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 fac
tor 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.
