Exceptional Spin‐to‐Charge Conversion in Selective Band Topology of Bi/Bi1‐xSbx with Spintronic Singularity

In this study, spin‐to‐charge conversion (SCC) of various topological materials with ferromagnet is investigated using spintronic terahertz (THz) emission spectroscopy. Compared with other topological materials, significantly large THz emission is observed for topologically nontrivial phases of Bi1‐xSbx (x > 0.2) that predominantly originates from the topological surface state. When Bi is superposed above a certain stoichiometry of Bi1‐xSbx, it plays a crucial role in generating a highly spin‐split state and enhancing the spin‐mixing conductance, resulting in colossal THz emission. This proves that improving the SCC efficiency through interface engineering is a useful strategy to design a powerful spintronic device. Collectively, this study proposes a methodology for systematically analyzing SCC efficiency or spin Hall angle using THz emission spectroscopy and offers an efficient structure for future spintronic devices.


Introduction
The field of spintronics has recently attracted significant attention because it has the potential to replace present technologies, such as Von Neumann architecture-based computers, with power-efficient magnetoresistance random-access memory-based in-memory computing systems. [1] Researchers are attempting to enhance the spin-charge interconversion efficiency as the main factor for low-power devices, which is defined as the on the Bi 2 Se 3 family has not been sufficient to overcome the limitation of the TI-based THz emitter in terms of emission intensity, a study on SCC in stack systems using stronger SCC materials is required. For low power applications, the material should have a large SH and high conductivity. However, most TIs have low conductivity, albeit with a large SH . This problem can be solved by using a Bi 1-x Sb x alloy (Bi 0.9 Sb 0.1 ), which is the first 3D TI, because it has a large SH (52) and one-order higher conductivity (> 10 5 Ω −1 m −1 ) compared with other TIs. [4] Accordingly, we characterized epitaxial Bi 1-x Sb x grown on sapphire substrate by considering x = 0 to 0.8 with a step of 0.1 and investigated its SCC efficiency using THz emission spectroscopy. [14] Because the THz emission wave originated from multiple optical effects, [15,16] extraction of the pure SCC contributions from the measured THz emission is required.
In this study, we developed a method that can perfectly separate the pure SCC and non-spintronic contributions, thus helping to evaluate SCC efficiency. Using the method, we demonstrated Bi 1-x Sb x to be the most efficient spin-to-charge converter over other TIs. Moreover, we investigated the THz emission of the Co/HM/Bi 1-x Sb x heterostructure and demonstrated considerable enhancement in the SCC efficiency. The THz emission amplitude can be increased by ≈171% compared to that of Co/Bi 0.8 Sb 0.2 when Bi 3 BL (BL represents bilayers) was inserted between Co and Bi 0.8 Sb 0.2 , which was the largest THz wave among all TI-based THz emitters. Considering no material simultane-ously exhibiting strong SCC and charge-to-spin conversion (CSC) has been reported, a strong spin-charge interconversion phenomenon was proposed as a new concept (spintronic singularity). We identified that only Bi 3 BL /Bi 0.8 Sb 0.2 exhibited such singularity. The increased THz emission demonstrates that optimizing the FM/HM/TI trilayer can have implications in the development of powerful spintronic devices.

Results and Discussion
Because SCC can be detected as THz emission by ultrafast SCC dynamics between FM and topological materials or HM, [3,14,17,18] THz emission spectroscopy can be used to directly measure the SCC and qualitatively compare its efficiency. Although there are non-spintronic origins that radiate THz waves, we can successfully separate the pure SCC contributions and non-spintronic contributions (such as shift current) from the measured emission spectra by varying experimental parameters (sample's azimuthal angle, optical pump polarization, etc.), as shown in Figure 1.
