Introduction

Topological insulators (TIs) are a novel class of quantum materials exhibiting topologically nontrivial band structures and hosting a wide range of exotic spin phenomena that have been a subject of extensive research over the past decade. Essentially, TIs are gapped band insulators in the bulk exhibiting band inversions at specific high-symmetry points in the band structure traversed by linearly dispersive metallic surface states. The surface states in 3D TIs1,2,3 have a Dirac cone character shown by angle-resolved photoemission spectroscopy studies4 and are populated by massless Dirac fermions5, which enable conduction when the Fermi level resides in the bulk band gap. The presence of band inversions constitutes a key component of the topological phase6 and has been variously attributed to strong spin-orbit coupling (SOC), which leads to the opening of gaps in the bulk band structure7, as well as to scalar relativistic effects and lattice strain8,9. Several exotic properties of TIs make them uniquely primed for spintronics applications, exemplified by the helical spin texture and spin-momentum locking exhibited by their surface states. The surface states in TIs are unique in that they are topologically protected by time-reversal symmetry7, causing them to be immune to backscattering. The helical spin polarization of the surface states4,10,11 protects surface carriers from spin-independent scattering and localization and promotes long spin coherence lengths desirable for device applications7,12. This hallmark feature is a manifestation of so-called “spin-momentum locking,” wherein the in-plane spin of the surface states is “locked” orthogonal to the direction of electron motion13,14. As a result, spin accumulation can be intrinsically generated when an unpolarized charge current flows in topological surface states, whose orientation and amplitude may be controlled by the charge current11,15. Spin-momentum locking promotes larger nonequilibrium spin accumulation in comparison to the Edelstein effect16 in the presence of Rashba-type SOC17,18. In addition to the high SOC, since the electrical resistivity of the topological insulators is at least an order of magnitude higher than that of most heavy transition metals, these insulators are excellent spin current detectors19.

In view of their appeal for spintronics and spin-orbitronics, topological insulator/ferromagnet (TI/FM) heterostructures have emerged as a subject of widespread interest. The charge-to-spin conversion efficiency in TIs is projected to be at least an order of magnitude higher than that attainable in heavy metals17,20,21. Several spin-orbit effects are reported in TI/FM systems, such as spin pumping17,22, the spin Hall effect20 and the inverse spin Hall effect of the bulk23, Rashba24 and inverse Rashba-Edelstein effects and the anomalous Hall effect25. Being free of the impedance mismatch problem, spin pumping provides an effective means to probe spin injection and transport in TIs23,26. Spin angular momentum from the precessing magnetization of an FM is injected or pumped into an adjacent nonmagnet (NM) in the form of pure spin current which manifests as an enhanced damping of magnetization in the FM layer. The efficiency of spin pumping in an NM/FM system is quantified by two parameters characterizing the interface: the spin-mixing conductance27 and the interfacial spin transparency28,29. The spin transparency of an interface controls the amount of spin current that can be transmitted across the interface without reflection or absorption. Identifying and engineering highly transparent interfaces promotes increased efficiency of spin current transfer, which is desirable for applications in spin-torque-based devices30. To date, most reports of spin-to-charge interconversion mechanisms in TI/FM have made use of magnetoresistance measurements11,15 or electrical detection of spin injection and transport17,22,23 and have focused on second-generation binary TIs, such as Bi2Se3, Bi2Te3 and Sb2Te3. These second-generation TIs are well known to suffer from the presence of parasitic crystalline defects in the bulk, leading to significant bulk conduction in transport measurements2,31,32, which causes the surface states to be difficult to isolate. In 2014, Ando et al.15 identified the alloy Bi2−xSbxTe3−ySey to have the lowest defect density and best bulk insulating properties to date. Thus, among the 3D TIs well studied in the literature, the alloy Bi2−xSbxTe3−ySey is considered to be an exemplary system for achieving the unique properties of TIs due to the tunability of the band structure and transport properties depending on its stoichiometry. For specific stoichiometries, the compensation of p-type carriers due to (Bi, Sb)/Te antisite defects by n-type selenium vacancies can lead to an effective cancellation of bulk carriers31,33,34. Well-defined topological surface states and surface-dominated transport at unprecedented temperatures can be observed in BSTS35,36,37, making it an ideal system for achieving the unique advantages of TIs.

