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Abstract
Electrically generated spin accumulation due to the spin Hall effect of Pt/GaAs is detected by circular polarized photoconductivity (CPPC), which shows electron spins with different polarizations accumulated around opposite sample boundaries. An optical absorption model incorporating spin is used to explain these features. The detailed analysis of the observed degree of circular polarization of the photocurrent strongly suggests that Pt and GaAs have the same spin accumulation length in the Pt/GaAs heterostructure.
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1. Introduction
The spin Hall effect (SHE) can generate spin currents in the absence of magnetic fields, driven by spin-orbit coupling or spin-dependent scattering. The detection and study of spin accumulation created by the SHE are related to a deeper understanding of the physical model of the SHE, and they are also important prerequisites for the preparation of spin-based devices with better performance.
Spin accumulation has been theoretically and experimentally studied in various materials, including magnetic materials, semiconductors, and metals [1–3]. Under various physical models and different boundary conditions, many theories have suggested that electron spins with opposite polarization directions accumulate around opposite edges of samples [4,5]. Research on SHE on metallic materials is mainly achieved by combining SHE and inverse SHE and using electrical methods to inject spin-polarized carriers into the metal [6,7]. For semiconductors, optical methods are also widely used in the research of SHE and spin diffusion, including Kerr rotation, Faraday rotation, ultrafast transient spin grating, magneto-optical Kerr effect, and spin density spin grating [8–11]. Drift-diffusion models based on space-resolved optical measurements have been used to explain these experimental results [8,9]. Among these, precise optical experiments and extremely low temperatures are indispensable. However, circularly polarized light can detect spin at room temperature [12,13]. The CPPC used in this research provides a simple optical method for studying the spin Hall effect at room temperature. In addition, the distribution of spin accumulation in the heterostructures of metals and semiconductors remains a problem. Experimentally, the edge asymmetry of the semiconductor may cause additional spin carriers [14]. Therefore, the problem of how to distinguish the spin polarization around the edges induced by the SHE from edge signals is also a research challenge.
In this study, SHE-induced spin accumulation driven by the applied electric field in Pt was detected by CPPC in a Pt/GaAs sample at room temperature. A model was established for the absorption of circularly polarized light affected by spin accumulation. The ratio of the SHE photocurrent to the ordinary photocurrent was measured to further calculate the spin-accumulation length of Pt. The study of the edge accumulation of spin-polarized carriers not only contributes to the development of spin electronics, but also helps to better apply the SHE to the preparation of electronic devices.
2. Experimental details
As shown in Fig. 1(a), the electron spins accumulated around the edges are introduced by an electric field and can be measured using CPPC. When an electric field is applied to the electrodes and the electrons along the x-direction, for the existence of SHE, the spin-up and spin-down (with respect to the z-axis) electrons move in the opposite direction of the y-axis. Thus, electrons with opposite spin directions accumulate on the opposite sides of the sample. The accumulated electron spins can induce a difference in the absorption of right-handed circularly polarized light (σ+) and left-handed circularly polarized light (σ-), which can further lead to the difference in the photoconduction of σ+ and σ-, namely, CPPC.
Fig. 1. (a) The schematic diagram of SHE. The origin is defined to be at the center of the Pt/GaAs sample. We set the x-axis and y-axis to be parallel to the length and width of the sample, respectively, and the z-axis to be parallel to the [001] crystal direction. When an external electric field along the x-axis is applied to the sample, for the existence of SHE, electron spins (yellow balls) with spin-up and spin-down (with respect to the z-axis) accumulate around the opposite edges (y = ±1.5 mm). The yellow arrows indicate the polarization direction of electron spins. (b)The schematic of the measurement geometry. The light blue and dark blue cubes indicate the Pt layer and GaAs substrate, respectively. Two stripe electrodes are attached to the sample to measure the photoconductivity. A laser with a wavelength of 900 nm was vertically incident on the sample after modulated by a chopper, a polarizer, and a PEM.
