Fully spin-polarized bulk states in ferroelectric GeTe

By measuring the spin polarization of GeTe films as a function of light polarization we observed that the bulk states are fully spin polarized in the initial state, in strong contrast with observations for other systems with a strong spin-orbit interaction and the surface derived states in the same system. In agreement with state-of-the-art theory, our experimental results show that fully spin-polarized bulk states are an intrinsic property of the ferroelectric Rashba semiconductor $\alpha$-GeTe(111). The fact that the measured spin-polarization vector does not change with light polarization can be explained by the absence of a mixing of states with a different total angular momentum $J$.

Figure 1

(a) High-resolution $\alpha$-GeTe ARPES band structure measured around the $Z$ point ($h\nu =22$ eV), showing the bulk Rashba-split bands $B_1$ and $B_2$, surrounded by surface resonances $S{R}_{1,2}$ and surface states $S{S}_{1,2}$. (b) Constant binding energy maps: Top panels are four selected slices from (a), and the bottom panels are corresponding BSF calculations. (c) BZ of quasicubic (rhombohedrally distorted) $\alpha$-GeTe. (d) Experimental geometry with $\pi$- and $\sigma$-polarized light, with $\overline{K\mathrm{\Gamma }K}$ sample alignment indicated and related $p$-orbital symmetries. (e) Representative $\alpha$-GeTe ARPES band maps at the $Z$ point ($h\nu =22$ eV). (f) ARPES band maps for selected photon energies showing the $k_z$ dispersion of the states. Yellow dashed lines for $h\nu =26$ eV serve as guides to the eye to track the different bands as used for the $h\nu =7$ eV data shown in Fig. 3.

Figure 2

(a) $\alpha$-GeTe BSF calculations with total intensity spectral function $I_{\text{tot}}$ decomposed to $s, p_{\frac{1}{2}}$, and $p_{\frac{3}{2}}$ orbital contributions; with analogous DFT analysis in (b). Color coding distinguishes the contribution from Ge and Te atoms, while circle radii represent weights of a given state projected to the corresponding relativistic orbitals, and $B_{1,2}$ are the bulk Rashba-type bands at the valence-band maximum. (c) BSF total spin-polarization initial state calculations $P_{\text{tot}}$ decomposed to individual orbitals.

Figure 3

ARPES band maps measured at 7 eV for (a) $\pi$- and (b) $\sigma$-polarized light. Dashed lines indicate the $S{S}_{1,2}, S{R}_{1,2}$, and $B_{1,2}$ bands consistent with data measured at $h\nu =26$ eV seen in Fig. 1. (c) Schematic diagram for $k$-space mapping showing normalized $k_z$ values based on an inner potential $V_0=8.5\mathrm{eV}$.

Figure 4

(a), (b) SARPES band maps measured at 7 eV for $\pi$- and $\sigma$-polarized light, respectively. For every panel the top left figure shows the total intensity and the other panels the respective spin polarizations along the three spatial directions. The yellow dashed lines serve as guides to the eye to track the band dispersion, and the circle highlights the region where the spin polarization changes due to spin hybridization effects.

Figure 5

(a)–(c) BSF total initial state spin-polarization calculations along the $Z-A$ and $Z-U$ directions. (a) shows total spin polarization $P_{\text{tot}}$, and the blue square indicates the locus of highest polarization. (b), (c) Band map with $|P_{\text{tot}}|\ge 80\%$ and $|P_{\text{tot}}|\ge 95\%$, respectively. (d) Total spin polarization $P_{\text{tot}}$ at the top of the valence band, and its spinor components $P_x, P_y$, and $P_z$, calculated for 16 selected momenta along the $Z\mathrm{\Gamma }$ direction, denoted in the BZ inset. A quiver plot of their in-plane $P_{x,y}$ spin texture is seen in the bottom of the panel. For comparison, $P_{\text{tot}2}$ indicates the maximum spin polarization found in a selected region around the top of the valence band. (e) Zoomed view [black frame in (a)] of total spin polarization along the BZ direction indicated in the inset of (d). Blue and yellow symbols show the energy and momenta where $P_{\text{tot}}$ and $P_{\text{tot}2}$ were obtained, respectively.