In this work, we report an all-optical investigation of spin pumping in BiSbTe1.5Se1.5(BSTS)/Co20Fe60B20(CoFeB) bilayer thin films with the objective of extracting the spin-mixing conductance and spin transparency of these heterostructures and determining the spin diffusion length in BSTS. To excite and detect the magnetization dynamics in these systems, we use time-resolved magneto-optical Kerr effect (TR-MOKE) magnetometry38, a local and noninvasive pump-probe detection scheme recently proposed to be a viable alternative to the more commonly used electrical techniques for the study of spin pumping in a heavy metal/FM bilayer system29. In contrast to electrical detection techniques, such as spin-torque ferromagnetic resonance (ST-FMR), TR-MOKE bypasses the need for any delicate microfabrication and avoids limiting factors that could be inherently present in those methods, such as large area averaging and inhomogeneous linewidth broadening39,40. The damping can be unambiguously extracted from the decaying amplitude of the oscillatory Kerr signal, free from experimental artifacts arising due to multimodal oscillation and impurity or defect scattering. By studying the modulation of damping as a function of BSTS thickness, we have extracted the intrinsic spin-mixing conductance G↑↓ of the BSTS/CoFeB interface and estimated the spin diffusion length λs in BSTS. Subsequently, the CoFeB-thickness-dependent modulation of damping was used to extract the effective spin-mixing conductance Geff, a quantity that can be derived from G↑↓ by including the backflow of the spin angular momentum into the FM. Additionally, the role of two-magnon scattering (TMS) in the modulation of damping in these systems was isolated, and control experiments were performed by inserting a thin copper (Cu) spacer layer of varying thickness between the BSTS and the CoFeB layers to confirm that spin pumping plays the primary role in the thickness-dependent modulation of damping observed in our system. The high efficiency of the observed spin pumping is directly related to the high SOC and the high resistivity of the PLD-grown BSTS topological insulator, highlighting its feasibility as a room-temperature spin current detector.

Results

The crystallinity of the pulsed laser deposition (PLD)-grown BSTS thin films was investigated by X-ray diffraction (XRD) measurements. BSTS crystallizes in a rhombohedral crystal structure with the R\(\bar{3}\) m space group31. The structure consists of repeated units of five atomic layers stacked along the crystallographic c-axis, otherwise known as the quintuple layers, as illustrated in the inset of Fig. 1b. The XRD pattern of a 25 nm-thick BSTS thin film is shown in Fig. 1a. The XRD peaks were obtained at (0,0,3n) indexed as (0,0,3), (0,0,6), (0,0,9), (0,0,12), (0,0,15) and (0,0,18), reflecting the preferred c-axis orientation31. The obtained peaks showed an exact match with a PLD-grown BSTS sample of identical stoichiometry reported previously34 as well as with multiple other reports in BSTS41 and similarly c−axis oriented polycrystalline Bi2Se342,43, Bi2Te344 and Bi2Te3−xSex45 thin films. Additionally, clear Laue oscillations consistent with the film thickness were observed, as shown in the inset of Fig. 1a close to the (0,0,6) peak, demonstrating the high crystalline quality and uniformity of these films.

Fig. 1: Structural characterization of the sample and verification of the bulk insulating nature.
figure 1

a XRD pattern of a 25 nm BSTS thin film. Inset: Laue oscillations observed in the vicinity of the (0,0,6) XRD peak. b Micro-Raman spectrum for a 25 nm BSTS thin film. Inset: Schematic representation of one quintuple layer of BSTS. c Atomic force microscopy images for Sub/BSTS(25 nm)/CoFeB(5 nm)/SiO2(3 nm) and (d) Sub/CoFeB(5 nm)/SiO2(3 nm) thin film samples. e Resistance as a function of temperature for a 25 nm BSTS thin film. The dashed line marks the transition to surface-dominated transport.