THz emissions of various materials were investigated in the common structure, as shown in Figure 1a, using THz emission spectroscopy (Note S1, Supporting Information). When a linearly polarized 800 nm pump laser hits the Co layer, ultrafast spin current is generated and diffused into the SCC layer. [19] This diffused spin current is converted into a transient charge current, resulting in THz radiation. The characterization details of various materials, including Bi 1-x Sb x alloy grown epitaxially on sapphire substrates using molecular beam epitaxy, are described in Note S2 (Supporting Information) and the THz emission amplitude of Co/Bi 0.8 Sb 0.2 as a function of Co thickness is presented in Note S3 (Supporting Information). Based on the saturated THz emission amplitude data at the Co 5 nm/Bi 0.8 Sb 0.2 , the Co thickness of all samples was fixed at 5 nm for variable control.
We investigated the pump polarization and sample azimuthal angle dependence of THz emission in various samples. Here, and indicate the pump polarization angle and sample azimuthal angle with arbitrary reference, respectively; = 0°points toward +x, which is orthogonal to the magnetic field fixed at −ŷ.
and dependent THz emissions of various samples are shown in Note S4 (Supporting Information). In a representative sample of Co 5 nm/Bi 0.8 Sb 0.2 10 nm (Co/Bi 0.8 Sb 0.2 ), we observe that the THz emission signals depending on and have specific symmetric characteristics, as shown in Figure 1b,c, respectively. THz emission data show characteristic dependencies on with a twofold symmetric signal and on with a one-fold symmetric signal. Thus far, the dependence on and in THz emission was considered only for the shift current mechanism, which arises from inversion symmetry breaking. [14,16] However, recently, other nonlinear optical effects for which the THz emission shows unique dependence on and have been reported. [14,20,21] As various contributions from non-spintronic effects are included in the THz emission spectra, a pure SCC signal must be extracted from the spectra to investigate the SCC efficiency. To extract a pure SCC signal, we conceived an elaborate method considering Equation (2), which describes the contribution of each effect to the total THz waveform and its dependence on and . We denote the THz waveform as E( , ) and THz amplitude as A( , ) henceforth.
In Equation (2), we considered both the shift current and other non-linear effects represented as general sinusoidal functions with different periods. Using the properties of the sinusoidal function, we can use Equation (3) to extract the pure SCC contributions, i.e., all non-spintronic effects that generate THz emission hitherto known (even unreported) can be completely separated. More details about Equation (3) are developed in Note S5 (Supporting Information) with mathematical descriptions.
The pure SCC contribution, as shown in Figure 1c, extracted using this method is represented by a constant term, as expected. Henceforth, pure SCC signals of all samples extracted using the above method are denoted as "pure SCC." In the case of SCC dominant THz emission, the THz signal should exhibit a one-fold sinusoidal function with respect to the magnetic field angle Φ, where Φ = 0°points toward +x. In other words, as we fixed and to 0°to investigate the Φ de-pendence, the THz waveform should follow the condition: E( , )∝sinΦ. [9,14,17] As shown in Figure 1d (and the inset for the magnetic field dependence of THz emission), the THz emission in Co/Bi 0.8 Sb 0.2 clearly shows a one-fold symmetry with respect to Φ, and the polarity of the signal is fully reversed when the magnetic field angle is rotated by 180°, indicating that the SCC is predominantly responsible for the THz emission in this system.
To compare the SCC of various materials, THz emission spectroscopy was performed. First, THz emission in the structure of AlO x 2 nm/Co 5 nm/SCC layer (Co/TI) was investigated. As shown in Figure 2a, the pure SCC signals extracted from the full THz emission spectra in several materials confirm that the emission intensity of Co/Bi 0.8 Sb 0.2 is stronger than that of other widely researched TIs (Bi 2 Se 3 family). Moreover, the THz emission data in Co/Pt 6 nm and commercial ZnTe 1 mm (Note S6, Supporting Information) indicate that Co/TIs used in this experiment show reliable THz emission characteristics, which is consistent with previously reported data. [3,9,11,14,17,18] Consequently, the THz emission of Co/Bi 0.8 Sb 0.2 is superior to that of other TIs and HM. The THz emission of Co/Bi 0.8 Sb 0.2 is ≈2.5 times greater than that of Co/Sb 2 Te 3 , 2 times greater than that of Co/Bi 2 Se 3 , and 1.5 times greater than that of Co/Pt 6 nm and Co/Bi 2 Te 3.
