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Background: Response to spin-dependent operators has been investigated in themagnetic dipole and Gamow-Teller transitions, which provides magneticproperties of a nuclear system. Purpose: I investigate an isotopic dependenceof the collectivity generated by the spin-dependent interactions in the Ca andNi isotopes through the isovector (IV) spin-flip excitations. The responses inthe neutral $(t_z)$ and charge-exchange $(t_{\pm})$ channels are considered ina unified way. Method: A nuclear energy-density functional approach is employedfor calculating the response functions based on the Skyrme-Kohn-Sham-Bogoliubovmethod and the quasiparticle-random-phase approximation (QRPA). I adopt thelike-particle QRPA and the proton-neutron QRPA for the neutral andcharge-exchange channels, respectively. I consider the fluctuation of theproton-neutron pair fields. Results: The collective shift due to RPAcorrelations for the response in the neutral channel is explained by theoccupation probability of neutrons in the $j_>=\ell+1/2$ orbital. Manyparticle-hole or two-quasiparticle excitations have a coherent contribution toform a giant resonance in neutron-rich nuclei for the charge-exchange channel.The IV spin susceptibility displays the isotopic evolution of the collectivityand the underlying shell structure. Conclusions: A repulsive character of theresidual interaction in the spin-isospin channel diminishes the IV spinsusceptibility due to the collectivity, while the dynamic ${}^{3}S$ pairingappearing in the charge-exchange channel opposes the reduction.

Isovector spin susceptibility: Isotopic evolution of collectivity in spin response