  The Fe-based Oxypnicide superconductors have generated a huge amount of
interest; they are a high temperature superconductor, with a Tc of 55K, but do
not have the two dimensional copper oxygen layer that was thought essential for
superconductivity at these high temperatures. Initial studies have hinted
towards the possibility of a spin density wave (SDW) in these compounds and how
they could play an important role in the superconductivity. SDW's occur at low
temperatures in low-dimensional materials with strong electron correlations or
in metals with a high density of states at the Fermi surface. A transition to
the SDW state has many similarities to the superconducting transition, driven
by the condensation energy with an energy gap opening, and in many materials
the SDW state occurs adjacent in the phase diagram to the superconducting
state. In these materials it is believed that electron doping suppresses the
SDW instability allowing superconductivity to emerge. In this paper we report
on the first direct experimental evidence of a SDW in the LaFeAsO parent
compound as observed with inelastic neutron scattering. We show that these
excitation derive from a two-dimensional Fermi surface nesting with a nesting
vector of (\pi,\pi,0).
