Unoccupied surface states of ${\mathrm{LaB}}_6\left(001\right)$ studied by $k$-resolved inverse photoemission

We have measured $k$-resolved inverse photoemission spectra of ${\mathrm{LaB}}_6\left(001\right)$ to study unoccupied surface states. The surface states are observed near the Fermi level $\left(E_F\right)$ and at $6.8\mathrm{eV}$ above $E_F$, which are originated from $\mathrm{La}5d$ and $\mathrm{La}4f$ states, respectively. The surface state near $E_F$ shows energy dispersion along the $\Gamma$–$M$ direction of the surface Brillouin zone, which does not agree with that of a recently reported theoretical calculation. It is deduced that at a ${\mathrm{LaB}}_6\left(001\right)$ surface, electrons are transferred from the subsurface to the topmost La layer. This charge redistribution can reduce surface dipole moments.

Figure 1

Surface structures of the ${\mathrm{LaB}}_6\left(001\right)$, (011), and (111) clean surfaces. The figures show the side views of the surfaces. In the (011) and (111) surfaces, the topmost La atoms are displaced from the ideal lattice plane upward by $1.66\mathrm{\AA }$ and downward by $1.2\mathrm{\AA }$, respectively (Ref. 7).

Figure 2

Normal incidence IPES spectra of a clean ${\mathrm{LaB}}_6\left(001\right)$ surface and ones after oxygen adsorption. The spectra intensities are normalized to sample impinging current. (a) The solid line is a spectrum from a clean surface. The dotted line is from the surface exposed to $0.1\mathrm{L}$ of oxygen. (b) The dashed-dotted line is a spectrum from the surface exposed to $0.2\mathrm{L}$ of oxygen.

Figure 3

KRIPES spectra of a clean ${\mathrm{LaB}}_6\left(001\right)$ surface varying angles of electron incidence from $-18°$ to 54° by 3° along the $\Gamma$–$M$ direction. The angle of incidence $\theta$ is measured relative to the surface normal. The inset shows the surface Brillouin zone of ${\mathrm{LaB}}_6\left(001\right)$ and the small vertical rods represent the peak positions. The peak $A$ at $\theta \sim 45°$ and the peak $E$ at $\theta \sim 33°$ correspond to the $M$ point.

Figure 4

The energy dispersion of the surface state (peak $A$ in Fig. 3) of ${\mathrm{LaB}}_6\left(001\right)$. The closed black circles show the band in the first Brillouin zone and the open circles are reduced from the second zone to the first zone. The gray circles show the calculated surface bands of ${\mathrm{LaB}}_6\left(001\right)$, which are strongly localized in the outermost La layer (Ref. 11).