Introduction

One of the challenges in developing semiconductor spintronics is to generate spin-polarized electrons at room temperature1,2. A partial solution is spin injection from ferromagnets, which has seen significant progress for GaAs3. Although semiconductor devices are also proposed for spin filtering4 and generation of spin-polarized current5,6 on the basis of the Rashba spin splitting7,8 for two-dimensional electrons, these have not yet been realized. Recently, the Rashba effect at crystal surfaces9,10 has been discovered to exhibit spin splitting orders of magnitude larger than those at semiconductor heterojunctions, and sometimes comparable with the separation between conduction bands11,12. For a spintronic application of the surface giant Rashba effect, (i) a large spin splitting of (ii) a metallic surface-state band on (iii) a semiconductor surface is required. The first and second requisites are because of the requirement for significant spin transport, and the third is indispensable because the large bulk current in metallic substrates sweeps off any surface spin signals. In this paper, we show that a large Rashba spin splitting is realized for a metallic surface-state band on a semiconductor surface. This opens a new field of surface spin transport/accumulation13, which also has implications for efficient spin accumulation, filtering and injection into semiconductors.

The surface Rashba effect was first discovered on Au(111)9,10 and then on other metal surfaces such as W14, Bi15 and Bi-covered Ag11,12. The charge density distribution along the surface normal in the vicinity of the nuclei is crucial for the surface Rashba effect because the potential gradient is most prominent at closest proximity to nuclei16. Premper et al.17 suggested that the size of Rashba spin splitting could be further enhanced by the existence of in-plane structural inversion asymmetry. The studies on Bi/Ag systems indicated that large Rashba spin splitting is possible even on the surface of a light element when it is covered with a monolayer of a heavier element. This accelerated the search for the large Rashba effect on semiconductor surfaces such as Si and Ge, as this has potential importance in spintronic applications. Although some studies have been carried out on the Rashba effect on heavy-element-covered Si(111) and Ge(111) surfaces18,19,20,21,22,23,24, these studies show only nonmetallic spin-split bands, which contribute little to spin transport, or lack direct experimental evidence of spin splitting. Pb thin films with a thickness of ∼10 monolayers on Si(111) were shown to exhibit a Rashba spin-split quantum-well state25. The films, however, had a high density of spin-degenerated metallic bands and hence would not exhibit detectable spin-dependent transport properties. Thus, it is of crucial importance to establish a semiconductor surface with Rashba spin-split metallic surface bands. In this paper, we report on the Rashba spin splitting of a metallic surface-state band on a Ge(111) surface induced by a Pb monolayer.

Results

Angle-resolved and spin-resolved photoelectron spectroscopy

Figure 1a shows the structural model26 and low-energy electron diffraction pattern of the surface. The nominal Pb coverage is 4/3, with one of four Pb atoms per unit cell located at an H3 site and the other three on off-centred bridge positions between T1 and T4 sites.

Figure 1: Schematic structure model and low-energy electron diffraction (LEED) pattern of Pb/Ge(111).
figure 1

(a) Top view of . The large and small circles indicate Pb adatoms and Ge atoms in the first bilayer, respectively. The solid parallelogram denotes the unit cell. (b) LEED pattern of .

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Figure 2a shows the band dispersion along 112 measured by angle-resolved photoelectron spectroscopy (ARPES) at 30 K (left panel) and at room temperature (right panel). Three Pb-induced bands denoted as S1, S2 and S3 can be clearly seen. These bands are not observed on the clean Ge(111)-c(2×8) surface. The S1 band, which is located in the projected bulk band gap and crosses the Fermi level, EF, is clearly split into two. Although the bands are thermally broadened at room temperature, the S1 band clearly shows splitting near EF. At binding energies greater than ∼0.4 eV, the S1 band is merged into the projected bulk bands. The effective mass for the S1 band is estimated to be 0.028 me at EF. Figure 2b was obtained by imaging the photoelectron intensity within a 50 meV energy window centred at EF and it shows the Fermi surface due to S1. The Fermi surface is composed of two concentric hexagons, which agrees with expectations for the Rashba spin-split bands.

Figure 2: Energy band dispersion measured by ARPES.
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(a) Experimental energy band dispersions along 112 of the surface Brillouin zone (SBZ) at 30 K and room temperature are shown in the left and right panels, respectively. The dashed line indicates the upper edge of the projected bulk bands of Ge(111). (b) Fermi surface map. The bold dashed (red) rectangle shows the region actually measured. The rest of the image was obtained by mirror symmetry operations. Bold and thin solid lines denote and (1×1) SBZs, respectively. (c) Momentum splitting Δk||, multiplied by 2/2m*, for S1 in the M1 (diamonds) and M2 (crosses) sides as a function of binding energy.

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Figure 3c shows spin-resolved ARPES spectra taken at several selected angles along 112 in the direction. Energy and angular resolution were set at 110 meV and 2.0°, respectively. It was found that the spectra for spin-up and spin-down measured at the emission angle of 30° are almost identical and show the S2 peak at ∼0.9 eV. The emission angle of 30° corresponds to the 1 point. This indicates that the spin-up and spin-down states of S2 are degenerate at , as expected for the Rashba splitting. The good overall agreement of the spin-up and spin-down spectra indicates the high accuracy of the present spin-resolved measurement.

