Topological Surface‐Dominated Spintronic THz Emission in Topologically Nontrivial Bi1− x Sb x Films

Abstract Topological materials have significant potential for spintronic applications owing to their superior spin–charge interconversion. Here, the spin‐to‐charge conversion (SCC) characteristics of epitaxial Bi1− x Sb x films is investigated across the topological phase transition by spintronic terahertz (THz) spectroscopy. An unexpected, intense spintronic THz emission is observed in the topologically nontrivial semimetal Bi1− x Sb x films, significantly greater than that of Pt and Bi2Se3, which indicates the potential of Bi1− x Sb x for spintronic applications. More importantly, the topological surface state (TSS) is observed to significantly contribute to SCC, despite the coexistence of the bulk state, which is possible via a unique ultrafast SCC process, considering the decay process of the spin‐polarized hot electrons. This means that topological material‐based spintronic devices should be fabricated in a manner that fully utilizes the TSS, not the bulk state, to maximize their performance. The results not only provide a clue for identifying the source of the giant spin Hall angle of Bi1− x Sb x , but also expand the application potential of topological materials by indicating that the optically induced spin current provides a unique method for focused‐spin injection into the TSS.

. (a) XPS spectra of 10-nm-thick Bi1-xSbx films. (b) Post-annealing temperatures (red dot) and phase diagram of Bi1-xSbx (solid line) adapted from theoretical calculation. [1]  The Sb concentration was reconfirmed using lattice parameters obtained from the (003) peak position with Vegard's law, which assumes that the lattice parameter of an alloy is given by a simple linear interpolation between the lattice parameters of each component. We used the lattice parameters of Bi and Bi0.5Sb0.5 as standards because the Sb film was polycrystalline. The estimated Sb concentrations are listed in Table S1 and were mostly consistent with the XPS data. In addition, Laue oscillations of the (003) peak originating from the finite thickness of the crystalline layer were observed and became distinct as the Bi1-xSbx thickness increased ( Figure S2). Using the Laue oscillations, the crystalline film thickness ( ) can be obtained by where +1 and are adjacent maxima of the oscillations, and is the X-ray wavelength.
Accordingly, we fit the XRD spectra of the 20-nm-thick Bi0.8Sb0.2 film with a pseudo-Voight function to obtain the first and second maxima positions ( Figure S2b). As a result, the obtained crystalline thickness was ~20.0 nm, which was equal to the film thickness; this meant that the entire film was composed of the crystalline layer without an amorphous region. The in-plane ferromagnetic behavior of Co (5 nm)/Bi0.8Sb0.2 (10 nm) was confirmed by a vibrating sample magnetometer (VSM) ( Figure S3). The saturated magnetization density of our sample was very similar with the reported value of the e-beam evaporated Co film. [3] The externally applied 1200 G magnetic field was sufficiently strong to saturate the sample magnetization during THz measurements. Figure S3. In-plane ferromagnetic hysteresis of Co (5 nm)/Bi0.8Sb0.2 (10 nm).

