Bismuth induced enhancement of Rashba spin–orbit interaction in GaAsBi/GaAs heterostructures

Spin–orbit interaction (SOI) is of great interest in spintronics research because its role as an intermediary between spin and electric fields underlies various phenomena that are potentially useful for exploring new physics¹ and developing new applications.² Semiconductor heterostructures that host two-dimensional (2D) electrons have been used as basic platforms for spin manipulation using SOIs. This is because such platforms enable application of a vertical electric field to induce SOIs while keeping the electrons confined in the 2D channels. The electrons moving in the channels are affected by the effective magnetic field generated by the SOIs, enabling modulation of their spin dynamics by applying an external gate voltage^3–5 or by controlling the electron motion^6,7 even in the absence of external magnetic fields. Since these spins evolve on a timescale of the rate characterized by a precession frequency proportional to the SOI strength, finding a way to obtain stronger SOIs has become a key issue for applications that need to manipulate spins more quickly in smaller areas.

The strength of the SOI depends on the material, and, in particular, the mass of the constituent atoms is one of the factors linked to SOI strength. When we focus on the nanoscale structures of semiconductors, the local electric fields produced by the nucleus vary spatially on the scale of the lattice constants. These local electric fields are a direct cause of the SOIs due to the bulk crystal inversion asymmetry and/or the interface inversion asymmetry at heterointerfaces.⁸ Atoms with a higher atomic number have more positive charges in their nuclei and, thus, can generate larger electric fields and stronger SOIs. Therefore, the idea of introducing heavy elements into conventional semiconductor materials, which generally consist of light elements, is attractive because of their ability to yield stronger SOIs for the carriers.

Bismuth (Bi), a heavy element with an atomic number of 83, is promising for enhancing SOIs in semiconductors as it can form alloy semiconductors with group III–V semiconductors.⁹ A typical semiconductor bismide, GaAs_1–xBi_x, has been investigated¹⁰ for use in optical devices, in which the incorporation of a small fraction of Bi reduces the bandgap energy dramatically,¹¹ while it ensures the stability of the bandgap energy against temperature changes.⁹ Similar Bi-induced band modification appears in the spin split-off energy Δ_SO¹² as well; the giant p-state SOI in Bi atoms should induce a large Δ_SO for GaBi,¹³ and the hybridization of the GaAs valence band and Bi-related localized state results in a substantial bowing effect for Δ_SO in GaAsBi as well.¹¹ Thus, incorporating Bi into GaAs-based heterostructures should lead to efficient spin-control technologies that take advantage of both Bi-induced strong SOIs and the tunability of spin–orbit effective magnetic fields for the 2D electrons in semiconductor channels.

Here, we investigated the effect of Bi incorporation into GaAs heterostructures on the enhancement of SOI. Optical measurements revealed momentum dependence of the spin–orbit effective magnetic fields experienced by electrons diffusing in an epitaxially grown GaAsBi thin film. We found that the SOIs in this system were dominated by the Rashba-type momentum dependence; that is, the effective magnetic field was always perpendicular to the momentum vector. Theoretical analysis of the SOI parameters suggests that the spatial inversion asymmetry at the interface between the GaAsBi and GaAs cap layers is the main factor in the enhancement of the Rashba SOI. Our findings provide deeper insight into the effect of the SOIs resulting from incorporating heavy atoms into semiconductor heterostructures.

We performed time- and spatially resolved magneto-optic Kerr rotation measurements on a GaAs_0.961Bi_0.039/GaAs quantum well (QW). The sample was grown on a p-GaAs (001) substrate by low-temperature molecular beam epitaxy. It consisted of a 140-nm-thick GaAs buffer, a nominally undoped 71-nm-thick GaAs_0.961Bi_0.039 QW, and a 6-nm-thick GaAs cap. We expected that the Bi cluster formation in the GaAsBi layer was sufficiently suppressed,^14,15 and Kerr rotation results shown later mainly reflect the band structure of the GaAsBi material in which Bi atoms are uniformly incorporated. The spatial distribution and time dependence of the electron spins in an external magnetic field (B_ext) parallel to the sample plane were measured by scanning Kerr rotation microscopy at 13 K with a mode-locked Ti:sapphire laser, which generated 100-fs pulses. We used a wavelength of 955 nm for both the pump and probe beams because the Kerr rotation signal reached its maximum at this wavelength. The full-widths at half maximum of the focused pump and probe lasers were 14 and 3 μm, respectively. Spin-polarized electrons were generated with circularly polarized pump pulses, and the subsequent spin density dynamics was measured using a linearly polarized probe pulses via the Kerr rotation angle θ_K.

