Signals of strong electronic correlation in ion scattering processes

Previous measurements of neutral atom fractions for $\mathrm{S}{\mathrm{r}}^{+}$ scattered by gold polycrystalline surfaces show a singular dependence with the target temperature. There is still not a theoretical model that can properly describe the magnitude and the temperature dependence of the neutralization probabilities found. Here, we applied a first-principles quantum-mechanical theoretical formalism to describe the time-dependent scattering process. Three different electronic correlation approaches consistent with the system analyzed are used: (i) the spinless approach, where two charge channels are considered $(\mathrm{S}{\mathrm{r}}^0$ and $\mathrm{S}{\mathrm{r}}^{+})$ and the spin degeneration is neglected; (ii) the infinite-U approach, with the same charge channels $(\mathrm{S}{\mathrm{r}}^0$ and $\mathrm{S}{\mathrm{r}}^{+})$ but considering the spin degeneration; and (iii) the finite-U approach, where the first ionization and second ionization energy levels are considered very, but finitely, separated. Neutral fraction magnitudes and temperature dependence are better described by the finite-U approach, indicating that $e$-correlation plays a significant role in charge-transfer processes. However, none of them is able to explain the nonmonotonous temperature dependence experimentally obtained. Here, we suggest that small changes in the surface work function introduced by the target heating, and possibly not detected by experimental standard methods, could be responsible for that singular behavior. Additionally, we apply the same theoretical model using the infinite-U approximation for the Mg-Au system, obtaining an excellent description of the experimental neutral fractions measured.

Figure 1

Affinity (solid line) and ionization energy levels of the projectile as a function of the ion-surface distance referred to the target-surface Fermi level (dotted line). The energy-level widths ${\mathrm{\Gamma }}_0$(double shaded region) and $\mathrm{\Gamma }$(single shade region) are included. The total Au(100) DOS (horizontal strips) is also shown.

Figure 2

Spectral density ${\rho }_2$ plotted as a function of the energy for three different ion-surface distances: 6 a.u. (a), 7 a.u. (b), and 9 a.u. (c), and four different temperatures: 5 K (solid line), 300 K (dashed line), 600 K (dotted line), and 900 K (dash-dotted line).

Figure 3

The double (a) and single (b) electronic occupations are shown as a function of the target temperature for five different projectile-surface distances: 6 a.u. (squares), 7 a.u. (triangles pointing up), 8 a.u. (circles), 9 a.u. (triangles pointing left), and 10 a.u. (triangles pointing right).

Figure 4

Experimental (full squares) neutral fraction as a function of the target temperature contrasted with theoretical calculations under three different approximations: Spinless (triangles), infinite-$U$ limit (empty squares), and finite-$U$ approximation (circles). Measured neutral fraction magnitudes are better described by the latter (and more complete) model.

Figure 5

(a) Neutral fraction as a function of the projectile trajectory calculated under the three approximations: spinless (triangles), infinite-$U$ limit (squares), and finite-$U$ (circles). (b) Evolution of the $\mathrm{S}{\mathrm{r}}^0$ and the $\mathrm{S}{\mathrm{r}}^{++}$ probabilities during the collision. Negative/positive distances indicate incoming/outgoing part of the trajectory. The first and second ionization energy levels are shown with their corresponding ${\mathrm{\Gamma }}_0$ widths. The total surface DOS is also shown (shaded region).

Figure 6

(a) Calculated neutral fraction as a function of the target temperature under the three approximations above described: spinless (a), infinite-$U$ limit (b), and finite-$U$ (c). Each solid line corresponds to the calculation performed for different values of the work function around 5.1 eV (indicated in the figure). The figure shows how sensitive the neutral fraction is to small variations in the surface work function. Moreover, typical precision in work-function measurements (0.1 eV) introduce sufficiently large errors in the calculation to match the experimental neutral fractions obtained (shaded region, finite-$U$ approach).

Figure 7

Calculated neutral fraction under the finite-$U$ approach when the work function is kept constant at $\mathrm{\Phi }=5.1\mathrm{eV}$ (full circles) and when a small temperature dependence in the work function (inset) is assumed (empty squares with crosses). Work-function variation rates in the order of ${10}^{-4}\mathrm{eV}/\mathrm{K}$ are typical in metals.

Figure 8

Neutral fraction $\left(\mathrm{M}{\mathrm{g}}^0\right)$ evolution along the projectile trajectory calculatesd under the infinite-$U$ approach for two incoming energies: 1 keV (circles) and 2 keV (squares). An almost complete neutralization is achieved for both incoming energies consistent with an energy level far from the surface Fermi level (also shown with its corresponding ${\mathrm{\Gamma }}_0$ width). The total Au(100) DOS is also included (shaded region).

Figure 9

Calculated (empty symbols) and experimental [5] (full symbols) are compared for two incoming energies: 1 keV (circles) and 2 keV (squares) when the work-function temperature is kept constant $\left(\mathrm{\Phi }=5.1\mathrm{eV}\right)$. If the temperature dependence in the work function (inset Fig. 7) is incorporated, the calculated neutral fraction (crosses) is practically not altered. A noticeable agreement between experimental and calculated neutral fractions is achieved.