  We study the spin-dependent electronic excitations in alkali-metal
nanoparticles. Using numerical and analytical approaches, we focus on the
resonances in the response to spin-dependent dipole fields. In the spin-dipole
absorption spectrum for closed-shell systems, we investigate in detail the
lowest-energy excitation, the "surface paramagnon" predicted by L. Serra et al.
[Phys. Rev. A 47, R1601 (1993)]. We estimate its frequency from simple
assumptions for the dynamical magnetization density. In addition, we
numerically determine the dynamical magnetization density for all low-energy
spin-dipole modes in the spectrum. Those many-body excitations can be traced
back to particle-hole excitations of the noninteracting system. Thus, we argue
that the spin-dipole modes are not of collective nature. In open-shell systems,
the spin-dipole response to an electrical dipole field is found to increase
proportionally with the ground-state spin polarization.
