  We investigate the effect of external pressure on the Fe magnetic moment in
undoped LaOFeAs within the framework of density functional theory and show that
this system is close to a magnetic instability: The Fe moment is found to drop
by nearly a factor of 3 within a pressure range of $\pm$ 5 GPa around the
calculated equilibrium volume. While the Fe moments show an unusually strong
sensitivity to the spin arrangement (type of anti-ferromagnetic structure), the
low temperature structural distortion is found to have only a minor influence
on them. Analysis of the Fermi surface topology and nesting features shows that
these properties change very little up to pressures of at least 10 GPa. We
discuss the magnetic instability in terms of the itinerancy of this system.