The sample discussed in this manuscript was fabricated from a Pt/GaAs heterostructure with 5 nm thick Pt, which was grown by molecular beam epitaxy on a (001) semi-insulating GaAs wafer with a 1 μm undoped GaAs buffer. The Pt/GaAs sample had a length of 10 mm and a width of 3 mm, and it was cut along the GaAs [110] crystal directions. A pair of ohmic contacts were made by indium and annealed at 420 °C for 12 min [Fig. 1(b)]. In our CPPC experiment, different electric fields were applied to the ohmic contacts to generate and measure the accumulated electron spins around the edges. We used a photoelastic modulator (PEM) to periodically change the light from linear polarization to σ+ and σ-. The Gaussian-distributed beam with a 900 nm wavelength and a 0.8 mm diameter is a normal incident to the sample after passing through a polarizer and a PEM. A lock-in amplifier operating at the frequency of the PEM was used to acquire the signals generated by the circularly polarized light, which are referred to as circular polarized photocurrents in this study. Additionally, an optical chopper was inserted into the optical path, and a lock-in amplifier operating at the same frequency as the optical chopper gathered polarization-independent ordinary photocurrent. The sample was placed on a motorized translation stage to study the dependence of the photocurrents on the light spot positions.
3. Results and discussion
The spatially circular polarized photocurrents along the y-direction were measured when different levels of electric fields were applied to Pt/GaAs, as shown in Fig. 2(a). The electric-field-dependent circular polarized photocurrents can be divided into two parts - a linear function and a square function of the electric field. Circular polarized photocurrents, which are linear with the electric field, exist in both the bulk and edges of Pt/GaAs, and reach the maximum at the edges. However, the component of circular polarized photocurrents, in which the square of the electric field only exists around the edges of the sample, is negligible in the bulk. In the following, we would show that these signals are derived from circular dichroism and the spin Hall effect. Besides, polarization-independent thermal currents may also play a critical role in photocurrents [15]. Therefore, we measured the polarization-independent ordinary photocurrents, as shown in Fig. 2(b). The absence of edge signals in ordinary photocurrents reveals that edge signals are contributed by circularly polarized light and not yielded by thermal currents.
Fig. 2. (a) Circular polarized photocurrents of Pt/GaAs were measured as a function of light spot positions in different applied electric fields ranging from -5 V/cm to 5 V/cm. (b) The dependences of ordinary photocurrents of Pt/GaAs on light spot positions were measured when different electric fields were applied. (c) In the GaAs epilayer, circular polarized photocurrents of GaAs were measured as a function of light spot positions.
To remove GaAs signals from the circular polarized photocurrents of Pt/GaAs, the light spot position dependence of the circularly polarized photocurrent was measured in a GaAs epilayer in the presence of applied electric fields, ranging from 5 V/cm to -5 V/cm, as shown in Fig. 2(c). The circular polarized photocurrents in GaAs show a linear dependence on the applied electric field, and they reach the maximum at the edges. These features clearly indicate that the linear terms of the circularly polarized photocurrents in Pt/GaAs are contributed by the GaAs layer.
The component of the circularly polarized photocurrents linear with the electric field is related to the residual stress in the GaAs epilayer, which cannot be avoided during the growth process [16,17]. The stress along the [100] crystal direction can break the mirror symmetry (σx and σy), and hence cause circular dichroism for light incident along the [001] crystal direction [18]. It is expected that stress-induced circular dichroism will be amplified around the edges of the sample, because the symmetry will be further decreased with the existence of the surface. [19]. Owing to circular dichroism, the concentrations of carriers generated by σ+ and σ- in GaAs are different. This circular-dichroism-related CPPC did not vary with the applied electric field. Thus, in the presence of an applied electric field, the circularly-polarized-light-induced carriers generate a circular polarized photocurrent proportional to the electric field in GaAs.
In Fig. 3(a), we show the SHE-induced circular polarized photocurrents (ISHE) of Pt/GaAs obtained by subtracting the part that was linear with the electric field from the total circular polarized photocurrents. Because of the Gaussian distribution of the light spot intensity, the dependence of the ISHE on the light spot positions is also Gaussian profiles. To describe the ISHE, an optical absorption model incorporating spin was established. Compared to Pt, the spin carriers in GaAs are negligible because the spin Hall angle and carrier concentration of GaAs are far less than those of Pt. It is reasonable to assume that all the spin carriers originate from the SHE of Pt. In the Pt layer, owing to the SHE, electron spins with opposite orientations accumulate around opposite edges, whose concentrations are proportional to the applied electric field. The accumulated electron spins cause differences between the transmittances of σ+ and σ-, which are proportional to the concentrations of accumulated electron spins. For GaAs, circularly polarized light excites photoelectrons in GaAs after being partly absorbed by the Pt layer, so the differences in the photoelectrons between σ+ and σ- show linear dependences on the concentrations of electron spins accumulated around the edges of Pt and the electric fields. Hence, in the presence of an electric field, the difference in the photocurrent generated in GaAs between σ+ and σ- relates to the square of the electric field, which is ISHE. Figure 3(a) shows that the circular polarized photocurrents have opposite signs around opposite edges, which agrees with the characteristic of SHE that spin-up and spin-down electron spins move in opposite directions. The dependence of the ISHE at the edges on electric fields is explicitly shown in Fig. 3(b), which is proportional to the square of the electric field.
