  Background: Magnetic quadrupole (M2) excitation represents a fundamental
feature in atomic nucleus associated to nuclear magnetism induced by spin and
orbital transition operator. So far it has only been investigated within the
non-relativistic theoretical approaches, and available experimental data are
rather limited. Purpose: We aim to investigate the properties of M2 transitions
in closed and open-shell nuclei using the framework of relativistic nuclear
energy density functional. The calculated M2 transition strengths could be used
to constrain the quenching of the spin gyromagnetic factors. Methods: The M2
excitations are described using the relativistic quasiparticle random phase
approximation (RQRPA) with the residual interaction extended with the
isovector-pseudovector term. Results: The M2 transition strength distributions
are described and analyzed for closed and open shell nuclei. The results are
compared with available experimental data and the strength missing from the
experiment is discussed. The evolution of M2 transition properties has been
investigated within the $^{36-64} \rm Ca$ isotope chain. Conclusion: The main
M2 transitions have rather rich underlying structure and their collectivity
increases with the mass number due to larger number of contributing
particle-hole configurations. Pairing correlations in open shell nuclei have
strong effect, causing the M2 strength reduction and shifting of the centroid
energies to higher values. The analysis of M2 transition strengths indicate
that considerable amount of experimental strength may be missing, mainly due to
limitations to rather restricted energy ranges. The calculated M2 strengths for
Ca isotopes, together with the future experimental data will allow constraining
the quenching of the $g$ factors in nuclear medium.