Supplementary Note 2
A standard THz time-domain spectroscopy setup was employed to measure the timedomain THz waveforms. To radiate the THz pulses, a femtosecond laser (80 MHz repetition rate, 1.55 eV, and 100 fs pulse width) was illuminated to the samples. A 300-mm bi-convex lens was used with a focal diameter of approximately 100 μm on the sample to focus the pump pulse. A λ/2 waveplate was used to control the pump polarization. The emitted THz pulse was detected using a 5-μm dipole gap photoconductive antenna on a low-temperature grown GaAs substrate with a 5-mW fs-laser power. During the measurements, the sample saturated magnetizations were maintained by applying an external magnetic field of 1200 G.
In transmission geometry, the shift current is frequently a principal source of THz radiation via a linearly polarized pump in topological insulators. [4,5] A real-space change in the electron distribution between the valence and conduction bands generates a shift current along the atomic bonds. Based on the notation of sample azimuthal angle ( ) used in the XRD measurements, we depict the top view of a Bi1-xSbx bilayer for twin domains, proven to exist using a scan, with two different pump polarizations in Figure S4. Whereas the inversion symmetry was preserved for the blue polarization ( = 90°), it was broken at surface for the red polarization ( = 0°), resulting in the directional shift current in each twin domain. Accordingly, the possible THz signal from the shift current can be described by where ℎ is the THz amplitude from the shift current. However, as shown in Figure 2c and 2d, we could not observe any contribution from the shift current. This is because the directions of the shift current from each twin domain were opposite, and hence it was cancelled out. The other possible sources of THz radiation in the Bi1-xSbx films are the photo-Dember effect, the surface depletion field, and optical rectification. [5] The significant difference between the electron and hole mobility induces a charge dipole after photoexcitation, which is the called photo-Dember effect. Accordingly, the photo-Dember effect and surface depletion field both induce photocurrent surge along the surface normal direction. However, we could not identify which one is the principal source of the surge current in our experimental variation. In non-centrosymmetric materials, the second-order nonlinear optical effect can exist and result in optical rectification. Although the crystal structure of the Bi1-xSbx is inversion symmetric, the crystallographic misorientation between the Bi1-xSbx film and the substrate enables the nonlinear optical effect to exist. The charge polarization induced by the optical rectification is given by (2) is the second-order nonlinear optical susceptibility relevant to the optical rectification, and is the electric field of the pump pulse. [6] Since the tilt direction is [110], the induced polarization is also in the [110] direction, resulting in a one-fold symmetric THz emission on the with a two-fold on the . Consequently, as discussed in the main manuscript, the obtained THz signal from the surge current and optical rectification can be described by where and are the THz amplitude from the surge current and optical rectification, respectively. Subsequently, we can extract the THz signals from each contribution using We plotted extracted THz signals of the 10-nm-thick Bi0.8Sb0.2 from the surge current and optical rectification (Figure S5a). The THz amplitude from the surge current was larger than the optical rectification for the 10-nm-thick Bi0.8Sb0.2, but it can be varied depending on the Bi1-xSbx thickness and Sb concentration.
In addition, because the THz signal from the surge current and optical rectification is spin-independent, it is identical for the opposite magnetization directions, ± ( Figure S5b).
Therefore, we can also extract the spin-independent and -dependent contributions in the THz signal of the Co/Bi1-xSbx using where + ( ) and − ( ) are the THz signal for ± . The spin-dependent signal results from the spin-to-charge conversion (SCC) in the Bi1-xSbx layer. Figure S6a shows the THz emission signals of the Co/Bi0.8Sb0.2 (10 nm) for ± , which exhibited opposite polarities as expected. The dependence of the THz amplitude exhibited a one-fold symmetry independent of the magnetization direction (Figure S6b), which resulted from the surge current and optical rectification as the 10-nm-thick Bi0.8Sb0.2.

Figure S7a
shows the THz signals of Co ( nm)/Bi0.8Sb0.2 (10 nm) as a function of the Co thickness. The THz amplitude increased as the Co thickness increased up to 6 nm, and then, the amplitude decreased. [7] Figure S7b shows the spintronic THz amplitude of Co (5 nm)/Bi0.8Sb0.2 (10 nm) as a function of the pump power. The THz amplitude was proportional to the pump power, but it exhibited saturation behavior in the high-power region, as reported in many studies. [4,8,9] We compared the THz signal of Co/Bi0.8Sb0.2 to that of other materials under identical experimental setup and conditions. The THz signal of Co/Bi0.8Sb0.2 exhibited the same polarity as that of Co/Bi2Se3 and Co/Pt, indicating the same sign of the spin Hall angle ( Figure S8a). Whereas the THz amplitude of Co/Bi0.8Sb0.2 reached a maximum value at 15 nm, those of Co/Bi2Se3 and Co/Pt reached maximum values at 10 nm and 7 nm, respectively. [4,7] Consequently, the maximum THz amplitude for Co/Bi0.8Sb0.2 (344 pA at 15 nm) was significantly larger than those for Co/Bi2Se3 (174 pA at 10 nm) and Co/Pt (233 pA at 7 nm) owing to the large spin Hall angle. [4,10] In addition, we compared the THz signal of Co/Bi0.8Sb0.2 with that of a standard THz crystal, 2-mm-thick ZnTe (110). Although Co/Bi0.8Sb0.2 exhibited the strongest spintronic THz emission, its THz signal was much weaker than that of ZnTe ( Figure S8b). To obtain a comparable THz amplitude with that of the standard THz crystal, a fabrication strategy such as use of a trilayer structure is required. [10] Meanwhile, a characteristic change in Fouriertransformed THz spectra was observed (inset of Figure S8b). The THz spectrum from SCC was shifted to a lower frequency compared to that of ZnTe; the normalized THz spectra of Co/Bi2Se3, Co/Pt, and Co/Bi1-xSbx were similar owing to the same origin, i.e., SCC. Normalized Fourier spectra of ZnTe, Co/Bi2Se3, Co/Pt, and Co/Bi0.8Sb0.2.