Figure 3: Spin-resolved ARPES.
figure 3

(a, b) Spin-unpolarized ARPES. Dashed lines indicate the angles for which spin-resolved ARPES are shown. (c) Spin-resolved ARPES spectra measured at several selected angles along 112. The probed spin orientation axis is parallel to , which is parallel to the surface and perpendicular to . The intensities for spin-up and spin-down, defined as spins oriented towards and , respectively, are plotted by the blue solid and red open circles, respectively.

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Except for the spectra taken at 30°, the spectra for spin-up and spin-down show k||- and binding-energy-dependent asymmetry. In particular, the S1 and S3 states show clear energy splitting, depending on the spin polarization. For emission angles of 19°, 20.5° and 22° (1 side), the spin-up peaks of S1 and S3 are located at lower binding energies than the corresponding spin-down peaks. Comparing the spin-unpolarized ARPES data, we find that the higher (lower) binding energy branch of the S1 band is spin-down (spin-up). For emission angles of 41° and 43.5° (2 side), the positions of the spin-up and spin-down branches of the S1 band are inverted; that is, the spin-up branch is located at binding energies higher than the spin-down branch. Note that the spin-down branch is above EF for emission angle 43.5°. These results indicate that the splitting observed by ARPES for the S1 band is due to Rashba spin splitting.

The spin polarization for the S1 band at emission angles of 22° and 41° may be small because the band is merged into the projected bulk bands. On the other hand, although the S3 band does not appear to be split in the spin-unpolarized spectra, spin-resolved data suggest that S3 is also spin-split up to ∼100 meV.

The binding energy dependence of the momentum splitting Δk|| for S1 times 2/2m* is plotted in Fig. 2c. The Δk|| values were evaluated by fitting the momentum distribution curves with two Gaussian functions. Note that the ideal Rashba model for two-dimensional free electrons yields two free-electron-like parabolas that are shifted in opposite k|| directions by a constant value from the point. The Rashba parameter is then expressed by the momentum splitting Δk|| as αR=Δk||2/2m*. The observed momentum splitting for S1 shows an almost constant value, Δk||=0.028±0.002 Å−1, in the binding energy range of 0.2–0.6 eV. The Rashba parameter is therefore deduced to be αR=0.24±0.02 eV Å−1. On the other hand, momentum splitting in the binding energy range of 0–0.2 eV deviates from the constant value and reaches Δk||=0.04 Å−1 at EF. The energy splitting value between the spin-up and spin-down states for S1 is 200 meV at kF1=0.36 Å−1.

First-principles calculation

Figure 4a,b shows the calculated band structure. The spin quantization axis is , which is perpendicular to k||(1). In Fig. 4a, the radii of the circles are proportional to the net contribution of Pb 6p, with the spin oriented towards (blue) and (red), indicating spin splitting of the Pb-induced bands. The U1, S2 and S3 bands are in resonance with the bulk bands near , which prevents unambiguous identification of a Rashba-type k||-linear spin splitting near . However, the absence of spin polarization at , as indicated by the absence of circles in Fig. 4a, is consistent with Rashba-type spin splitting. In Fig. 4b, the radii of the circles are proportional to the total contribution of Pb 6p, and the colour index represents the relative contributions of Pb 6pxpy and 6pz. The calculation reproduces the characteristic Pb-induced features, S1, S2 and S3, observed by ARPES. The S1 band has a strong Pb 6pxpy character. The S3 band also has a Pb 6pxpy character and a larger contribution from Ge orbitals. The S2 and unfilled U1 bands have characters of bonding and antibonding, respectively, between Pb 6pz and Ge 4pz of the topmost Ge atoms.

Figure 4: Calculated band structure and charge density distribution.
figure 4

(a) Band structure calculated for the surface. The spin quantization axis is . Opposite spin orientations are indicated by blue and red circles. The radii of the blue (red) circles are proportional to the net contribution of Pb 6p with spin-up (spin-down). (b) Band structure with relative contributions of Pb 6pxpy and 6pz shown by colour scale. The sizes of the circles are proportional to the total contribution of Pb 6p. (c) Charge density contour for the state at which S1 crosses EF. (d) (Top panel) Charge density distribution near a Pb nucleus located at the H3 site (left) and line profile along the surface normal (dashed line) (right); z=0 corresponds to the nuclear position. (Bottom panel) The same as the upper panel but for Pb located at the bridge site.

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The calculation indicates that the split pairs of S1 are spin polarized in opposite directions, in agreement with the result of spin-resolved ARPES. Spin splitting is calculated to be 165 meV at kF1=0.366 Å−1, in good agreement with the experiment. The dispersion calculated for S2 and S3 bands is also in agreement with the ARPES and spin-resolved ARPES. Thus, we conclude that the experimentally observed splitting is due to the Rashba effect. We also note that the Ge-derived surface state (SGe) appears just above the bulk bands in the vicinity of the point. This state has negligible contribution from Pb orbitals.

