Theoretical Fe $L_{2,3}$- and $K$-edge x-ray magnetic circular dichroism spectra of free iron clusters

A fully relativistic ab initio theoretical scheme is employed for investigating $L_{2,3}$- and $K$-edge x-ray absorption near-edge structure (XANES) and x-ray magnetic circular dichroism (XMCD) spectra of free Fe clusters of 9–89 atoms. The $L_{2,3}$-edge spectra of clusters differ from spectra of bulk only quantitatively; a higher degree of localization of the $d$ electrons in clusters is reflected through a higher intensity of the main XANES and XMCD peaks at the absorption edge. The $K$-edge XANES and XMCD spectra of clusters, on the other hand, differ from their bulk counterparts more significantly, even for the largest clusters investigated within our study. Several features, which could serve as spectroscopic markers of the difference between the clusters and bulk, were identified in both the $L_{2,3}$- and $K$-edge spectra. Contracting the bond lengths in clusters changes XMCD spectra only quantitatively.

Figure 1

Calculated $L_{2,3}$-edge spectra of Fe crystal compared to experiment of Chen et al. (Ref. 60). The upper panel shows x-ray absorption spectra; the lower panel shows XMCD spectra. Theoretical spectra are displayed either without accounting for the photoelectron-lifetime-related broadening (thin dashed lines) or including it (thin solid lines). Experimental curves are represented by thick lines.

Figure 2

Theoretical $K$-edge spectra of Fe crystal compared to experiment. The upper panel shows x-ray absorption spectra; the lower panel shows XMCD spectra. The upper half of each panel displays our real-space calculation (long-dashed lines) together with the real-space calculation of Brouder et al. (Ref. 49) (dotted-dashed lines). The lower half of each panel displays spectra calculated in a reciprocal space, together with experimental results of Pizzini et al. (Ref. 67) (thick lines). Our spectra were calculated either without accounting for the photoelectron-lifetime-related broadening (short- and long-dashed lines) or including it (thin solid lines).

Figure 3

Calculated $L_{2,3}$-edge XANES of free clusters (thin solid line) compared to theoretical XANES of a crystal (thick dashed line). The number of atoms in the cluster is shown in each graph. Note that the curve representing the crystal XANES is the same in each of the four graphs.

Figure 4

Calculated $L_{2,3}$-edge XMCD of free clusters (thin solid line) compared to theoretical XMCD of a crystal (thick dashed line). The number of atoms in the cluster is shown in each graph.

Figure 5

Calculated $L_{2,3}$-edge XMCD spectra of individual atoms in a 27-atom cluster. Each graph is devoted to atoms of one coordination shell. Spectra of atoms belonging to the same coordination shell which are nonetheless inequivalent due to the presence of magnetization and spin-orbit coupling are distinguished by line types (solid lines for atoms of the majority group, dash-dotted lines for atoms of the minority group). The spectrum of the whole cluster (normalized to one atom) is shown by a thick dashed line in each graph for comparison.

Figure 6

Calculated $K$ edge XANES of free clusters (thin solid line) compared to theoretical XANES of a crystal (thick dashed line). The number of atoms in the cluster is shown in each graph.

Figure 7

Calculated $K$-edge XMCD of free clusters (thin solid line) compared to theoretical XMCD of a crystal (thick dashed line). The number of atoms in the cluster is shown in each graph.

Figure 8

Calculated $K$-edge XMCD spectra of individual atoms in a 27-atom cluster. The meaning of the lines is the same as in Fig. 5.

Figure 9

$L_{2,3}$-edge XMCD of 27-atom clusters with contracted bond lengths. The type and magnitude of contraction is indicated at each curve. A spectrum of a nondeformed 51-atom cluster is shown at the bottom. Dashed thick gray lines represent the spectrum of a nondeformed 27-atom cluster in each subgraph.

Figure 10

$K$-edge XMCD of 27-atom clusters with contracted bond lengths. The meaning of the lines in the same as in Fig. 9.