Spin-polarized surface electronic structure of Ta(110): Similarities and differences to W(110)

Tantalum and tungsten, direct neighbors in the periodic table, exhibit a very similar electronic structure. Compared with tungsten, however, the bands of tantalum are less occupied due to the lack of one electron. As a consequence, an exceptional Dirac-cone-like surface state, observed below the Fermi level for W(110), may appear above the Fermi level for Ta(110). To prove this conjecture, we investigate the unoccupied surface electronic structure of Ta(110) by spin- and angle-resolved inverse photoemission and electronic-structure calculations. Surprisingly, our results do not show the expected Dirac-cone-like surface state. Instead, spin-polarized unoccupied surface bands are identified, which have no equivalent in W(110). These findings are explained by the difference in the energetic positions of the surface states relative to the bulk states for Ta(110) and W(110) caused by the different lattice constants.

Figure 1

(a) LEED pattern of the Ta(110) surface with superimposed surface Brillouin zone (SBZ). (b) Experimental geometry of the spin- and angle-resolved inverse-photoemission experiment.

Figure 2

Spin-resolved IPE spectra for different angles of electron incidence along $\overline{\mathrm{\Gamma }}\overline{\mathrm{H}}$ (a) and $\overline{\mathrm{\Gamma }}\overline{\mathrm{N}}$ (b). Spin-up (spin-down) polarization of the incident electrons is marked by red up-pointing (blue down-pointing) triangles. Distinct intensity structures are indicated by $T_1$ to $T_3$, and S. A pale red line in (a) marks the dispersion of S.

Figure 3

$E\left({\mathbf{k}}_{\parallel }\right)$ diagrams along $\overline{\mathrm{\Gamma }}\overline{\mathrm{H}}$ (top row) and $\overline{\mathrm{\Gamma }}\overline{\mathrm{N}}$ (bottom row): (a)–(c), (e)–(g) Spectral-density calculations; (d), (h) experimental results derived from spin-resolved IPE spectra in Fig. 2. The spectral density was calculated (a), (e) for the bulk, (b), (f) for the surface layer, and (c), (g) as the difference of the spin projection. The dashed parabolic lines in (c) and (g) mark those $\left(E,k_{\parallel }\right)$ that are accessed by an IPE measurement at $\theta ={40}^{\circ }$.

Figure 4

(a) Spin-integrated IPE spectra of Ta(110) along $\overline{\mathrm{\Gamma }}\overline{\mathrm{H}}$ for various angles of incidence $\theta$. The gray-dotted data were taken approximately 2 h after the black-dotted data. (b) Spin-resolved IPE spectra of Ta(110) for incidence angles $\theta =+{30}^{\circ }$ and $-{30}^{\circ }$ along $\overline{\mathrm{\Gamma }}\overline{\mathrm{H}}$ in a reduced energy range. The surface-related feature S appears close to a bulk-band edge B. Therefore, the spectra were decomposed into a spin-polarized surface and a spin-independent bulk contribution on top of a spin-independent background intensity. For details, see text.

Figure 5

Calculated bulk spectral densities (gray) for (a) Ta(110) and (b) W(110) along $\overline{\mathrm{\Gamma }}\overline{\mathrm{H}}$. Spin differences of the surface layers are superimposed on the bulk data as red (spin-up) and blue (spin-down) lines to highlight spin-dependent surface contributions. For comparison, the energy scale with respect to $E_{\mathrm{F}}$ is shifted by 1.9 eV.