$\alpha$-Sn phase on Si(111): Spin texture of a two-dimensional Mott state

The $\alpha$-Sn reconstruction on Si(111) is a prototype system for a two-dimensional Mott phase. In this study we performed spin-resolved photoemission experiments and analyzed in detail the spin structure of this electronically correlated surface state. The analysis of the spin-integrated bands as well as the spin texture of the surface states along different crystallographic directions provide clear evidence for the formation of collinear antiferromagnetic $(2\sqrt{3}\times \sqrt{3})$ domains, while the Sn reconstruction reveals a $(\sqrt{3}\times \sqrt{3})$ symmetry. The Rashba splitting of the highest occupied Mott state was found to be $\mathrm{\Delta }k=0.05{\AA }^{-1}$, i.e., the $\alpha$-Sn phase should be termed a weakly spin-orbit coupled Mott system.

Figure 1

(a) LEED image of $\alpha$-Sn taken at an electron energy of 76 eV at a temperature of 40 K. Dashed lines connect the first order diffraction spots of $(1\times 1)$ (green) and $(\sqrt{3}\times \sqrt{3})$ (red). The feature next to the electron gun stems from a defect on the screen. (b) STM (+1 V, 0.1 nA) image of the $\alpha$-Sn phase with a vacancy taken at room temperature. (c) Top view of the $\alpha$-Sn reconstruction on Si(111). Blue and violet circles represent Sn atoms on $T_4$ adsorption sites with different spin polarizations; Si atoms are gray. Red and blue lines indicate the $(\sqrt{3}\times \sqrt{3})$ and $(2\sqrt{3}\times \sqrt{3})$ unit cell, respectively. (d) SBZs of the $(1\times 1)$ (green), $(\sqrt{3}\times \sqrt{3})$ (red), and three rotational $(2\sqrt{3}\times \sqrt{3})$ domains (blue). The domain labeled as ‘1’ is referred to as the horizontal domain, while domains ‘2’ and ‘3’ are termed rotated domain structures.

Figure 2

(a) Extended CEM taken at $E_B=0.38$ eV. Only the phase space shown in the lower left was measured. The superimposed red and blue lines show the SBZs of the $(\sqrt{3}\times \sqrt{3})$ and of the three rotational domains of $(2\sqrt{3}\times \sqrt{3})$, respectively. Dots symbolize high symmetry points of both structures; gray lines highlight the directions of the (S)ARPES measurements. (b) Band map along the $k_x$ direction (1). (c) Band map along the $k_y$ direction (2). Dashed white curves show the positions of the Si valence band. Details of the band maps within the blue boxes are shown in Fig. 3.

Figure 3

(a),(b) MDCs along the $k_x$ and $k_y$ directions taken at 380 meV, respectively. (c),(d) Band maps along the $k_x$ and $k_y$ directions. (e),(f) curvature maps of (c) and (d) to highlight details of the band structure. Green lines show the position of the MDCs. Solid and dashed blue curves indicate (spin-degenerate) calculated surface bands from domain 1 and domains 2, 3 of the $(2\sqrt{3}\times \sqrt{3})$ structure, respectively. The band structure was taken from Ref. [17].

Figure 4

(a) Band map along the direction denoted by (3) in Fig. 2, where the MDCs were taken. The dashed curves show the $\sqrt{3}\times \sqrt{3}$-replica states of the Si valence bands. (b) MDC curves taken along the $k_y$ direction with $C^{+}$ and $C^{-}$ polarization. (c) and (d) show the difference and sum of the two MDC spectra, respectively.

Figure 5

(a) Spin-resolved MDC along the $k_x$ direction taken at 0.38 eV below $E_{\text{F}}$. The upper axis shows the high symmetry points [cf. Fig. 1]. (b) Corresponding spin-polarization vectors $S_x, S_y$, and $S_z$. The shaded areas represent the uncertainty by simultaneously fitting all four data sets. (c) $S_x$ and $S_y$ spin components of the peaks shown in (a). The $0^{\circ }$ and ${90}^{\circ }$ denote the positive $x$ and $y$ directions, respectively.

Figure 6

(a) Spin-resolved MDC along the $k_y$ direction taken at 0.38 eV below $E_{\text{F}}$. The upper axis shows the high symmetry points of the three domains [cf. direction (3) in Fig. 2]. (b) Corresponding spin-polarization vectors $S_x, S_y$, and $S_z$. The shaded areas represent the uncertainty by simultaneously fitting all four data sets. (c) $S_x$ and $S_y$ spin components of the peaks shown in (a).

Figure 7

(a) Electronic structure and spin texture in the SBZ of the $(2\sqrt{3}\times \sqrt{3})$ structure at a binding energy of 0.4 eV with a Rashba splitting of $\mathrm{\Delta }k\approx 0.05{\AA }^{-1}$. (b) Band structure reproduced after Lee et al. [17]. The Mott state was complemented by Rashba splitting. (c) SBZs consisting of three rotational $(2\sqrt{3}\times \sqrt{3})$ domains. Red and blue spin vectors belong to the horizontal domain as seen in (a). Spin components of the other two domains are shown in gray, the resulting spins of those domains along the $k_x$ and $k_y$ direction in orange and green. The broad gray lines indicate the positions of measurements along the $k_x$ and $k_y$ direction shown in Fig. 3 and coincide with the lines denoted by (1) and (3) in Fig. 2.