  We apply the time-dependent local-spin-density approximation as general
theory to describe ground states and spin-density oscillations in the linear
response regime of two-dimensional nanostructures of arbitrary shape. For this
purpose, a frequency analysis of the simulated real-time evolution is
performed. The effect on the response of the recently proposed spin-density
waves in the ground state of certain parabolic quantum dots is considered. They
lead to the prediction of a new class of excitations, soft spin-twist modes,
with energies well below that of the spin dipole oscillation.