In particular, we observed that SCC efficiency can be effectively increased or tuned in with the Co 5 nm/HM/Bi 1-x Sb x 10 nm (Co/HM/Bi 1-x Sb x ) heterostructure. This increment is significant compared with that obtained using the hybrid state of the RSS and TSS in the heterostructures of strong SOC materials (Bi and Ag) with TI (Bi 2 Se 3 and Bi 2 Te 3 ) [8][9][10] Among the several HMs (Bi, Sb, and Pt) inserted between Co and Bi 1-x Sb x , the THz emission amplitude in the case of Co/Bi/Bi 0.8 Sb 0.2 showed the best performance. Moreover, Co/Bi 3 BL /Bi 0.8 Sb 0.2 radiates a stronger THz wave than Co/Bi 7 BL /Bi 2 Te 3 (Note S7, Supporting Information). A detailed analysis for Bi insertion is illustrated in Figures 3 and 4.
To investigate the dependence of THz emission on the Bi 1-x Sb x layer, we measured the THz emission amplitude of Co/Bi 1-x Sb x as a function of the Sb concentration x and thickness of Bi 1-x Sb x , as shown in Figure 2b-d. As shown in Figure 2b, the large THz emission amplitude for x > 0.2 indicates that TSS plays a major role in generating the THz emission for Co/Bi 1-x Sb x among various other states that exist in different phases of Bi 1-x Sb x depending on x, which is consistent with the results of a previous study. [14] For example, the THz emission amplitude of Bi 0.8 Sb 0.2 and Bi 0.2 Sb 0.8 differs by ≈8%, exhibiting the TI phase and topologically non-trivial semimetal phase (which possesses TSS near the Γ point), respectively. [22] As shown in Figure 2c,d, the thickness dependence in the specific phases of Bi 1-x Sb x (x = 0.2 and x = 0.8) indicate that Co/Bi 1-x Sb x show high THz emission amplitude at the thickness of which TSS can be formed without the gap opening at the Γ point (after 9 nm). [14,23,24] Thus, THz waves are not emitted when Bi 1-x Sb x is thinner than a certain thickness where hybridization of the bottom and top TSS occurs, which is consistent with the TSS dominant THz emission in Co/Bi 1-x Sb x . [14] Therefore, we chose Bi 1-x Sb x 10 nm (with x = 0.2 and 0.8) to investigate SCC in Bi 1-x Sb x or HM/Bi 1-x Sb x : 1) to ensure THz emission from Bi 1-x Sb x with non-hybridized TSS, 2) to exclude the effect of increase in the thickness in HM/Bi 1-x Sb x , and 3) to ensure easy comparison with references. The dependence of THz emission in Co/Bi 1-x Sb x on a thickness up to 15 nm is described more in detail in Note S8.2 (Supporting Information). In addition, the pump power dependence of THz emission in Co/Bi 1-x Sb x (with x = 0.2 and 0.8), and Co/Bi 3 BL /Bi 0.8 Sb 0.2 is illustrated in Figure S12 (Supporting Information); the THz emission of all samples is investigated in the linear region of the pump power.
To determine the tunability of SCC efficiency obtained by inserted HM, we measured the THz emission of Co/HM/Bi 1-x Sb x as a function of the HM thickness. We selected two different phases of Bi 1-x Sb x 10 nm in the structure of Co/HM/Bi 1-x Sb x , Bi 0.8 Sb 0.2 (TI) and Bi 0.2 Sb 0.8 (topologically non-trivial SM), because these two phases show near equivalent THz emissions but have slightly different band structures. [25][26][27] The Bi insertion as an HM successfully enhances SCC, as shown in Figure 3, while other HM insertions decrease it (Note S11, Supporting Information). As shown in Figure 3a,b, when the inserted Bi has a thickness of 3 BL in Co/Bi n BL /Bi 0.8 Sb 0.2 , the THz emission amplitude increases by approximately a factor of 1.71. This is the maximum THz emission amplitude obtained in this study. The THz emission amplitude then gradually decreases with the increasing thickness of Bi. However, when Bi is inserted between Co and Bi 0.2 Sb 0.8 , the THz emission does not show a considerable increment compared with the case with Bi 0.8 Sb 0.2 , as shown in Figure 3c,d.
