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We investigate the magnetic dipole moments in even-even self-conjugate nucleifrom ${}^{12}\mathrm{C}$ to ${}^{44}\mathrm{Ti}$. For the latter, the measuredgyromagnetic factors of excited states turn out to assume the same value of $g\approx + 0.5$ within statistical errors. This peculiar feature can beinterpreted on the basis of collective excitations of $\alpha$-clusters.Analogously, the behaviour of the same observable is studied for all isotopesobtained by adding one or two neutrons to the considered self-conjugate nuclei.It is found that for the $N = Z + 1$ isotopes the $\alpha$-cluster structurehardly contributes to the observed negative g- factor value, corroboratingmolecular $\alpha$-cluster models. The addition of a further neutron, however,restores the original $\alpha$-cluster g-factors, except for the semi-magicisotopes, in which the deviations from $g \approx + 0.5$ can be associated withthe relevant shell closures. Secondly, we analyze the same observable in theframework of a macroscopic $\alpha$-cluster model on a finite lattice of sidelength $L$. We focus on the discretization effects induced in the magneticdipole moments of the $2_1^+$ and the $3_1^-$ states of ${}^{12}\mathrm{C}$ atdifferent values of the lattice spacing $a$.

Magnetic dipole moments as a strong signature for $\alpha$-clustering in even-even self-conjugate nuclei