Electronic signature of the vacancy ordering in $\mathbf{NbO}\left({\mathbf{Nb}}_{\mathbf{3}}{\mathbf{O}}_{\mathbf{3}}\right)$

We investigated the electronic structure of the vacancy-ordered $4d$-transition-metal monoxide $\mathrm{NbO}\left({\mathrm{Nb}}_3{\mathrm{O}}_3\right)$ using angle-integrated soft- and hard-x-ray photoelectron spectroscopies as well as ultraviolet angle-resolved photoelectron spectroscopy. We found that density-functional-based band-structure calculations can describe the spectral features accurately provided that self-interaction effects are taken into account. In the angle-resolved spectra we were able to identify the so-called ‘vacancy’ band that characterizes the ordering of the vacancies. This together with the band-structure results indicate the important role of the very large inter-Nb-$4d$ hybridization for the formation of the ordered vacancies and the high thermal stability of the ordered structure of niobium monoxide.

Figure 1

Crystal structure of the standard rock-salt lattice (left) and the long-range vacancy-ordered rock-salt lattice with one quarter of the atoms missing from both sublattices (right). The large and small spheres depict niobium and oxygen atoms, respectively. Niobium monoxide in the hypothetical rock-salt structure is labeled as ${\mathrm{Nb}}_4{\mathrm{O}}_4$ and in the real vacancy-ordered structure is labeled as ${\mathrm{Nb}}_3{\mathrm{O}}_3$.

Figure 2

Valence-band spectra of niobium monoxide taken with photon energies $h\nu =700,1486.6\mathrm{eV}$, and 6.5 keV together with the total and orbital projected partial density of states calculated using the hybrid functional and PBE-GGA exchange-correlation functional.

Figure 3

Total and projected DOS for ${\mathrm{Nb}}_3{\mathrm{O}}_3$ (top panel) and the hypothetical $\mathrm{fcc}{\mathrm{Nb}}_4{\mathrm{O}}_4$ (middle panel) using the screened hybrid functional with $\alpha =0.14$. The bottom panel shows the DOS for the Nb metal in the fcc crystal structure. A lattice constant of $a=4.21\mathring{\mathrm{A}}$ has been used for all three calculations.

Figure 4

Calculated band structure including the orbital character for ${\mathrm{Nb}}_3{\mathrm{O}}_3$ using the screened hybrid functional with $\alpha =0.14$.

Figure 5

(a) Experimental ARPES images along $M-X-M$ with $h\nu =168\mathrm{eV}$. (b) Calculated band structure along $M-X-M$ using the screened hybrid functional with $\alpha =0.14$. The ‘vacancy’ band is highlighted using the dotted and dashed lines in both panels.

Figure 6

Calculated band structure of ${\mathrm{Nb}}_3{\mathrm{O}}_3$ including (the orange lines) and excluding (the blue-green lines) the $\mathrm{Nb}-5s$ states. The arrow indicates the ‘vacancy’ band. See the text for details.

Figure 7

Total and $d$-projected density of states for fcc NbO, Nb, VO, V, NiO, and Ni. The calculations were performed using the wien2k code and the PBE parametrization within the GGA.

Figure 8

Schematics of the experimentally probed cuts on the momentum space $k_y-k_z$ plane with $k_x=0$. The cuts are for photoelectrons with zero binding energy with the corresponding photon energies indicated. An inner potential of $V_0=9\mathrm{eV}$ has been used. Cuts which pass through the high-symmetry points at normal emission are highlighted by the thick red lines. The electron energy analyzer has a $\pm {18}^{\circ }$ angular acceptance with a work function of 3.87 eV.