As we eliminate the non-spintronic THz signal for all samples, only spin-dependent factors are required to be analyzed to determine the increased THz emission in Co/Bi/Bi 1-x Sb x . In particular, Figure 2b demonstrates that the increased THz emission in Co/Bi/Bi 1-x Sb x is not caused by the locally increased concentration of Bi at the interface of Bi/Bi 1-x Sb x , because the THz emission amplitude decreases in Bi-rich conditions (x ≤ 0.2). Figure 2c,d demonstrate that the increased THz emission in Co/Bi/Bi 1-x Sb x is not attributed to the increased thickness of the SCC layer, Bi/Bi 1-x Sb x . Meanwhile, the increase in the THz emission amplitude caused by the HM insertion has thus far been mainly attributed to the existence of a largely spin-split state. [8,9,28] However, recently, some analyses have shown that SCC enhancement can be understood in terms of spin mixing conductance rather than the enhancement model of RSS. [29] Therefore, a rigorous study on the FM/HM/TI trilayer is required to understand the SCC enhancement.
We considered possible spintronic causes to accurately analyze the SCC enhancement. Case 1: A notable difference in the optical impedance Z( ) or generated spin currents; Case 2: Efficient spin-momentum locked state-mediated SCC efficiency enhancement; Case 3: Increase in spin transmission efficiency. First, the equation for spintronic THz emission indicates that increasing Z( ) and the generated spin current (or injected spin current) can also result in increased THz emission, as shown in the following: where Z( ) is the optical impedance, i (z) is the spin Hall angle, and j s (z, ) is injected spin current. [18] Using THz time-domain spectroscopy, as shown in Figure  S14 (Supporting Information), we confirmed that Z( ) calculated using the Tinkham formula decreased as the inserted thickness of Bi was increased for both Bi 0.8 Sb 0.2 and Bi 0.2 Sb 0.8 . [30,31] As shown in Figure S16 (Supporting Information), the saturated magnetization of Co 5 nm in Co/Bi n BL /Bi 1-x Sb x with different thicknesses of Bi can be confirmed to be equivalent as measured using a vibrating sample magnetometer (VSM), indicating that the generated spin currents between the various samples do not differ. Therefore, Case 1 can be excluded for the reason of increased THz emission amplitude.
In situ ultraviolet photoelectron spectroscopy (UPS) was performed to determine whether an intrinsic electric field can be applied perpendicularly to the interface of Bi/Bi 1-x Sb x . The work function difference between Bi/Bi 1-x Sb x and Bi 1-x Sb x indicates that an intrinsic electric field can be applied by the superposed Bi layer, as shown in Figure 4a,b. However, to confirm Case 2 with more certainty, the band structure must be considered. Based on the mechanism of SCC in Bi 1-x Sb x that was revealed recently, the S1 surface band plays a key role in SCC for Bi 1-x Sb x . [14] In order to be a non-trivial phase from the SCC point of view, the S1 band must be connecting the bulk T valence and L conduction bands, otherwise trivial phase. [14] Henceforth, the non-trivial phase is represented as a state that affects SCC, whereas the trivial phase is represented as a state that does not affect SCC.
