  We present a theory of time-dependent tunneling between a metal and a
partially spin-polarized two-dimensional electron system (2DES). We find that
the leakage current which flows to screen an electric field between the metal
and the 2DES is the sum of two exponential contributions whose relative weights
depend on spin-dependent tunneling conductances, on quantum corrections to the
electrostatic capacitance of the tunnel junction, and on the rate at which the
2DES spin-polarization approaches equilibrium. For high-mobility and
homogeneous 2DES's at Landau level filling factor $\nu=1$, we predict a ratio
of the fast and slow leakage rates equal to $(2K+1)^2$ where $K$ is the number
of reversed spins in the skyrmionic elementary charged excitations.
