  Using a first principles based, magnetic tight-binding total energy model,
the magnetization energy and moments are computed for various ordered spin
configurations in the high pressure polymorphs of iron (fcc, or $\gamma$-Fe,
and hcp, or $\epsilon$-Fe), as well ferromagnetic bcc iron ($\alpha$-Fe). For
hcp, a non-collinear, antiferromagnetic, spin configuration that minimizes
unfavorable ferromagnetic nearest neighbor ordering is the lowest energy state
and is more stable than non-magnetic $\epsilon$ iron up to about 75 GPa.
Accounting for non-collinear magnetism yields better agreement with the
experimental equation of state, in contrast to the non-magnetic equation of
state, which is in poor agreement with experiment below 50 GPa.
