• Nuclear density functional theory
• Nucleon-nucleon interactions
• Spectroscopic factors & electromagnetic moments