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

Abstract

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 nonmagnetic 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 symmetrybreaking paradigm and proceeds without a topological transformation, while the latter also involves a topological catastrophe. Bader's topological theory of molecular structure, Atoms in Molecules (AIM), has been successfully applied to a variety of crystalline systems [1][2][3][4][5][6][7][8][9][10][11]. It has been employed to investigate the nature of bonding in materials ranging from high temperature alloys to biological systems. These have yielded surprising results, such as second neighbor bond paths in B2 ionic crystals [3] and transition metal aluminides [4], with the magnitude of the latter correlating to failure properties [5]. Other studies have used bond path properties to offer first principles explanations of stress-induced failure in brittle and ductile alloys [7], as well as shear elastic constants in a variety of pure metals and alloys [8][9][10]. Building on these ideas and using the rigorous definitions of bond paths afforded by the theory, the anomalous behavior of iridium under shear was also explained [11].One of the attractive features of AIM is its reliance on the charge density, a quantum mechanical observable, that is most often calculated but can, in principle, be measured via X-ray diffraction techniques [12][13][14][15]. In a similar fashion, the spin-polarized charge density is an observable that can be calculated or measured using spinpolarized neutron diffraction. Despite the information and insights that have come from topological investigations of the total charge density, the same analysis has yet to be performed on spin-polarized densities. Here, we report the results from the first such studies, exploring the spin-minority and spin-majority topologies of bodycentered-cubic (bcc) and face-centered-cubic (fcc) iron.This first application of AIM to spin-density sheds light on the origins of the magnetic phase transitions of fcc iron. It is argued that this system undergoes two distinct phase transitions during volume expansion: a second- * Electronic address: trjones@mines.edu order phase change, from a paramagnetic to a l...

Exchange interaction function for spin-lattice coupling in bcc iron

“…The minority-spin subband, on the other hand, are only ϳ40% occupied and predominantly ͑ϳ75%͒ by t 2g electrons. This is consistent with the results of Jones et al 49 Unequal occupancy of the spin subbands creates a MM and drives the nonmagnetic/ ferromagnetic transition as the lattice parameter increases beyond 2.3 Å.…”

“…5 is very much in line with those of Jones et al 49 The difference between the electron-density distributions for two spin states is obvious with the minority spins showing stronger bonding tendency than the majority spins. In this regard, the minority spins mostly occupy the t 2g states ͑note the square shape of the electron cloud͒ producing the bonds between the 1NNs.…”

Topological Catastrophe and Isostructural Phase Transition in Calcium

“…It was not until the transition was interpreted as a topological change of the elctronic charge density, ρ( r), that the underlying nature of the phase change became apparent [4]. While this approach is promising, no general correlations have been drawn between isostructural phase transitions and ρ( r).…”

Origin of Predominance of Cementite among Iron Carbides in Steel at Elevated Temperature

“…It was shown that cementite, as a weak magnet, shows almost no thermal expansion (Invar behavior) at the temperature below its Curie temperature [8,9]. Notwithstanding many theoretical efforts, very basic questions on steel remain unanswered [3][4][5]10]. One prominent question is why the cementite phase is observed much more frequently than other carbide phases in steel.…”

“…Despite the fact that steel is one of the most commonly used materials in both old and modern times, the physical understanding of the formation and stability of iron and iron carbide phases is still in a premature state [1][2][3][4][5].…”