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

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.

Topological Catastrophe and Isostructural Phase Transition in Calcium

We predict a quantum phase transition in fcc Ca under hydrostatic pressure. Using density functional theory, we find at pressures below 80 kbar, the topology of the electron charge density is characterized by nearest neighbor atoms connected through bifurcated bond paths and deep minima in the octahedral holes. At pressures above 80 kbar, the atoms bond through non-nuclear maxima that form in the octahedral holes. This topological change in the charge density softens the C elastic modulus of fcc Ca, while C$_{44}$ remains unchanged. We propose an order parameter based on applying Morse theory to the charge density, and we show that near the critical point it follows the expected mean-field scaling law with reduced pressure.

Electronic Selection Rules Controlling Dislocation Glide in bcc Metals

The validity of the structure-property relationships governing the deformation behavior of bcc metals was brought into question with recent {it ab initio} density functional studies of isolated screw dislocations in Mo and Ta. These existing relationships were semiclassical in nature, having grown from atomistic investigations of the deformation properties of the groups V and VI transition metals. We find that the correct form for these structure-property relationships is fully quantum mechanical, involving the coupling of electronic states with the strain field at the core of long $a/2<111>$ screw dislocations.