  Pairing correlation of Cooper pair is a fundamental property of multi-fermion
interacting systems. For nucleons, two modes of the Cooper-pair coupling may
exist, namely of $S_{12}=0$ with $L_{12}=0$ (spin-singlet s-wave) and
$S_{12}=1$ with $L_{12}=1$ (spin-triplet p-wave). In nuclear physics, it has
been an open question whether the spin-singlet or spin-triplet coupling is
dominant, as well as how to measure their role. We investigate a relation
between the magnetic-dipole (M1) excitation of nuclei and the pairing modes
within the framework of relativistic nuclear energy-density functional (RNEDF).
The pairing correlations are taken into account by the relativistic
Hartree-Bogoliubov (RHB) model in the ground state, and the relativistic
quasi-particle random-phase approximation (RQRPA) is employed to describe M1
transitions. We have shown that M1 excitation properties display a sensitivity
on the pairing model involved in the calculations. The systematic evaluation of
M1 transitions together with the accurate experimental data enables us to
discern the pairing properties in finite nuclei.