Discussion

The size of the Rashba splitting for the S1 band is orders of magnitude larger than that of semiconductor quantum wells (typically a few meV). Simulations of spin-dependent phenomena such as spin accumulation/transport and spin filtering for Rashba spin-split surface bands have been reported recently27,28,29. It should, however, be difficult to study the spin transport phenomena experimentally on the previously known metallic-surface Rashba systems, because these are all based on metallic substrates, and large bulk current interferes as background. The Pb/Ge(111) system now serves as an ideal prototype for surface spin transport. Several types of nonequilibrium spin-dependent transport/accumulation phenomena are expected to be observed, as the surface conductivity on this surface should be dominated by the electrons in the spin-split S1 band. An experiment along this line is underway.

The charge density contour for the S1 state at EF is shown in Fig. 4c, which indicates that the state is mostly localized in the Pb monolayer. The contributions of different Pb atomic orbitals to the wavefunction of the S1 state are in the ratio 6s:6p=1:5.5. The 6p component is predominantly of in-plane character as shown in Fig. 4b.

According to Nagano et al.16, the size of Rashba spin splitting is determined by the integral of the potential gradient along the surface normal times the charge density, Because the potential gradient is most prominent at closest proximity to the nuclei, the charge density asymmetry along z in the vicinity of the nuclei governs the splitting. The charge density profiles in the z direction near the Pb nuclei are illustrated in Fig. 4d. Whereas for Pb at the bridge position, the distribution shows a nearly symmetric feature near z=0, the Pb atom on the H3 site exhibits an asymmetric charge distribution at |z|<0.05 a.u. (atomic units: 1 a.u.=0.529 Å), which therefore makes a dominant contribution to the Rashba spin splitting. In principle, the Rashba spin splitting at surfaces can be as large as the spin-orbit splitting in a free atom16, as for Bi/Ag11,12. The spin splitting observed here is considerably smaller than the spin-orbit splitting of the 6p orbital in a free Pb atom, 1.75 eV, which is because the S1 band is predominantly of an in-plane p character. A larger contribution of s and pz, which could be possible for different adsorption geometry, would lead to more prominent charge density asymmetry along the z direction and hence to a larger spin splitting.

We conclude that a metallic surface-state band on Pb/Ge(111) exhibits a Rashba spin splitting of 200 meV and an effective mass of 0.028 me at EF, thus serving as a basis for surface spin transport. The size of the spin splitting is larger by a factor of 8 than the thermal energy kBT at room temperature. The low effective mass is important because it is associated with a high electron mobility. As the effect does not depend on any peculiar properties of Ge, it would be possible to realize a similar electronic structure on a Si surface. Once a spin asymmetry is induced on the Si surface, whether by spin filter, spin accumulation or any other effect, it enables spin injection into the substrate. It is also possible to grow a thin epitaxial Ge film on a Si substrate and then deposit Pb on it to obtain surface spin asymmetry. In addition, the surface would be covered by a stable insulating film such as metal oxide without destroying the surface electronic state, which enables us to study various properties under ambient conditions.

Methods

Sample preparation method

The ARPES experiment was performed in an ultrahigh-vacuum system with a base pressure of 1.0×10−10 Torr. A Ge(111) substrate was prepared by several cycles of 0.7 keV Ar+ bombardment and subsequent annealing up to 870 K for a few seconds. Pb was deposited onto the surface at room temperature, which was then annealed at 570 K for 10 min.

ARPES and spin-resolved ARPES

The intensities of the low-energy electron diffraction pattern (Fig. 1b) and the Pb 5d photoemission were monitored to optimize the Pb coverage. ARPES measurements were carried out by a hemispherical electron energy analyser (VG Scienta R3000) in an angular mode and monochromatized He Iα radiation (hν=21.218 eV). The sample was maintained at 30 K or at room temperature during the ARPES measurement. The spin-resolved ARPES experiments were performed at Hiroshima Synchrotron Radiation Center (HSRC), Hiroshima University, using He Iα radiation and a Mott detector operating at 25 keV30,31. In the spin-resolved ARPES measurement, the sample temperature was kept at 100 K.

First-principles calculation

First-principles calculation was performed using the WIEN2K computer code on the basis of the 'augmented plane wave+local orbitals' (APW+lo) method32 with the spin-orbit interaction being taken into account. The surface was modelled by repeated slabs consisting of a 24-layer Ge(111) slab, with one side covered with a layer and the opposite side terminated by hydrogen atoms. Starting from the structural model determined by X-ray diffraction,26 the atomic positions were optimized until the root mean square of the forces exerted on all the atoms becomes negligibly small (<2 mRy per a.u.).

Additional information

How to cite this article: Yaji, K. et al. Large Rashba spin splitting of a metallic surface-state band on a semiconductor surface. Nat. Commun. 1:17 doi: 10.1038/ncomms1016 (2010).