Since we superposed Bi, which has a strong spin-orbit coupling (SOC), the occurrence of the RSS at the interface should be considered in regard to Equation (S8, Rashba Hamiltonian) and Rashba SOC (see Note S10, Supporting Information). Therefore, to figure out the band structure of Bi/Bi 1-x Sb x as a function of Sb concentration x, we conducted density functional theory (DFT) calculations on Bi 3 BL /Bi 1-x Sb x (with x = 0.25, 0.5, 0.75, and 1) by constructing a supercell (see Experimental Section). In Figure 4d-g, colors were assigned to the states according to the contribution of Bi and Bi 1-x Sb x in the band structure of Bi/Bi 1-x Sb x . The closer the color is to red (cyan), the greater the contribution of Bi (Bi 1-x Sb x ). The states in which Bi and Bi 1-x Sb x each make a 50% contribution are displayed in purple. The DFT calculations for the bulk band of Bi 1-x Sb x (with x = 0.25, 0.5, 0.75, 1) are also shown in Figure S17 (Supporting Information). First, we identified that the Rashba-type surface states of Bi (S1 and S2) exist in Bi/Bi 1-x Sb x . Interestingly, we also discovered that when a thin layer of bismuth is superposed on Bi 1-x Sb x , they exhibit an entirely different band structure compared to that of the superposition of bismuth on the Bi 2 Se 3 family, as shown in Figure 4d-g (for x = 0.5, 1, see Note S10, Supporting Information). The energy level denoted as "edge" is that of the Dirac point of the Bi 1-x Sb x bands (bottom surface), which is the minimum Fermi energy level where SCC can occur in the pristine Bi 1-x Sb x . The colored bulk L bands were imported from the bulk band calculation data in Figure S17 (Supporting Information). The band structure was strongly tuned by the Sb concentration x although DFT calculations were conducted on the fixed thickness of bismuth (3 BL). We found that the Rashba-type surface states of Bi 3 BL (which is a trivial phase individually) [14,25,32] superposed on Bi 0.75 Sb 0.25 converted into a non-trivial phase, whereas Bi 3 BL above Bi 0.25 Sb 0.75 exhibited a trivial phase.
To determine the dependence of this phase transition on the Sb concentration, we investigated the band contribution of Bi 3 BL in Bi 3 BL /Bi 1-x Sb x (with x =0.25, 0.5, 0.75, 1) (see Note S10, Supporting Information). We identified that the S1 band of Bi 3 BL forms a non-trivial phase when x is 0.25 in Bi 3 BL /Bi 1-x Sb x , and then the Rashba-type surface bands of Bi 3 BL gradually rise toward the conduction band as x increases deforming their band shape dramatically and forms a trivial phase that does not contribute to the SCC. The reason for the different band structures of Bi 3 BL depending on the Sb concentration is described in Note S10 (Supporting information). Therefore, we assume that our Bi/Bi 0.75 Sb 0.25 and Bi/Bi 0.25 Sb 0.75 calculation results correspond to Bi/Bi 0.8 Sb 0.2 and Bi/Bi 0.2 Sb 0.8 , respectively, because the interface band structure of Bi/Bi 1-x Sb x gradually varies with a consistent tendency from x =0.25 to 1.
Thus, the SCC efficiency should be investigated if the Bi layer exhibits a non-trivial phase when it is superposed on Bi 1-x Sb x . On the other hand, if the Bi layer superposed on Bi 1-x Sb x exhibits a trivial phase in terms of SCC, it does not influence SCC efficiency. Instead, it only serves to transfer spin-polarized current between Co and Bi 1-x Sb x , because Bi has a negligible SCC with a long spin diffusion length, [32,33] resulting in the exclusion of the additional effect in the analysis of Case 2. Meanwhile, since UPS measurement results confirmed that the work function decreases when Bi is superposed on Bi 1-x Sb x , the Fermi level near the interface of Bi and Bi 1-x Sb x is located at a higher energy level compared to www.advancedsciencenews.com www.afm-journal.de that of Bi 1-x Sb x . Further, we confirmed that the band structure of Bi 3 BL in Bi 3 BL /Bi 0.75 Sb 0.25 is a non-trivial phase and an electronlike Rashba-type surface state. Therefore, as shown in Figure 4e, we can exploit a more efficient spin-split band of the non-trivial phase Bi generated at the interface of Bi/Bi 0.75 Sb 0.25 because it possesses a larger Fermi velocity compared to the TSS of Bi 1-x Sb x , which is similar to the previous report. [34] On the other hand, the THz emission results upon inserting Sb and Pt, which exhibit a trivial phase between Co and Bi 1-x Sb x , [25][26][27]35,36] clearly show a decreased THz emission signal compared to that for Co/Bi 1-x Sb x (Note S11, Supporting Information).
