Probing Single Jumps of Surface Atoms

Jumps of single atoms can be followed on their time and space scale (nanoseconds and Angstroms) by applying nuclear resonance scattering of synchrotron radiation. Here we develop the theory for jump diffusion in two-dimensional systems. Two types of phenomena are noteworthy: apparent acceleration of the nuclear decay and relaxation of hyperfine interactions, in particular, electric quadrupole interactions. The latter effect becomes for the first time one of significance and well measurable due to the inherent anisotropy of the surface. We show how, by way of motional narrowing, to distinguish between the motion of the probe atom itself and the motion of adatoms.

Figure 1

(a) Diffusion of atoms in iron monolayer on the (110) surface of tungsten. 1, $-1$, 2, $-2$ designate possible vacancy positions at NN sites of the probe atom; N a site outside the NN shell to which a NN atom can jump. (b) Diffusion of adatom A on top of an iron surface.

Figure 2

Simulations of NRS (time spectra, left column) and Mössbauer emission (energy spectra, right column) for jump diffusion of probe atoms via vacancies in a surface layer [Fig. 1a]. The reason for the beat structure in the NRS spectra and for the line splitting in the Mössbauer spectra are the quadrupole interactions due to (a) the asymmetry of the surface and (b) the vacancy. For quantitative values of quadrupole interactions see the text. In the Mössbauer spectra the outer doublet is due to the electric field gradient from the vacancy. Of the inner doublet caused by the asymmetry of the surface, only the component at positive energies is excited because of the polarization of the synchrotron beam. In the NRS spectra note that quadrupole relaxation is accompanied by a marked acceleration of the intensity decay with increasing jump frequency of the probe atom corresponding to line broadening in the Mössbauer spectra.

Figure 3

Simulations of NRS (time spectra, left column) and Mössbauer emission (energy spectra, right column) for an immobile probe atom in a surface layer [Fig. 1b] when an adatom is jumping on top of the surface layer. The essential difference to the spectra of Fig. 2 is the much gentler decay of the NRS spectra in time with the decay completely vanishing for fast adatom jumps. This corresponds to the motional narrowing of the Mössbauer spectra.

Figure 4

Left: Measured NRS spectrum [11, 12] of ${}^{57}\mathrm{Fe}$ submonolayer on (110) W at room temperature before (open squares) and after (closed circles) an NRS measurement at 670 K. Right: NRS spectrum according to theory with probe atom immobile, jump frequencies of adatoms 5 MHz. Quadrupole interactions and defect concentration as in Fig. 3.