Abstract
The Rashba effect is a momentum‐dependent splitting of spin bands in two‐dimensional systems such as surface, interface and heterostructure. The effect is caused by broken space‐inversion symmetry and spin‐orbit coupling and allows to manipulate and generate the spin by the electric fields, that is, without the magnetic field. It means that the devices applied to the Rashba effect have many advantages. Bismuth is known as a promising candidate to investigate the surface Rashba effect, and the spin structure of Bi surface has also been intensively discussed. However, it is unclear to what extent the so far believed simple vortical spin structure is adequate. To understand the surface properties of the Rashba system is particularly important when utilizing the Rashba effect to the spintronic devices, since it is desirable to control the spin polarization when developing new types of devices. In this chapter, we report that the surface spin states of the Bi thin film exhibit unusual characteristics unlike the conventional Rashba splitting by using a spin‐ and angle‐resolved photoemission spectroscopy measurement.
Keywords
- Rashba effect
- spin‐resolved ARPES
- thin film
- bismuth
1. Introduction
As we know and use, spintronic devices to use a spin‐polarized electrons have actualized. The magnetic storage technology uses giant magneto‐resistance [1]. A more advanced approach is to control spin‐polarized electrons without the aid of a ferromagnetism nor to apply the magnetic field [2]. Spin‐orbit coupling (SOC) makes it possible to generate and manipulate spin‐polarized electrons only by the electric field, since the electric field acts on a moving charge carrier as an effective magnetic field. Thus, it is regarded as an essential ingredient for further development of next‐generation spintronic devices such as the spin‐field‐effect transistor [3]. In nonmagnetic solids, the electronic states with opposite spin have the same energy (Kramers degeneracy) because of the time‐reversal and the space‐inversion symmetries (TRS and SIS). In the strong SOC environment with the broken space‐inversion symmetry (typically at the surface or interface), the energy band splits in the momentum (
which is well known as the Rashba effect, where
The first observation of the surface Rashba effect by ARPES is the Au(1 1 1) surface [7]. After that, various materials such as group‐V semimetals and their alloy surfaces [8–16], as well as heavy‐atom adsorbed semiconductor surfaces [17–22] and so on, are studied. Among them, the group‐V semimetal bismuth (Bi) is a prime candidate to investigate the surface Rashba effect and many experiments and theoretical calculations studied in order to clarify the fundamental properties of the Rashba effect [8, 10–14]. However, in previous researches, although the band structure and Fermi surfaces of Bi distinctly show strong anisotropy, the spin structure of Bi was argued by assuming an isotropic two‐circular Fermi‐surface model like Au(1 1 1) [7, 20–22]. The reason is because the energy and momentum resolutions of the previous spin‐resolved ARPES machine are insufficient. To understand whole aspect of the Rashba effect, it is necessary to clarify that the spin structure of Bi consists with the conventional Rashba model or not. Moreover, in the film, electronic states originating from the bulk Bi are quantized, and they are connected to the surface bands continuously. So it would be necessary to take into account the relationship between bulk and surface states. On the other hand, intensive attempts have been made to extend the investigations on 2D Rashba systems to quasi one‐dimensional (1D) system like artificially grown nanowires and quantum wires, because of the merits in downsizing of devices.1D Rashba effect in utilization of vicinal surfaces such as in Au chains on vicinal Si [23] and the vicinal Bi surface is also reported [24]. In such a case, breaking the TRS by applying magnetic field or adding magnetic impurities would create an energy gap at the Kramers point, and when the chemical potential is tuned to be located in the spin‐orbit gap, the dissipation‐less spin transport and the quantized conductance [25, 26] may be realized (Figure 1c). However, the Rashba effect in edge state is not known because the signal from the edge is extremely faint. To understand the proposed novel properties of a true 1D system, we may be able to apply them to advanced spintronic devices.
In this chapter, we introduce the electronic structure of Bi thin film to elucidate the details of the Rashba effect by utilizing the high‐resolution spin‐resolved ARPES spectrometer equipped with a highly efficient mini‐Mott detector. We show three novel Rashba effects of Bi thin film: (i) anisotropic Rashba effect from momentum‐dependent measurement [27], (ii) the interface Rashba effect between metal‐semiconductor from thickness‐dependent [28] and (iii) 1D Rashba effect of edge state [29]. The present finding provides a useful platform to study the Rashba effect and at the same time opens a pathway to utilize the novel properties to advanced spintronic devices.
