  Nuclear magnetic-dipole (M1) and Gamow-Teller (GT) transitions provide
insight into the spin-isospin properties of atomic nuclei. By considering them
as unified spin-isospin transitions, the M1/GT transition strengths and
excitation energies are subject to isospin symmetry. The excitation properties
associated to the M1/GT symmetry need to be clarified within consistent
theoretical approach. In this work, the relationship between the M1 and GT
transitions in Ca isotopes is investigated in a unified framework based on the
relativistic energy-density functional (REDF) with point-coupling interactions,
using the relativistic quasi-particle random-phase approximation (RQRPA). It is
shown that the isovector-pseudovector (IV-PV) residual interaction affects both
transitions, and the symmetry of M1 and giant-GT transitions is disrupted by
this interaction in closed-shell nuclei. In open-shell Ca isotopes, the
proton-neutron pairing in the residual RQRPA interaction also plays a role in
GT transitions. Due to the interplay between these interactions, the M1/GT
symmetry can be restored especially in the $^{42}$Ca nucleus, i.e., the
giant-GT strength can become comparable to that of the M1 mode in terms of the
unified spin-isospin transitions by adjusting the PN-pairing strength to
reproduce the experimental low-lying GT-excitation energies. The mirror
symmetry of both M1 and GT transitions is also demonstrated for open-shell
mirror partners, $^{42}$Ca and $^{42}$Ti. Further improvements are required to
achieve simultaneous reproduction of M1 and GT-transition energies in the REDF
framework.