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Micro-Raman spectroscopy measurements using a Lab Ram HR 800 micro-Raman spectrometer (Horiba France SAS; λ = 533 nm, objective = 100×, grating 1800 lines/mm, spot size 10 µm) were carried out on the BSTS films to investigate their molecular structure. Five atoms are present in the primitive unit cell of BSTS, producing (3N-3) = 12 optical phonon modes. An irreducible representation of Γvib = 2A1g + 2Eg can be derived46, where A1g represents out-of-plane and Eg represents in-plane vibrational modes. The Raman spectrum of a 25 nm-thick BSTS film is presented in Fig. 1b, showing three of the four normal modes at 71.6 cm−1, 113.9 cm−1 and 166.2 cm−1. Out-of-plane vibrations induce smaller displacements of vibrating atoms, leading to higher phonon frequencies compared to the corresponding in-plane modes46,47. Correspondingly, the three Raman modes in Fig. 1b were designated as the A1g1, Eg2 and A1g2 modes48. These results effectively agreed with previous reports of Raman measurements in PLD-grown BSTS having the same stoichiometry as our films34.

The surface topography of the samples was studied using atomic force microscopy (AFM). AFM images of Sub/BSTS(25 nm)/CoFeB(5 nm)/SiO2(3 nm) and Sub/CoFeB(5 nm)/SiO2(3 nm) films are shown in Fig. 1c, d. The average topographical roughness (Ra) of the Sub/BSTS(25 nm)/CoFeB(d)/SiO2(3 nm) samples with different thicknesses d of the CoFeB layer are listed in Table 1 along with the Ra values of the reference CoFeB films of the corresponding thickness. The Ra value was found to be slightly higher for the bilayers than for the reference films which is not surprising given the PLD growth of the BSTS, which can lead to the granular nature of the film surface49. Due to the low thickness of the CoFeB films, the Ra value obtained from AFM analysis bears the signature of the interfacial roughness. In the presence of BSTS, Ra was found to slightly increase with decreasing CoFeB thickness, indicating higher interfacial disorder at lower thicknesses. The Ra values in the reference CoFeB films were found to be independent of CoFeB thickness. The roughness values negligibly varied in different regions of the same sample, indicating uniform film growth. For all samples, the average topographical roughness was found to be quite low in the sub-nm range.

Table 1 Average topographical roughness values obtained from the AFM data analysis.
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Figure 1e shows the temperature dependence of the resistance of a 25 nm-thick BSTS thin film. The R-T behavior is characteristic of the bulk insulating nature of BSTS and has been previously reported in BSTS systems49. The measured resistance increases with decreasing temperature until approximately 66 K, marked by the dashed line in Fig. 1e. At lower temperatures, a transition to the surface-dominated metallic conduction regime becomes apparent by the sharp change in the curvature and a dip in the measured resistance. This transition can be considered to be a qualitative signature of the weak antilocalization effect in highly insulating topological insulators, such as BSTS49,50, as the metallicity of the topological protected surface states became apparent even at temperatures as high as 66 K. On the other hand, the small upturn in the R-T curve at even lower temperatures ≤ 14 K can be attributed to the freezing of the bulk carriers.

Enhancement of Gilbert damping due to spin pumping

The magnetization dynamics of a ferromagnetic system in the presence of a magnetic field consists of the Landau-Lifshitz torque and the intrinsic Gilbert damping; the Landau-Lifshitz torque leads to the precession of the magnetization direction around the effective magnetic field direction, and the intrinsic Gilbert damping results in the precessional oscillations steadily diminishing in amplitude until an equilibrium time-independent magnetization direction is attained. In addition to the local material-specific Gilbert damping, nonlocal effects occur when an FM layer is placed adjacent to certain NM materials, which can lead to an enhancement of the effective damping. Tserkovnyak et al. in 200251 proposed one such mechanism the so-called “spin-pumping” effect, in which the precessing magnetization in the FM pumps angular momentum into the adjacent NM layer, thus losing energy and hence damping out more rapidly51,52,53. The overall dynamics of the magnetization vector can be theoretically described by a modified version of the Landau-Lifshitz-Gilbert equation, given by the following:

$$\frac{d{\boldsymbol{m}}}{{dt}}=-\gamma \left({\boldsymbol{m}}{\boldsymbol{\times }}{{\boldsymbol{H}}}_{{eff}}\right)+{\alpha }_{0}\left({\boldsymbol{m}}{\boldsymbol{\times }}\frac{d{\boldsymbol{m}}}{{dt}}\right)+\frac{\gamma }{V{M}_{s}}{I}_{0}$$
(1)