As a result, one of the factors that improves the SCC efficiency in Bi 3 BL /Bi 0.8 Sb 0.2 is the highly efficient spin-momentum locked state: the Rashba surface state of Bi 3 BL (non-trivial phase). The DFT calculation results are consistent with the results of SCC enhancement depending on the band topology of Bi 1-x Sb x in Figure 3.
In situ X-ray photoelectron spectroscopy (XPS) was also performed on the same sample to identify the variation in the core level of chemical bonds in Bi 1-x Sb x when Bi was superposed, as shown in Figure 4c. As the Bi 4f peak of both Bi/Bi 0.8 Sb 0.2 and Bi/Bi 0.2 Sb 0.8 does not shift in contrast to that of Bi 0.8 Sb 0.2 and Bi 0.2 Sb 0.8 , respectively, the Bi superposition does not induce a core-level shift.
However, as the THz emission occurs during the decay of spinpolarized hot electrons from the conduction band to the valence band, it cannot be suggested that only the non-trivial phase of Bi contributes to the SCC enhancement. Moreover, because a new interface is generated by the inserted Bi layer, an increase in the THz emission by interface engineering is also evidence of an increase in the spin mixing conductance (G ↑↓ ), which represents spin transmission efficiency, as considered in Case 3. Thus, the Bi layer inserted in Co/Bi/Bi 1-x Sb x can play an additional role in enhancing the G ↑↓ . In contrast with the significantly enhanced G ↑↓ in the Ag/Bi 0.85 Sb 0.15 , [29] a slightly increased THz emission is observed in Bi/Bi 0.2 Sb 0.8 in our study. Ag can enhance G ↑↓ more than Bi, whereas it exhibits a trivial phase for SCC. However, since it is nearly impossible to distinguish the degree of contribution of spin-momentum locked state and G ↑↓ in the increased THz emission amplitude, it can be concluded that the increased THz emission amplitude in Co/Bi/Bi 0.8 Sb 0.2 by 171% is a collaboration of the non-trivial phase of Bi and enhanced G ↑↓ . Notably, Bi generates a highly efficient spin-momentum locked state depending on the band topology as well as increases G ↑↓ .
Finally, we qualitatively evaluate SH of the Bi 1-x Sb x family using THz emission spectroscopy. In the absence of an established methodology to evaluate SCC efficiency or SH using THz emission spectroscopy, we introduced a reasonable methodology to evaluate SH based on Equation (4). As the initially generated spin current in Co 5 nm by the pump laser is identical for each sample and SH is isotropic for the region where IREE occurs, Equation (4) can be simplified as E( )∝Z( ) · SH · J s . As shown in Figure S15 (Supporting Information), Z( ) for all samples is measured. Bi 1-x Sb x has the lowest Z( ) compared to other TIs as expected. Now, we can evaluate SH of the Bi 1-x Sb x family by comparing the amplitudes of the radiated THz wave (A) and Z( ) with that of a reference material. We used Bi 2 Se 3 and Bi 0.85 Sb 0.15 as reference because their dominant origin of spintronic THz emission is also reported to be TSS as well as Figure 5. Outstanding spin-charge interconvertor Bi 1-x Sb x family. Spintronic parameters of various materials. Various reported SH values at room temperature were used for Pt, [37] Bi 2 Te 3 , [38] Sb 2 Te 3 , [39] Bi 2 Se 3 , [7] Bi 0.85 Sb 0.15 , [6] and Bi 0.9 Sb 0.1 (012). [5] For Bi 7 BL /Bi 2 Te 3 and the Bi 1-x Sb x family, the SH values were evaluated by comparing the THz emission amplitudes and expressed as half-filled shapes. Data from Figure 2a were used for the amplitude A values. The THz emission amplitude of Bi 0.9 Sb 0.1 (012) was used for Bi 0.9 Sb 0.1 .
the Bi 1-x Sb x . Evaluation values with the parameters are listed in Table 1. For example, SH of Bi 0.8 Sb 0.2 can be evaluated as: analysis of the advantages of our method with mathematical descriptions and the evaluated SH for Bi 5 BL /Bi 0.2 Sb 0.8 are described in Note S12 (Supporting Information).
