  We investigate the topology of the spin-polarized charge density in bcc and
fcc iron. While the total spin-density is found to possess the topology of the
non-magnetic prototypical structures, in some cases the spin-polarized
densities are characterized by unique topologies; for example, the
spin-polarized charge densities of bcc and high-spin fcc iron are atypical of
any known for non-magnetic materials. In these cases, the two spin-densities
are correlated: the spin-minority electrons have directional bond paths with
deep minima in the minority density, while the spin-majority electrons fill
these holes, reducing bond directionality. The presence of two distinct spin
topologies suggests that a well-known magnetic phase transition in iron can be
fruitfully reexamined in light of these topological changes. We show that the
two phase changes seen in fcc iron (paramagnetic to low-spin and low-spin to
high-spin) are different. The former follows the Landau symmetry-breaking
paradigm and proceeds without a topological transformation, while the latter
also involves a topological catastrophe.