where γ is the gyromagnetic ratio, α0 is the intrinsic Gilbert damping, Heff is the effective magnetic field, V is the volume of the FM and Ms is the saturation magnetization. The total pumped current I0 consists of the DC charge current Idc (zero in our case), the spin current Ispump pumped into the NM layer and the backflow current Isback, that returns back into the FM:

$${I}_{0}={I}_{{dc}}+{I}_{s}^{{pump}}+{I}_{s}^{{back}}$$
(2)

The resultant flow of angular momentum across the NM/FM interface depends on the relative balance between the forward and backflow currents. The forward current depends on the intrinsic spin-mixing conductance G↑↓27, which acts as a measure of the spin transfer across it. Under the ballistic approximation valid for film thicknesses less than the momentum mean free path54, G↑↓ can be extracted from the variation of the effective Gilbert damping αeff with the thickness t of the NM layer using the following relationship54,55:

$${\alpha }_{{eff}}={\alpha }_{0}+\frac{g{\mu }_{B}{G}_{\uparrow \downarrow }}{4\pi {M}_{s}d}\left(1-{e}^{\frac{-2t}{{\lambda }_{s}}}\right)$$
(3)

where d is the thickness of the FM layer and λs is the spin diffusion length in the NM. On the other hand, spin current backflow occurs primarily due to spin accumulation at the interface, which reduces the efficiency of spin transfer. The spin accumulation can be quantified by the backflow factor β:

$$\beta ={\left({G}_{\uparrow \downarrow }\sqrt{\frac{4\epsilon }{3}}\tanh \left(\frac{t}{{\lambda }_{s}}\right)\right)}^{-1}$$
(4)

where ϵ is the spin-flip scattering probability, a material-specific parameter given by55,56:

$$\epsilon ={\left(\frac{z{e}^{2}}{{{\hslash }}c}\right)}^{4}={(z{\alpha }_{{fine}})}^{4}$$
(5)

where αfine = 1/137 is the fine structure constant and z is the atomic number of the NM. The magnitude of ϵ is larger for heavier elements and does not allow the backflow effect to vanish even when the ratio t/λs » 1. However, the intrinsic spin-mixing conductance G↑↓ is a direct measure of the pure spin current transfer and does not consider the spin backflow. For diffusive spin transport, another quantity, the effective spin-mixing conductance Geff, can be derived from G↑↓ by including the backflow factor as53:

$$\frac{1}{{G}_{{eff}}}=\frac{1}{{G}_{\uparrow \downarrow }}+\beta$$
$$\Rightarrow {G}_{{eff}}=\frac{{G}_{\uparrow \downarrow }}{{\left[\sqrt{\frac{4\epsilon }{3}}\tanh \left(\frac{t}{{\lambda }_{s}}\right)\right]}^{-1}+1}$$
(6)

Inclusion of the backflow factor causes Geff to be element-dependent and dependent on the thickness of the NM layer. Geff can also be experimentally determined by studying the dependence of the damping on the FM layer thickness d39,53.

$${\alpha }_{{eff}}={\alpha }_{0}+\frac{g{\mu }_{B}}{4\pi {M}_{s}d}{G}_{{eff}}$$
$$={\alpha }_{0}+\frac{g{\mu }_{B}}{4\pi {M}_{s}d}\frac{{G}_{\uparrow \downarrow }}{{\left[\sqrt{\frac{4\epsilon }{3}}\tanh \left(\frac{t}{{\lambda }_{s}}\right)\right]}^{-1}+1}$$
(7)

The latter half of the above equation, derived by substitution of the result in Eq. (6), can be used in the diffusive approximation to model the NM layer thickness dependence of spin pumping for a fixed FM layer thickness d.