The effect of the SOIs in the conduction band appears in the spin precession dynamics of photo-injected electrons that travel to distant positions due to diffusion. Figure 1(a) plots time-resolved Kerr rotation signals observed under an external magnetic field of 0.3 T. The pump laser position was fixed at the origin, the probe was set at three different positions on the x (ǁ $1 1 ¯ 0$⁠) axis, and B_ext was applied in the y (ǁ[110]) direction. All the data show similar oscillatory and decaying time-dependent Kerr rotation signals, which represent the typical precession dynamics of photo-injected electron spins in semiconductors. The Kerr rotation signal for x = 0 μm decayed with a time constant of 0.36 ns and oscillated at 4.44 GHz. This spin precession frequency corresponds to an electron g-factor of 1.06, which is close to the 1.2 estimated for GaAs_1−xBi_x (x = 3.83%) by time-resolved PL measurement at T = 200 K,¹⁶ indicating that the spin of excess electrons generated by optical doping¹⁷ determined the Kerr rotation dynamics. When the probe laser spot was set at x = 5 μm (−5 μm), the Kerr rotation oscillation was slower (faster) than that at the origin, indicating that the time-averaged effective magnetic field that had been acting on electrons arriving at the probe position by diffusion was in the same direction as (opposite direction to) B_ext [Fig. 1(c)].¹⁸ On the other hand, regardless of the position of the probe laser spot in the y direction, the period of the Kerr rotation oscillation was constant, as shown in Fig. 1(b). The probe position dependence of the precession frequency, thus, contains information about the direction and magnitude of the effective magnetic field vectors.

We further performed the same measurement with the application of B_ext in the $−$x direction and plotted the extracted $d ω so/dr$ values as functions of the scanning direction angle from the x axis [Fig. 2(i)]. As discussed elsewhere,¹⁸ the value of $d ω so d r$ measured in B_ext applied along the x(y) direction is proportional to the x(y)-component of the effective magnetic fields acting on the electrons moving in the direction of r. Thus, the parameters plotted in Fig. 2(i) enabled us to obtain the two-dimensional configuration of the effective magnetic field vectors in momentum space. The reproduced effective magnetic field vectors [shown in Fig. 2(j)] are clearly consistent with the symmetry of the Rashba SOI field, $B R∝ k y , − k x$⁠, rather than the Dresselhaus SOI field, $B D∝ − k y , − k x$⁠, where $k= ( k x, k y)$ is the in-plane wavenumber of electrons.

The pump power dependences of the aforementioned parameters agree with the inference that the Rashba SOI was dominant in our sample. The spatiotemporal mapping of the Kerr rotation signal for several pump intensities and the extracted parameters is shown in Fig. 3. Figures 3(a) and 3(b) show that D_s increases and τ_s decreases with increasing P_pump, whereas Fig. 3(c) shows that $d ω so d r$ does not change much for both scanning directions. By substituting the obtained fitting parameters into Eq. (2), we found that Rashba SOI parameter α decreases monotonically as P_pump increases [Fig. 3(d)]. We attribute this to that the screening of the built-in potential¹⁷ by the excess photoexcited carriers suppresses the potential gradient in the GaAsBi QW and consequently reduces the Rashba effect. In contrast, Dresselhaus SOI parameter β remained small regardless of the pump intensity.

To examine the validity of these results, we calculated the SOI parameters theoretically. We first calculated the energy band diagram of the present heterostructure. We used the band-anti-crossing model,²² which gives the Γ point energies of GaAs and GaAs_0.961Bi_0.039 (conduction band Γ_6c, valence band Γ_8v, and spin split-off band Γ_7v) and their band offsets at the heterointerfaces. As discussed earlier, we infer that the built-in potential gradient responsible for the Rashba SOI is reduced when the carriers are excited with a higher pump power. Such tunability of the vertical electric field was incorporated into the calculation by setting a variable surface state energy (0 V < Δϕ < 1.5 V) relative to the Fermi energy of the p-type GaAs substrate; that is, increasing P_pump corresponds to decreasing Δϕ. By solving the Poisson-Shrödinger equation, we obtained the energy band diagrams for Γ_6c, Γ_8v, and Γ_7v and the probability density (|Ψ(z)|²) of the conduction band electrons confined in the GaAsBi layer, as shown in Fig. 4(a).

