Probing the Ground State Electronic Structure of a Correlated Electron System by Quantum Well States: $\mathrm{Ag}/\mathrm{Ni}(111)$

The ground state electronic properties of the strongly correlated transition metal Ni are usually not accessible from the excitation spectra measured in photoelectron spectroscopy. We show that the bottom of the Ni $d$ band along $[111]$ can be probed through the energy dependence of the phase of quantum-well states in $\mathrm{Ag}/\mathrm{Ni}(111)$. Our model description of the quantum-well energies measured by angle-resolved photoemission determines the bottom of the ${\Lambda }_1$ $d$ band of Ni as 2.6 eV, in full agreement with standard local density theory and at variance with the values of 1.7–1.8 eV from direct angle-resolved photoemission experiments of Ni.

Figure 1

(a) Development of $sp$- and $d$-quantum-well states in Ag overlayers on Ni(111) measured by photoemission upon increasing the thickness of the Ag film up to 14 ML (normal emission). (b) Full range reference photoelectron spectra of clean Ni(111) and of a 14 ML-thick Ag film grown on top.

Figure 2

(a) Graphical solution of the extended phase equation (1). Intersections of phase shift due to propagation $2kd$ for increasing thickness $d$ (in ML) with interface phase shifts (shifted by multiples of $2\pi$). (b) and (c): Band structures of Ag and Ni given along $\Gamma \mathrm{\text{−}}L$ on the same energy scale in double- and single-group notation, respectively. Gray in (c): experiment [8, 9, 10]; black: local density theory [23]. The Ni(111) surface projected gap for which quantum-well energies are derived is represented by the gray bar.

Figure 3

Thickness-dependent electronic structure of quantum-well states in Ag on Ni(111). Measured binding energies are given as open circles. Squares denote optimal quantum-well state energy levels obtained for the gap 4.8–2.6 eV. Red triangles represent the quantum-well state energies calculated for the experimentally measured gap taken from Refs. 8, 9, 10, which deviate by one monolayer for most of the energy range. A similarly large deviation occurs when the band gap is completely absent (magenta stars).

Figure 4

Comparison of measured quantum-well energies to model calculations. The plot shows the energy difference between $n=1$ quantum-well states (QWS) for subsequent thicknesses. The Ni band gap reveals itself as a kink in this plot. The present experiment (○) agrees with a band gap boundary at 2.6 eV as calculated by local density theory [21, 22, 23] and not with the value from Ni photoemission of 1.7–1.8 eV [8, 9, 10].