Fig. 3. (a) The dependence of the ISHE on the light positions was measured in the presence of various electric fields ranging from -5 V to 5 V. (b) The ISHE at the edges (y = ±1.5 mm) was measured as a function of the electric field in Pt/GaAs.
Some spin-related effects were ruled out from the ISHE, including the circular photogalvanic effect (CPGE) and photoinduced SHE. When circularly polarized light is normally incident, because of the symmetry of GaAs, CPGE does not contribute to the spin photocurrent [20]. Photoinduced SHE is that the accumulated electron spins are generated by circularly polarized light and then driven by SHE, instead of electron spins generated by the applied electric field because of SHE. If there is photoinduced SHE in our experiment, the ISHE would show a quadratic dependence on the power of circularly polarized light. Because circularly polarized light yields photogenerated electron spins, which will further affect the absorptivity of circular polarized light. To exclude the influence of the photoinduced SHE, the dependence of the ISHE on light powers was measured in the presence of a 5 V applied voltage, as shown in Fig. 4(a). The circular polarized photocurrents increased linearly with increasing optical power when the optical power was less than 70 mW. Then, the increasing tendency slowed down until reaching saturation. Due to the absence of the squared term in Fig. 4(a), we confirm that the electron spins originate from the applied electric field.
Fig. 4. (a) The light power dependences of the ISHE were measured at the edges of Pt/GaAs. (b) The electron spins in Pt result in different absorption of σ+ (the orange area) and σ- (the area surrounded by dashed line).
The optical absorption model incorporating the spin is elaborated here. Because of SHE, spin-up and spin-down electron spins accumulate on the opposite edges of Pt in the y-direction. As shown in Fig. 4(b), spin accumulation contributes to the transmittance difference between σ+ and σ-, according to optical transition selection rules and conservation of angular momentum. The Drude-like equations are used to describe the absorption of circularly polarized light. In the Pt layer, for one of the edges, the absorption coefficients of σ+ and σ- are given by $\alpha _{Pt}^ \pm{=} A\sqrt {({n \pm {n^z}} )}$ with $A = 2e\textrm{/}\left( {\textrm{c}\sqrt {{\varepsilon_{Pt0}}{m_{Pt}}} } \right)$, where n is the electron concentration of Pt, nz is the concentration of electron spins accumulated around the edge of Pt, c is the speed of light, ${\varepsilon _{Pt0}}$ is the dielectric constant of Pt, and mPt is the mass of Pt [21]. Hereafter, the transmittances of σ+ and σ- are given by $T_{Pt}^ \pm{=} {e^{ - \alpha _{Pt}^ \pm d}}$, where d is the thickness of the Pt film. Finally, the difference in transmittance between σ+ and σ- can be written as $\varDelta {T_{Pt}} = T_{Pt}^ -{-} T_{Pt}^ +{=} {e^{ - dA\sqrt n }}{n^z}dA/\sqrt n$, assuming ${n^z} \ll n$ for Pt. Note that the factor ${e^{ - dA\sqrt n }}$ is just the ordinary light transmittance of Pt, i.e., ${T_{Pt}} = {e^{ - {\alpha _{Pt}}d}} = {e^{ - dA\sqrt n }}$. One further has $\varDelta {T_{Pt}}/{T_{Pt}} = d{\alpha _{Pt}}{n^z}/n$. Clearly, the transmittance difference is proportional to the concentration of electron spins accumulated around the edge. For the other edge, the above analysis can be established with the nz changing signs.