In addition to the spin pumping effect, the magnetic disorder and intermixing at an NM/FM interface can lead to loss of spin information and a corresponding decrease in the spin transmission efficiency in the presence of certain interfacial effects other than spin pumping. One such effect is known as spin memory loss (SML), in which interfacial SOC mediates spin-flip scattering events at the interface, leading to reduced spin transmission to the NM57,58. Further losses can occur owing to the TMS effect occurring in the presence of defects and inhomogeneities at the interface59,60, leading to the dephasing of the uniform FMR mode and its scattering into degenerate magnons. The presence of SML or TMS can lead to a larger modulation of effective damping than that arising from pure spin pumping. However, while the modulation due to SML scales inversely with FM thickness similar to spin pumping, that due to TMS scales quadratically, making it possible to straightforwardly isolate its contribution from FM-thickness-dependent measurements of the damping. The total damping modulation arising due to the combined effect of spin pumping and TMS can be expressed as61,62:

$${\varDelta \alpha =\alpha }_{{eff}}-{\alpha }_{0}=\frac{g{\mu }_{B}}{4\pi {M}_{s}d}{G}_{{eff}}+{\beta }_{{TMS}}{d}^{-2}$$
(8)

The effect of all these interfacial effects is included in a parameter known as the interfacial spin transparency T which is given by28,63:

$$T=\frac{{G}_{{eff}}\tanh \left(\frac{t}{{2\lambda }_{s}}\right)}{{G}_{{eff}}\coth \left(\frac{t}{{\lambda }_{s}}\right)+\frac{h}{2\rho {\lambda }_{s}{e}^{2}}}$$
(9)

The interfacial spin transparency is directly correlated to its effective spin-mixing conductance Geff and regulates the flow of the spin angular momentum across the NM/FM interface. Differences in spin transparency can account for the disparities in the measured spin-Hall angle independent of the SML effect28. Identifying and engineering highly transparent interfaces for efficient spin transfer is crucial for device applications.

All-optical measurement of damping parameter

TR-MOKE magnetometry was used for all-optical probing of magnetization dynamics in the Sub/BSTS(t)/CoFeB(d)/SiO2(3 nm) samples. A two-color setup with a noncollinear pump-probe geometry was used40, as shown in Fig. 2a. Typical time-resolved Kerr rotation data showing different temporal regimes of laser-induced magnetization dynamics are provided in Fig. 2b. Regime I displays the ultrafast demagnetization phenomenon in which laser excitation leads to an ultrafast quenching of magnetization at the picosecond timescale64. Regime II displays the fast magnetization recovery process, while the oscillatory Kerr signal of Regime III represents the magnetization precession with the characteristic Gilbert damping, superposed on a background signal arising from slow relaxation occurring via heat dissipation into the substrate.

Fig. 2: Schematic of the spin pumping measurements and representative time-resolved data.
figure 2

a Schematic of the sample structure and TR-MOKE measurement geometry. b Time-resolved Kerr rotation data for the Sub/BSTS(25 nm)/CoFeB(10 nm)/SiO2(3 nm) thin film showing three distinct temporal regimes. Regime I displays the ultrafast demagnetization phenomenon, Regime II displays the fast magnetization recovery process, and Regime III represents the magnetization precession with characteristic Gilbert damping.

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To extract the Gilbert damping parameter αeff, the background-subtracted oscillatory Kerr signal is first fitted with a damped sinusoidal function

$$M\left(t\right)=M(0){e}^{-\left(\frac{t}{\tau }\right)}\sin \left(2\pi {f}_{{FFT}}t+\varphi \right)$$
(10)

where fFFT is the precessional frequency, τ is the relaxation time, and ϕ is the initial phase of precession. To extract the effective saturation magnetization Meff of the samples, the bias magnetic field dependence of fFFT is fitted to the Kittel formula relevant for ferromagnetic systems65:

$${f}_{{FFT}}=\frac{{\gamma }_{0}}{2\pi }\sqrt{H\left(H+4\pi {M}_{{eff}}\right)}$$
(11)

