Surface Diffusion of Cr Adatoms on Au(111) by Quantum Tunneling

The low-temperature surface diffusion of isolated Cr adatoms on Au(111) has been determined using nonperturbing x rays. Changes in the x-ray magnetic circular dichroism spectral line shape together with Monte Carlo calculations demonstrate that adatom nucleation proceeds via quantum tunneling diffusion rather than over-barrier hopping for temperatures $<40\mathrm{K}$. The jump rates are shown to be as much as 35 orders of magnitude higher than that expected for thermal over-barrier hopping at 10 K.

Figure 1

(a) XMCD spectra for a collection of isolated atoms ($\approx 0.05\mathrm{\text{atom}}/{\mathrm{nm}}^2$) and for a full monolayer Cr film ($\approx 14\mathrm{\text{atoms}}/{\mathrm{nm}}^2$), deposited at 10 K. The continuous line is a multiplet-based calculation for a single Cr atom with a $d^5$ electronic configuration. (b) Time evolution of the XMCD for a surface adatom density of $\approx 0.7\mathrm{\text{atom}}/{\mathrm{nm}}^2$ on Au(111) deposited at 10 K. The line is a linear combination of the experimental atomic and bulklike XMCD spectra.

Figure 2

XMCD magnetization curve recorded at the $L_3$ Cr edge at $T=10\mathrm{K}$ for a collection of isolated Cr atoms. The full line is a Brillouin function fit.

Figure 3

Ratio $R$ of the number of isolated Cr adatoms to the total number of deposited Cr atoms as a function of coverage, as determined from XMCD spectra for several coverages and temperatures. Lines represent Monte Carlo simulation of $R$ for a random atomic deposition, $N_{\mathrm{MC}}=0$ (dashed line) and after $N_{\mathrm{MC}}=35$ Monte Carlo steps (solid line) for a random atomic diffusion. The error on the coverage is less than 10%. Inset: time evolution of $R$ at 10 K for a 0.004 atomic layer Cr deposit ($\sim 0.05\mathrm{\text{atom}}/{\mathrm{nm}}^2$) (disks) and corresponding Monte Carlo simulation (solid line).