We investigate the magnetic dipole moments in even-even self-conjugate nuclei from $$^{12}$$
12
C to $$^{48}$$
48
Cr. For these nuclei, the measured gyromagnetic factors of excited states turn out to assume the same value of $$g \approx + 0.5$$
g
≈
+
0.5
within statistical errors. This peculiar feature can be interpreted on the basis of collective excitations of $$\alpha $$
α
-clusters. Analogously, the behaviour of the same observable is studied for all isotopes obtained by adding one or two neutrons to the considered self-conjugate nuclei. It is found that for the $$N = Z + 1$$
N
=
Z
+
1
isotopes the $$\alpha $$
α
-cluster structure hardly contributes to the observed negative g- factor value, corroborating molecular $$\alpha $$
α
-cluster models. The addition of a further neutron, however, restores the original $$\alpha $$
α
-cluster g-factors, except for the semi-magic isotopes, in which the deviations from $$g \approx + 0.5$$
g
≈
+
0.5
can be associated with the relevant shell closures. Secondly, we analyze the same observable in the framework of a macroscopic $$\alpha $$
α
-cluster model on a finite lattice of side length L. We focus on the discretization effects induced in the magnetic dipole moments of the $$2_1^+$$
2
1
+
and the $$3_1^-$$
3
1
-
states of $$^{12}$$
12
C at different values of the lattice spacing a.