  Background: Response to spin-dependent operators has been investigated in the
magnetic dipole and Gamow-Teller transitions, which provides magnetic
properties of a nuclear system. Purpose: I investigate an isotopic dependence
of the collectivity generated by the spin-dependent interactions in the Ca and
Ni isotopes through the isovector (IV) spin-flip excitations. The responses in
the neutral $(t_z)$ and charge-exchange $(t_{\pm})$ channels are considered in
a unified way. Method: A nuclear energy-density functional approach is employed
for calculating the response functions based on the Skyrme-Kohn-Sham-Bogoliubov
method and the quasiparticle-random-phase approximation (QRPA). I adopt the
like-particle QRPA and the proton-neutron QRPA for the neutral and
charge-exchange channels, respectively. I consider the fluctuation of the
proton-neutron pair fields. Results: The collective shift due to RPA
correlations for the response in the neutral channel is explained by the
occupation probability of neutrons in the $j_>=\ell+1/2$ orbital. Many
particle-hole or two-quasiparticle excitations have a coherent contribution to
form a giant resonance in neutron-rich nuclei for the charge-exchange channel.
The IV spin susceptibility displays the isotopic evolution of the collectivity
and the underlying shell structure. Conclusions: A repulsive character of the
residual interaction in the spin-isospin channel diminishes the IV spin
susceptibility due to the collectivity, while the dynamic ${}^{3}S$ pairing
appearing in the charge-exchange channel opposes the reduction.