The transmittance difference between σ+ and σ- causes a difference in the photocurrent excited in GaAs. The difference between the carrier concentration generated by σ+ and σ- in GaAs is $\Delta {n_{GaAs}} = {\alpha _{GaAs}}\varDelta {T_{Pt}}{I_0}\tau$, where I0 is the light intensity on the surface of Pt, and τ is the lifetime of the photoelectrons. When the electric field E is applied to the sample, this absorption difference leads to the SHE current density, given by ${j_{SHE}} = \Delta {n_{GaAs}}e\mu E$. Similarly, the ordinary current density is $j = {n_{GaAs}}e\mu E$, with ${n_{GaAs}} = {\alpha _{GaAs}}{T_{Pt}}{I_0}\tau$, which is a linear function of E.
To further discuss the polarizability of the electron spins nz/n, we introduce the ratio of the SHE-related photocurrent ISHE to the ordinary photocurrent, which is defined as the degree of circular polarization (DCP) of the photocurrent. For a 5 V/cm applied electric field, the DCP reaches the maximum ±0.0005 at the edges of the sample, as shown in Fig. 5.
Fig. 5. The dependence of DCP on light spot positions was measured when a 5 V/cm electric field was applied to the Pt/GaAs sample.
According to phenomenological theory, the electron concentration nz with spin polarization parallel to the z-axis generated by the SHE in the Pt film can be described as [22]
The diameter of the light spot (0.8 mm) is far larger than LPt (in the range of micrometers or less), so the distribution of light intensity must be considered. Assuming a Gaussian distribution for the incident light intensity, the total ISHE and ordinary photocurrent I can be directly calculated by the integral of nz over the illuminated area. Noting that LPt is much smaller than the light spot. Thus, the variations in the ISHE (shown in Fig. 3(a)) and ordinary photocurrent (shown in Fig. 2(b)) with y reflect the actual intensity distribution of the light and the distribution of electron spins. The DCP for the spot at the edges is given by
For 900 nm incident light, the reported extinction coefficient k of Pt is 5 to 9.2 [23,24]. With the absorption $\alpha = 4\pi k/\lambda$ and d = 5 nm, αPtd is estimated to range from 0.35 to 0.64. Taking k0T = 0.026 eV, γ=0.08 [25], r = 0.4 mm, E = 5 V/cm, and DCP = 0.0005, LPt can be calculated from Eq. (2) and (3), which varies from 19 μm for αPtd = 0.35 to 14 μm for αPtd = 0.64. LPt is significantly larger than the spin diffusion length of the Pt film (ranging from 1 nm to 10 nm) [26]. This can be reasonably attributed to the proximity effect of the Pt/GaAs heterostructure, which means that the wave function of the electrons in Pt can penetrate GaAs, or vice versa. Regardless of the case, the electron spins in the ultrathin Pt layer are affected by GaAs and behave to some extent, similar to the electron spins in GaAs. Generally, spin accumulation in GaAs is mainly due to spin diffusion and spin drift. The spin diffusion length ranges from 9 μm to 15 μm in n-type GaAs, measured with Kerr rotation at 10 K to 60 K [8,9,27,28], and it is more than 450 nm in semi-insulating GaAs, measured with an ultrafast transient spin grating at 15 K to 150 K [10]. Spin drift can cause spins to accumulate within 40 μm around the edges at 30 K [29]. In this research, the spin accumulation may be due not only to spin diffusion and drift but also to other effects, such as spin-orbit couplings induced by the Pt/GaAs interface and the reduction of the symmetry of the edge of the sample. The coexistence of Dresselhaus and Rashba spin-orbit couplings could extend the spin diffusion length, and even lead to infinite spin diffusion length [30], so the additional spin-orbit couplings may cause the electron spins around edges to have much longer accumulation lengths than the original spin diffusion lengths of Pt and GaAs. Thus, in this case, spins accumulate within a dozen micrometers around the GaAs edges of the Pt/GaAs sample. In our experiment, Pt and GaAs have similar spin accumulation lengths, which range from approximately 14 μm to 19 μm. However, the mechanism still requires further experimental and theoretical investigation.
4. Conclusion
In summary, the spin accumulation of Pt induced by the SHE was detected by optical measurements and separated from other edge signals. The optical absorption model with spin factors agrees with the spatial profiles of the accumulation. Furthermore, these measurements demonstrate that Pt and GaAs have similar spin accumulation lengths because of the spin diffusion between Pt and GaAs. This practical approach paves the way for optically exploring SHE in metals. The results can also be used as a reference for spin device preparation, especially for spin accumulation around the edges.
Funding
National Natural Science Foundation of China (61474114, 61991431); National Key Research and Development Program of China (2018YFA0209103).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available in Ref. [23–25].
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