  It has been known for some time that the exchange-correlation potential in
time-dependent density functional theory is an intrinsically nonlocal
functional of the density as soon as one goes beyond the adiabatic
approximation. In this paper we show that a much more severe nonlocality
problem, with a completely different physical origin, plagues the
exchange-correlation potentials in time-dependent spin density functional
theory. We show how the use of the spin current density as the basic variable
solves this problem, and we provide an explicit local expression for the
exchange-correlation fields as functionals of the spin currents.
