  Electronic and magnetic structure of $(100)$ films of K and Cs are calculated
within the plane-wave projector augmented wave (PAW) formalism of the density
functional theory (DFT) using both local spin density approximation (LSDA) and
the PW91 generalized gradient approximation (GGA). Only a 6 layer Cs film is
found to have a ferromagnetic (FM) state which is degenerate with a
paramagnetic (PM) state within the accuracy of these calculations. This is at
variance with the results obtained from a finite thickness uniform jellium
model (UJM). Implications of these results for the experiments on transition
metal doped alkali metal thin films and bulk hosts are discussed.