Although Bi 1-x Sb x (with x = 0.2 and 0.8) and Bi 3 BL /Bi 0.8 Sb 0.2 are expected to have SH values of at least 8.08, 11.32, and 14.13, respectively, they have the potential to exhibit a much larger value compared with the SH values evaluated using Bi 0.85 Sb 0.15 as reference. Therefore, we represented the potential based on the SH of Bi 0.85 Sb 0.15 as a colored box in Figure 5. The measured THz emission amplitude and reported (or evaluated) SH of the materials used in our study are summarized in Figure 5. The materials on the right side of the red dotted line: SH = 1 (physically significant value) can be considered as efficient charge-to-spin converters. A value of A that is 0.2 times that of commercial ZnTe 1 mm, which is a criterion for evaluating a strong bilayer THz emitter, is also considered a suitable criterion for defining an efficient spin-to-charge converter (represented by the gray dotted line). The materials lying above the gray dotted line are considered efficient spin-to-charge converters. Because this is not a clear standard as that defined by SH = 1 for SCC, the gray dotted line may be shifted using a better standard than ZnTe.
Here, we suggest the strong spin-charge interconversion phenomenon as a novel concept named the spintronic singularity, because no material simultaneously exhibiting strong SCC and CSC has been reported yet. Thus, the spintronic singularity point occurring at the intersection of the gray and red dotted lines can be a criterion to determine a strong spin-charge interconversion. Therefore, our concept has great potential in evaluat- ing the spintronic applicability of specific materials. As shown in Figure 5, only Bi 3 BL /Bi 0.8 Sb 0.2 is located at the upper right side of the singularity point, exhibiting spintronic singularity. Moreover, Bi/Bi 0.8 Sb 0.2 shows an outstanding SCC compared with Bi 1-x Sb x (x > 0.2), providing the greatest potential for spintronic applications.
As a result, further investigation on the accurate measurement of SH of the Bi 1-x Sb x family by CSC is needed. Moreover, although SH measured by SCC and CSC should ideally be the same, they do not tend to match perfectly, and studies on the correlation between them are limited. Therefore, we suggest a methodology to study the spin-charge interconversion, as presented in Note S13 (Supporting Information).

Conclusion
In this study, we investigated novel spintronic materials of the Bi 1-x Sb x family (x > 0.2) using THz emission spectroscopy, which exhibited outstanding spin-charge interconversion. In addition, we demonstrated that SCC efficiency can be greatly improved in the structure of Co/Bi/Bi 1-x Sb x , thus highlighting their potential in the development of ultra-efficient spintronic devices. We established an efficient method of obtaining spintronic THz signal by considering pure SCC contributions excluding non-spintronic contributions. In particular, since enhanced SCC in FM/HM/TI trilayers have not been studied extensively, we analyzed several possible modifications that could improve SCC in FM/HM/TI structures. We found that Bi played a significant role in generating highly efficient spin-momentum locked state as well as in increasing G ↑↓ , and an increment of 171% was observed in the THz emission of Co/Bi/Bi 0.8 Sb 0.2 compared with that of Co/Bi 0.8 Sb 0.2 . Thus, our systematic study provides directions for analyzing the spintronic characteristics of multilayer devices. Finally, we propose the strong spin-charge interconversion phenomenon as a novel concept denoted as spintronic singularity, which can be further established by studying the correlation between SCC and CSC.

Experimental Section
THz Emission Spectroscopy Set-Up: A THz emission spectroscopy setup was constructed to measure the THz waveforms in the time domain. A commercial MIRA femtosecond laser of 800 nm wavelength, 100 fs pulse width, and 100 MHz repetition rate was used to generate the THz waves.