Supplementary Note 3
Based on the spin diffusion model, the spin current at distance from the interface is given by [11] ( ) = (0) where is the Bi1-xSbx thickness, and is the spin diffusion length. The initial spin current density (0) is proportional to the absorbed energy density of the pump pulse, described by , where is the absorptance of the sample and is the Co thickness. Thus, if we assume that the inverse spin Hall effect from the bulk state is a principal source of the spintronic THz radiation, the obtained THz signal should be described by [4,10] S( ) ∝ Z( ) + tanh 2 , Where Z( ) is the impedance of the sample, and is the spin Hall angle of the bulk state. Accordingly, we measured the THz transmittance to obtain the impedance of the Co/Bi0.8Sb0.2 ( nm). The measured THz transmittance ( ) was converted into the optical impedance Z( ) using the Tinkham formula, ( ) = � ( ) where 0 is the vacuum impedance, and is the refractive index of the substrate. [8] The obtained Z( ) of the Co/Bi0.8Sb0.2 ( nm) was almost constant within the observed frequency range (Figure S9a).
In addition, we measured the power of the transmitted and reflected pump pulse using a beam splitter to obtain the absorptance, given by = 1 − − , where is the transmittance, and is the reflectance (Figure S9b).
With the results of the impedance and absorptance, we attempted to fit the spintronic THz amplitude as a function of the Bi0.8Sb0.2 thickness (7-25 nm) with the spin diffusion model.
However, our experimental data could not be fitted with the hyperbolic tangent function that should cross the (0, 0) point ( Figure S10). To apply the spin diffusion model, we introduced a dead layer (amorphous region) in the Bi0.8Sb0.2, similar to other studies [4,12] and modified the equation as where is the dead-layer thickness. Thus, the spin-diffusion model with the dead layer seemed to fit the experimental data well and yielded fitting values of ~2.8 nm and ~7.1 nm. However, such a large value is unreasonable based on the XRD results; the crystalline Bi0.8Sb0.2 film was successfully grown even under 7 nm although the pseudocubic phase slightly remained, and the entire of the 20-nm-thick Bi0.8Sb0.2 film was composed of the crystalline layer (Supplemental Note 1). In addition, as indicated in thickness-dependent studies of Bi and Bi1-xSbx, [13][14][15] the multiphase consisting of the hexagonal and pseudocubic phases does not affect the SCC of the bulk state (i.e., inverse spin Hall effect). Therefore, we concluded that the inverse spin Hall effect from the bulk state is not the principal source of the large spintronic THz emission in Bi1-xSbx.
As discussed in the main manuscript, another possibility is that the surface and bulk states simultaneously contribute to the SCC with opposite directions: positive for the bulk state and negative for the surface state. Based on this consideration, the spintronic THz amplitude must exhibit a negative value under 7 nm owing to the negative spintronic THz emission from the surface state. However, the SCC amplitude of the Co/Bi0.8Sb0.2 (4 nm) was negligible, which excluded the possibility of this consideration ( Figure S10). Figure S10. Spintronic THz amplitude as a function of the Bi0.8Sb0.2 thickness and fitting results with the spin-diffusion model.
We also measured THz transmittance and pump absorptance to obtain the impedance and absorptance of the Co/Bi1-xSbx (10 nm). As the Sb concentration increased, the impedance increased slightly and then decreased after = 0.07, while the absorptance decreased monotonically, resulting in a decrease in the ultrafast spin current from the Co layer ( Figure   S11). Therefore, the rapidly increasing THz amplitude with Sb concentration for 0.04 ≤ ≤ 0.2 cannot be caused by the impedance and spin current based on the equation This implies that the spin Hall angle increased across the topological phase transition from trivial to nontrivial. Because atomic spin−orbit coupling of Bi is stronger than that of Sb, spin−orbit coupling strength decreased as the Sb concentration increased. Thus, it is natural to expect that the SCC of the bulk state is weakened in the nontrivial phase. [15,16] Therefore, we concluded that the enhancement of the SCC and spintronic THz emission is caused by the topological surface state. In addition, because the charge conductivity ( ) increases with Sb concentration, based on our results, the Bi0.2Sb0.8 film is the most promising for spin−orbit torque switching device whose power consumption is proportional to 1 ( 2 ) ⁄ .