Spin-orbit influence on $d_{z^2}$-type surface state at Ta(110)

The influence of spin-orbit interaction on an occupied surface state at Ta(110) is investigated with spin- and angle-resolved photoemission and electronic structure calculations. The surface state appears in a symmetry gap at a binding energy of 0.45 eV at $\overline{\mathrm{\Gamma }}$ and exhibits a free-electron-like $E({\mathbf{k}}_{\parallel })$ dispersion with an effective mass $m^{*}/m_e$ of about $-1.35$ along $\overline{\mathrm{\Gamma }}\overline{H}$. Photoemission results for excitation with $s$- and $p$-polarized light confirm the predicted $d_{z^2}$-type symmetry of the state close to $\overline{\mathrm{\Gamma }}$. Spin-resolved data for finite ${\mathbf{k}}_{\parallel }$ reveal a pure Rashba-type spin texture with a Rashba parameter of $0.063\pm 0.007\mathrm{eV}\AA$. These findings clearly prove a sizable impact of spin-orbit coupling on the $d_{z^2}$ surface state and resolve a longstanding disagreement on this issue.

Figure 1

Experimental geometry for spin-resolved ARPES using linearly polarized synchrotron radiation (a). Contour plots of the photoelectron intensities as a function of binding energy and ${\mathbf{k}}_{\parallel }$ along $\overline{\mathrm{\Gamma }}\overline{H}$ excited by $p$- and $s$-polarized light of $h\nu =43\text{eV}$ (b), (c) and by $p$-polarized light of $h\nu =22\text{eV}$ (d).

Figure 2

Calculated electronic structure of Ta(110) along $\overline{\mathrm{\Gamma }}\overline{H}$. Spectral densities $n_l(E,{\mathbf{k}}_{\parallel })$ for a bulk layer (a) and for the topmost surface layer (b), sharing a common color scale ($\text{dark}=\text{small}, \text{bright}=\text{large}$ values). (c) Difference $n_{l\uparrow }(E,{\mathbf{k}}_{\parallel })-n_{l\downarrow }(E,{\mathbf{k}}_{\parallel })$ of the spin-projected spectral densities, shown in red (blue) where spin-up (spin-down) intensity exceeds (white denotes zero spin difference). (d) Orbital decomposition of the surface spectral density of (b) with according symmetry representations assigned.

Figure 3

(a) ARPES results for Ta(110) obtained by $p$-polarized synchrotron radiation with $h\nu =43$ eV. The contour plot is superimposed by pointing-up and -down triangles, indicating the spin character of the corresponding spectral features, as derived from the spin-resolved spectra in (b) and (c). (b), (c) Spin-resolved ARPES spectra sensitive to $P_y$ for negative and positive emission angles along $\overline{\mathrm{\Gamma }}\overline{H}$. Spin-up (spin-down) intensities are marked as red (blue). (d), (e) Spin-resolved ARPES spectra sensitive to $P_x$ and $P_z$.

Figure 4

(a), (b) Spin-resolved ARPES spectra of $S_1$ sensitive to $P_y$ obtained by $p$-polarized synchrotron radiation of $h\nu =43$ and 22 eV. Spin-up (spin-down) intensities are marked as red (blue). (c) Energy difference $\mathrm{\Delta }E$ between spin-up and spin-down intensities of $S_1$ for $h\nu =43$ eV (solid dots) and $h\nu =22$ eV (open dots) as a function of ${\mathbf{k}}_{\parallel }$.