2. Experimental technique and sample fabrication
2.1. Spin‐ and angle‐resolved photoemission spectromete
Figure 2 shows a schematic diagram of the ultra‐high‐resolution spin‐resolved ARPES spectrometer with a highly efficient mini‐Mott detector [30]. This spectrometer consists of mainly four parts: (i) a photoemission measurement system including a hemispherical electron energy analyzer and an ultra‐high‐vacuum measurement chamber, (ii) a spin‐detection system based on a mini‐Mott detector, (iii) an intense xenon/helium plasma discharge lamp and (iv) a surface chamber to prepare the thin‐film samples. We explain the detail of each part. We have improved a MBS‐A1 electron energy analyzer to achieve both spin‐resolved and regular (non‐spin‐resolved) ARPES measurement. The spectrometer has two detectors: one is a multichannel plate for ARPES measurement, and the other is mini‐Mott detector for spin‐resolved ARPES. To determine the three‐dimensional spin polarization, an electron deflector has been placed between the analyzer and the Mott detector. The Mott detector observes the spin polarization of essentially two independent axes by using four channeltrons, enabling us to determine the in‐plane and out‐of‐plane spin component. The scattering efficiency of the Mott detector is as high as 2.3 × 10-2. The optical system consists of helium (He) and xenon (Xe) plasma discharge lamps and a monochromator with the gratings, in which we can select photon energy if necessary. In this study, we used one of the Xe I lines (
2.2. Sample fabrication
To get a high‐quality Bi(1 1 1) thin film, we prepare a clean surface of the Si(1 1 1) substrate. We use a commercially available Si wafer (n‐type, As‐doped: 0.001–0.005 Ω cm, Sb‐doped: 0.01–0.02 Ω cm), and the surface of Si forms native SiO2 in the air. So we must remove it by electrical heating in high vacuum. Figure 4 displays the design of a holder for the electrical heating system (Figure 4). The holder is made of molybdenum, and a main holder is insulated from a subholder by the alumina. We can control a current and temperature with 5 mA and 1°C, respectively. The sample size is 13 × 3 mm, and we have selected four different kinds of crystal orientations on the basis of orientation flat as shown in Figure 5. The sample geometry has been confirmed by the brightness symmetry of the LEED spots. The most stable structure of the Si(1 1 1) surface is the 7 × 7 reconstructed surface, as shown in Figure 6a [31, 32]. Now, we describe the method to prepare a Si(1 1 1)‐7 × 7 reconstructed surface. First, the Si wafers were outgassed for more than 12 h below 750°C. After the outgassing enough, we have carried out flash annealing. Figure 6b shows a flash‐annealing process to get a Si(1 11)‐7 × 7 reconstructed surface; sample was (i) heated at 750°C to 1050–1200°C for a few seconds, (ii) keep temperature to maximum for 5 s, (iii) cooled down to 850°C for a few seconds and (iv) cooled to 750°C in 30 s [33]. We have repeated this cycle, and all of the above processes should be performed under the ultra‐high vacuum of ~1 × 10-10 Torr. As shown in Figure 7a, we have obtained the LEED pattern of the well‐ordered 7 × 7 surface.
Next, Bi atoms are evaporated on Si substrate, which is called as a molecular beam epitaxy (MBE). Bi atoms are deposited at room temperature on Si(1 1 1)‐7 × 7 reconstructed surface. Then, the Bi thin film was annealed at 150°C. The deposition rate is estimated by the quartz oscillator thickness monitor, and the film thickness was controlled by varying the deposition time with keeping the constant deposition rate. We can also estimate the film thickness from the energy position of the quantum well states (QWSs) in the ARPES spectra [28]. It is noted that 1 bilayer (BL) Bi is defined as 1.14 × 1015 atoms/cm2, and the thickness is 0.39 nm [13]. In this study, we prepared several thickness sample (8–40 BL). After the deposition of Bi atoms, the LEED pattern shows the 1 × 1 surface structure as shown in Figure 7b and c, and the intensity of the LEED spot has threefold symmetry. When the sample has a multi‐domain structure, the LEED pattern shows circular features surrounding the 1 × 1 spots (Figure 7d). We could repeatedly use one Si substrate by a flashing. Here we describe a structure of Bi thin film on Si substrate. Details of the thin‐film growth process are shown in Figure 8a, which is reported in previous works such as STM and LEED [34]. Although the lattice constant of Bi (4.538 Å) is very different from Si (5.43 Å), it is possible to fabricate the Bi/Si thin film due to the existence of disordered layer called “wetting layer” between Bi and Si substrate. As shown in Figure 8b, the structural transition from {0 1 2} direction to (1 1 1) direction more than 8.4 ML suddenly takes place upon Bi deposition.