To determine the spin polarization of the Co layer, an external magnetic field of ≈120 mT was applied (−ŷ direction) perpendicularly to the direction in which the photoconductive antenna (PCA) read the THz signal. The THz emission spectroscopy set-up is illustrated in Figure S1 (see Note S1, Supporting Information).
We used a beam splitter to separate the pump laser into two parts: one for THz generation and the other for detection. The power of the pump laser was ≈500 mW following chopping of 1 kHz. The radiated THz wave was detected by a 5-μm dipole-gap PCA composed of a GaAs substrate with 5 mW fs-laser power, and the signal was extracted by a commercial lock-in amplifier. A /2 waveplate and commercial motor were used to control the pump polarization and sample rotation angles. The /2 waveplate is located before the sample to prevent a pump power difference induced by the reflective mirror because of the polarization differences.
Sample Fabrication and Characterization: All topological materials used in this work were grown by molecular beam epitaxy (MBE) equipped with Knudsen cells at a working pressure of 3 × 10 −9 Torr. A double-side polished c-plane sapphire (0001) 750 μm substrate was used to deposit the materials. To degas out the impurities from the surface of the sapphire before deposition, the substrate was annealed at 300°C for 30 min and at 600°C for 1 h. Co 5 nm and AlO x 2 nm cappings were deposited on various samples using the E-beam evaporation method, and all processes were performed in situ without air exposure. All samples were capped with AlO x at the top of the structure to prevent the oxidation of cobalt. The notation of the capping layer is omitted for convenience when denoting specific structures.
X-ray diffraction (XRD, Rigaku Smartlab) measurements were conducted to characterize the crystal orientation and used atomic force microscopy (AFM, Park system Nx-10) to measure the surface roughness. The composition of each sample was confirmed via in situ X-ray photoelectron spectroscopy (XPS, Ulvac PHI 5000 VersaProbe).
TEM Measurement: Samples for cross-sectional high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) were prepared using a focused ion beam (FIB) system (HITACH, Ethos NX5000). FIB samples were prepared using various ranges of voltage from 30 to 3 kV to reduce the damage caused by Ga ions to the sample. FEI Double Cs-corrected Titan Themis transmission electron microscope instrument equipped with Super-X EDX detector with an X-FEG module was operated at 300 kV to acquire HAADF-STEM images.
UPS Measurement: The in situ UPS measurements were performed in an ultra-high vacuum (UHV) condition better than 1.0 × 10 −10 mbar. The UPS spectra were acquired utilizing a PHOIBOS 150 hemispherical electron analyzer (SPECS GmbH, Germany) with a monochromatic He-II (h = 40.81 eV) gas discharge photon source (FOCUS GmbH, Germany). The work function of each sample was determined by finding the slowest end of the secondary cutoff (SEC) spectrum in angle-resolved mode. A negative sample bias of −5 V was applied to obtain the SECs.
DFT Calculations: Density functional theory (DFT) calculations were performed using the Vienna Ab initio simulation package (VASP) and PBEsol functional. First, the atomic positions and lattice parameters of bulk structures containing 48 atoms of Bi, Bi 0.75 Sb 0.25 , Bi 0.5 Sb 0.5 , Bi 0.25 Sb 0.75 , and Sb were optimized using 3 × 3 × 1 k-points and a 500 eV cut-off energy until the condition of 0.01 eV/Å was satisfied. Using the optimized structures, the heterostructures of Bi 3 BL with Bi 1-x Sb x (with x = 0.25, 0.5, 0.75, and 1) containing 120 atoms were constructed (see Figure  S18, Supporting Information). To minimize interactions between layers, the length of the c-axis of the heterostructures was set to be 95 Å (the size of the vacuum slab was >40 Å). Then, the atomic positions of the heterostructures were optimized with 3 × 3× 1 k-points and a 500 eV cut-off energy until the condition of 0.01 eV/Å was satisfied. For the optimized heterostructures, electronic structures were calculated with consideration of the spin-orbit coupling (SOC) effect using 3 × 3 × 1 k-points and a 500 eV cut-off energy. To obtain the band structure, band unfolding was performed based on the effective band structures (EBS) method. [40]

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.