First spin-resolved electron distributions in crystals from combined polarized neutron and X-ray diffraction experiments

Abstract

Since the 1980s it has been possible to probe crystallized matter, thanks to X-ray or neutron scattering techniques, to obtain an accurate charge density or spin distribution at the atomic scale. Despite the description of the same physical quantity (electron density) and tremendous development of sources, detectors, data treatment software etc., these different techniques evolved separately with one model per experiment. However, a breakthrough was recently made by the development of a common model in order to combine information coming from all these different experiments. Here we report the first experimental determination of spin-resolved electron density obtained by a combined treatment of X-ray, neutron and polarized neutron diffraction data. These experimental spin up and spin down densities compare very well with density functional theory (DFT) calculations and also confirm a theoretical prediction made in 1985 which claims that majority spin electrons should have a more contracted distribution around the nucleus than minority spin electrons. Topological analysis of the resulting experimental spin-resolved electron density is also briefly discussed.

Keywords: charge and spin densities; joint refinement; magnetization density; molecular magnetic materials; multipole refinement; polarized neutron diffraction.

Figure 1

Di-azido copper complexes. Schematic representation of (a) End-On and (b) End-to-End conformation of di-azido di-Cu complexes. (c) View of the Cu₂ L ₂(N₃)₂ molecule. N atoms are represented in blue, O in red, C in grey, F in yellow and Cu in orange. H atoms are not shown for reasons of clarity.

Figure 2

Charge and spin density maps in the plane containing Cu, O1 and N5. (a) Static deformation density map obtained by means of the joint refinement strategy. Isocontours are drawn for ± 0.01 × 2ⁿ e Å⁻³ with n = 0–13 (positive red, negative blue). (b) Spin density map obtained by means of the joint refinement strategy. Isocontours are drawn for ± 0.01 × 2ⁿ μB Å⁻³ with n = 0–13, spin up contours in red, spin down contours in blue.

Figure 3

Spin-resolved electron densities. Left: (a) Experimental spin up (majority) and (c) experimental spin down (minority) valence electron densities from joint refinement of the spin-split model. Right: (b) Theoretical spin up (majority) and (d) theoretical spin down (minority) valence electron densities from ab initio quantum computation. The density distributions are represented in the Cu—N1—O1 plane (contours 0.01 × 2ⁿ e Å⁻³ (n = 0–12)).

Figure 4

Schematic representation of the Cu d-orbital type function populations for up and down electrons. The arrows sizes are proportional to the respective spin populations.

Figure 5

Spin-resolved Laplacian maps in the plane containing Cu, O1 and N5: (a) spin up, (b) spin down; b.c. for bond critical point and r.c. for ring critical point (saddle point with two positive curvatures).