Topology of the Spin-Polarized Charge Density in bcc and fcc Iron

We report the first investigation of the topology of spin-polarized charge density, specifically in bcc and fcc iron. While the total spin-density is found to possess the topology of the non-magnetic prototypical structures, the spin-polarized charge densities of bcc and high-spin fcc iron are atypical. In these cases, the two spin densities are correlated: the spin-minority electrons have directional bond paths and deep minima, while the spin-majority electrons fill these holes, reducing bond directionality. The presence of distinct spin topologies allows us to 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 involves a topological catastrophe.

Figure 1

Total (a), spin-minority (b), and spin-majority (c) charge density contour plots in bcc Fe. The cut-plane passes through second neighbor atoms. Darker regions correspond to low charge density. Cage points, circled in white, are present in the total and spin-minority charge densities. Second neighbor bond points (one circled in white) replace these in the spin-majority charge density.

Figure 2

Topology of fcc prototype. Only bond points (white) and maxima (gray) are shown for clarity. Paramagnetic, LS, and the total and spin-majority density in HS fcc Fe display this topology. (Though not shown, cage points are present in the tetrahedral holes.)

Figure 3

Topology of the minority spin density in HS fcc Fe. Only bond points (white) and maxima (gray) are shown for clarity. The appearance of non-nuclear maxima allows the Fe atoms to adopt a bcc-like topology. The inset shows the tetrahedron of bond points around a non-nuclear maximum.