Spin-Dependent Electron Scattering at Graphene Edges on Ni(111)

We investigate the scattering of surface electrons by the edges of graphene islands grown on Ni(111). By combining local tunneling spectroscopy and ab initio electronic structure calculations we find that the hybridization between graphene and Ni states results in strongly reflecting graphene edges. Quantum interference patterns formed around the islands reveal a spin-dependent scattering of the Shockley bands of Ni, which we attribute to their distinct coupling to bulk states. Moreover, we find a strong dependence of the scattering amplitude on the atomic structure of the edges, depending on the orbital character and energy of the surface states.

Figure 1

(a) Topographic profile and constant height $dI/dV$ spectra taken along the yellow line that crosses the hexagonal island in the STM image shown on the right. The standing waves arising from scattering of the $S_1$ and $S_2$ surface states are indicated by green lines. Setpoint values: $I=4\mathrm{nA}$, $V_b=-3.0\mathrm{V}$. (b) $dI/dV$ spectra of the Ni surface (black), graphene island (red), and of a Ni impurity in the island (dotted grey). (c) Calculated density of states of majority and minority states, projected onto C (red areas) and Ni (black line) atoms. Graphene bands are labeled as $G_{u/l}^{\uparrow /\downarrow }$ for spin up/down ($\uparrow /\downarrow$) and upper and lower band ($u/l$). For visualization purposes, the PDOS of Ni has been divided by 50.

Figure 2

(a) Topographic ($V_b=0.1\mathrm{V}$) and (b) constant current $dI/dV$ maps simultaneously acquired at different energies, showing the interference patterns of the $S_1$ surface state scattered from graphene islands. Setpoint current: $I=0.3\mathrm{nA}$. Image size: $30\times 37{\mathrm{nm}}^2$. (c) Topographic and $dI/dV$ profiles along the yellow line in (b), illustrating the absence of interference patterns inside the island.

Figure 3

(a) Energy of the majority IFS as a function of the graphene-Ni distance. The energy of the $S_1$ state for pristine Ni(111) is represented by the red line. (b) Planar average of the density associated with the majority IFS at the equilibrium graphene-Ni distance ($2.1\AA$). (c) Topographic and constant current $dI/dV$ maps simultaneously acquired at the energy of the IFS. Setpoint current: $I=1.2\mathrm{nA}$. Image size: $9.7\times 9.7{\mathrm{nm}}^2$. (d) Topographic profile and constant current $dI/dV$ spectra taken along a line that goes from Ni to a graphene island [yellow line in (c)], showing the IFS and the higher lying FERs. Setpoint values: $I=1\mathrm{nA}$, $V_b=0.1\mathrm{V}$.

Figure 4

(a) Dispersion relation obtained from the standing wave periodicity. A parabolic curve is included as a guide (dashed line), with onset at $-0.110\mathrm{eV}$, as obtained from the $dI/dV$ spectra. (b) Planar average density of the majority and minority $S_1$ states at the $\mathrm{\Gamma }$ point.

Figure 5

(a) Atomically resolved topographic image of the boundary of a graphene island, where reconstructed edges ($r$) exhibit twice the periodicity of the nonreconstructed ones ($n$). (b) Constant height $dI/dV$ maps measured on a $50\times 50$ grid on the hexagonal island of Fig. 1. Setpoint values: $I=4\mathrm{nA}$, $V_b=-3.0\mathrm{V}$. (c) Topographic and $dI/dV$ profiles taken along the green line in (b). For better visualization, the profiles are normalized by subtracting the $dI/dV$ intensity of the Ni surface and divided by the intensity at the center of the island. (d) Asymmetry of the scattering intensity of $n/r$ edges for the $S_1$ (black) and $S_2$ (red) surface state, as defined in the text. Error bars indicate the standard deviation of data obtained from different edges of the hexagon.