Our theoretical analysis of the origin of the SOI parameters suggests that as a result of an increase in the spin–orbit split-off energy due to Bi, the offset energies of the valence band and spin split-off band at the GaAsBi/GaAs interface work constructively to enhance the Rashba SOI. The SOI parameters, α and β, calculated for different Δϕ conditions are shown in Fig. 4(b). The calculated α is much larger than β under reasonable Δϕ conditions, which is consistent with the experimental results. Although field contribution (Γ_F) in Eq. (5) is enhanced by the large spin split-off energy in the GaAsBi layer, it was only 15% contribution to α. In contrast, we found that 85% of the entire contribution to α was induced by the interface contribution (Γ_In) at the boundary [indicated by the red arrow in Fig. 4(a)] between the GaAsBi layer and the GaAs cap layer.

For comparison, we also calculated the interface contribution at GaAs/Al_0.3Ga_0.7As and In_0.039Ga_0.961As/GaAs interfaces with the same layer structure and built-in potential gradient. We found that the GaAs_0.961Bi_0.039/GaAs interface generates 9.1 and 6.7 times larger contributions, respectively, to the α value than the GaAs/Al_0.3Ga_0.7As and In_0.039Ga_0.961As/GaAs interfaces. Such a large contribution is due to the sum of the effects of the valence band offset (ΔE_Γ8v = −210 meV) and the split-off band offset (ΔE_Γ7v = 17 meV) [see Eq. (6)], which is considerably larger than those of the other two heterointerfaces. Note that while the In_0.039Ga_0.961As/GaAs interface has small offset values for both bands (ΔE_Γ8v = −19 and ΔE_Γ7v = −11 meV), the GaAs/Al_0.3Ga_0.7As interface has a substantial valence band offset (ΔE_Γ8v = −150 meV), which is counteracted by the split-off band offset (ΔE_Γ7v = −134 meV). Similar calculation for the Rashba SOI in heterostructures containing GaAsBi was reported in Ref. 24 in which the field contribution in the QW is mainly discussed. We infer that this is because of the difference in barrier material and QW thickness; the AlGaAs barrier layers assumed in Ref. 24 confine the electron wave function more tightly in the thin GaAsBi QW, resulting in a smaller interface contribution. In contrast, the GaAs barriers with a thicker QW in our sample enable the electrons to more easily penetrate from the GaAsBi layer into one of the barrier layers, leading to the larger interface contribution. The resultant probability density at the interface effectively increases the interface contribution to the Rashba effective magnetic fields, which determines the spin dynamics of electrons confined in the vicinity of the interfaces. These results indicate that GaAsBi/GaAs interfaces are promising as efficient sources for introducing electrically tunable Rashba SOI.

In conclusion, we have demonstrated that the incorporation of bismuth into GaAs heterostructures enhances the Rashba SOI of electrons. Our time- and spatially resolved Kerr rotation measurements on a sample containing an epitaxially grown 70-nm-thick GaAs_0.961Bi_0.039 layer revealed that the momentum dependence of the effective magnetic field has the symmetry of the Rashba SOI rather than that of the Dresselhaus SOI. We found that the Rashba parameter α decreases with increasing pump laser intensity due to the light-induced screening of the built-in potential gradient. Our theoretical calculation of the SOI parameters suggests that the band offset at the GaAsBi/GaAs interface substantially enhances the Rashba SOI parameter. Although the GaAsBi used in this study contained only a small amount of Bi (3.9%), the α value was estimated to be one order of magnitude larger than those in conventional GaAs/Al_0.3Ga_0.7As and In_0.039Ga_0.961As/GaAs heterostructures with similar layer structures. Crystal growth technology currently enables the introduction of Bi concentrations of up to 10.4%,²⁵ which promises further enhancement of the Rashba SOI, to values surpassing those previously reported for electrons in general semiconductor heterostructures. Thus, the introduction of bismuth into semiconductor engineering creates a new avenue for spintronics applications with highly efficient control of spins via electrically tunable SOIs.

This work was supported by JSPS KAKENHI (Nos. 20H02563 and 20H05670).