3. Results and discussion
3.1. Anisotropic Rashba effect of Bi thin film
At first, we have performed normal (non–spin‐resolved) ARPES measurement of the Bi thin film in order to check the sample quality and geometry, since even a subtle misalignment of the sample orientation would cause a significant error in determining the spin polarization. Figure 9a and b shows the band dispersion along the
This section focuses on the spin structure of the S2 band. In a conventional 2D Rashba model, the in‐plane spin has a vortical structure and isotropic magnitude as denoted by black arrows in Figure 10a. In Figure 10b and
First, we take a closer look at the spin polarization in regions A–D. In regions A and B, as seen in Figure 10b, the in‐plane spin polarization of the S2 band is dominated by the up spin. On the other hand, the down spin is barely superior in regions C and D. It means that the in‐plane spin structure is qualitatively consistent with the Rashba picture [13–14]. However, it seems that the spin polarization is markedly suppressed in C and D. In fact, the magnitude of the spin polarization along the
We have also observed a finite in‐plane and out‐of‐plane spin polarization in regions E–H. As shown in Figure 10c, the estimated maximum |
The data in regions I and J are also the same trend as shown in Figure 10d. The difference in |
Figure 11 shows a schematical view of the spin polarization vectors of the S2 band from Figure 10. We symmetrized the data by taking into account the threefold crystal symmetry due to the presence of a second bismuth layer. The in‐plane spin component has a vortical structure, but the magnitude of the spin polarization is perpendicular to
3.2. Rashba effect at interface of a Bi Thin film on Si(1 1 1)
In this section, we focus on the spin structure around the
In conventional Rashba picture, the in‐plane spin polarization of the S3 band is dominated by the up spin independently of a thickness at the cut 1 shown in Figure 12b. Figure 12c shows the spin‐resolved EDCs and spin polarization of
We discuss the physical mechanism behind the unusual thickness dependence of
3.3. 1D edge state with Rashba effect in Bi thin film
As observed by the atomic force microscopy of our Bi thin film (Figure 14), triangular‐shaped Bi BL islands with typically ~0.1 μm edge length are formed on the top surface of the Bi thin film as reported previously [34], and the edge of each island is perpendicular to the
We demonstrate the band dispersion of Bi thin film along the
As for the origin of the unexpected 1D state, we have taken into account various possibilities such as the mixture of domains with different film thickness, surface reconstruction, slight isolation of the topmost Bi bilayer and surface stacking faults. A most natural and convincing explanation is that it originates from the edge states of Bi bilayer. To further strengthen our conclusion, we have carried out first‐principles electronic band structure calculations for a specific crystal structure (Figure 16). Electronic band structure calculations were carried out by means of a first‐principles density functional theory approach with the all‐electron full‐potential linearized augmented‐plane‐wave method in the scalar relativistic scheme. The spin‐orbit coupling was included as the second variation in the self‐consistent‐field iterations. Thin‐film systems were simulated by adopting periodic slab models with sufficiently thick vacuum layer. In this model, Bi atoms in 1D allay are removed from the topmost Bi 1BL (Figure 16a) so as to reproduce the infinitely long edge structure along the
4. Conclusions
We have demonstrated anomalous Rashba effect of Bi thin film on Si(1 1 1) by using spin‐resolved ARPES. Major findings of the present work are the following three features: (i) the surface Rashba states of Bi exhibit the asymmetric in‐plane spin polarization and the giant out‐of‐plane spin polarization, (ii) the spin polarization of the surface states is reduced on decreasing thickness and (iii) 1D band dispersion from the edge state of Bi islands on Si(1 1 1) exhibits large Rashba effect. These observed peculiar spin states are not explained in terms of the conventional Rashba effect, and these results open a pathway for realizing exotic physical properties at the strong SOC systems.
Acknowledgments
This study is a collaborative research with Prof. Takahashi, Associate Prof. Sato and Associate Prof. Souma in Tohoku University and Prof. Oguchi in Osaka University. We thank K. Sugawara and K. Kosaka for his assistance in the ARPES experiment. This work was supported by JSPS, MEXT of Japan and the Mitsubishi foundation.
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