where γ0 = gµB/ℏ is the gyromagnetic ratio and H is the bias magnetic field. From the Kittel fit for the Sub/BSTS(25 nm)/CoFeB(d)/SiO2(3 nm) samples, Meff decreased with CoFeB thickness d, showing a linear dependence with 1/d. From a linear fit with the conventional relationship of Meff = Ms − 2Ks/(4πMsd), the saturation magnetization Ms was extracted from the intercept and the interfacial anisotropy Ks was extracted from the slope, as shown in Fig. S1 of the Supplementary Information. Ks serves as an indicator of the strength of the interfacial SOC61. The value of Ms was found to decrease from 1465 ± 43 emu/cc in the reference CoFeB films to 1324 ± 27 emu/cc in the BSTS/CoFeB bilayers, while Ks slightly increased from 0.962 ± 0.0269 erg/cm2 in the reference films to 0.988 ± 0.0283 erg/cm2 in the bilayers. The reduction in Ms in the TI/FM bilayers could potentially originate from the magnetic proximity effect at the BSTS/CoFeB interface, in which orbital hybridization between the 3d electrons in CoFe and the topological surface states of BSTS could introduce a perpendicular magnetic anisotropy manifested as a reduced Ms66,67 at low temperatures. However, under ambient conditions, a more likely cause is the presence of some degree of atomic intermixing at the BSTS/CoFeB interface68,69. Finally, the effective Gilbert damping parameter αeff is calculated using the extracted values of τ and Meff as follows:

$${\alpha }_{{eff}}=\frac{1}{{\gamma }_{0}\tau \left(H+2\pi {M}_{{eff}}\right)}$$
(12)

Details of the bias-field dependent TR-MOKE measurements are provided in Section I of the Supplementary Information.

Thickness-dependent modulation of damping

The background-subtracted precessional Kerr rotation data taken in the presence of an ~1.7 kOe saturating magnetic field for the Sub/BSTS(t)/CoFeB(5 nm)/SiO2(3 nm) sample are given in Fig. 3a, where t was varied from 7 to 40 nm. The lowest thickness of the BSTS studied in our experiments was well above twice the approximate surface state thickness70,71 to eliminate the possibility of a crossover from the topological phase to a trivial gapped insulator, which may occur due to quantum tunnelling between opposite surfaces if the thickness is reduced below a critical limit70. In the absence of the BSTS underlayer, the damping of 5 nm CoFeB was found to be 0.0084, which was considered the intrinsic Gilbert damping α0. As shown in Fig. 3b, the effective damping in the presence of the BSTS underlayer was found to show a nonmonotonic variation consisting of a sharp enhancement in αeff from its intrinsic value of 0.0084 to a saturating value of 0.0114 at high values of t. The observed dependence is a characteristic signature of spin pumping, showing a similar nature to those reported in various systems involving ferromagnetic thin films interfaced with a topologically trivial NM29,30,62. However, this dependence is not immediately expected in topological systems where the spin-to-charge conversion efficiency in several spin pumping experiments has been attributed to a dominant role played by the topologically protected surface states23,72, whose thicknesses do not vary with the film thickness. In topological insulators, the SOC strength is expected to be different in the surface states versus the bulk and spin pumping also contributes to the inverse Edelstein effect (IEE) in the spin-momentum-locked topological surface states. The pumped spin current from the ferromagnet results in a spin imbalance in the surface state, whereafter the spin-momentum locking results in the generation of a charge current \({J}_{c}\) confined to two dimensions22. This mechanism is distinct from the ISHE, where a spin current flowing within the bulk of the material is converted into a 3D charge current. However, in room-temperature spin-pumping experiments it is very difficult to distinguish the ISHE and the IEE of the surface state, and moreover ISHE is found to dominate over the latter17. Although it has been reported previously that the SOC of the topological surface states could enhance the pure spin current injected into the TI17, any contribution of the surface states to the spin pumping should be uniform over the entire experimental thickness range, and cannot explain on its own the variation in Fig. 3b. We concluded that in our case, the experimentally observed variation in αeff with BSTS thickness was likely caused as a consequence of strong bulk spin-orbit coupling of the heavy metallic bismuth-based alloy, analogous to a normal heavy metal. Since all measurements were carried out under ambient conditions, this observation could indicate the presence of surface-to-bulk scattering at room temperature, leading to the scattering of injected carriers into the bulk49. Studying the modulation of αeff as a function of temperature could elucidate the precise contribution of the surface states to the spin pumping effect; in particular, by lowering the temperature to traverse the inflection point at 66 K in the R-T characteristics which signals the emergence of surface-dominated transport. Such an investigation necessitates temperature-dependent TR-MOKE or FMR measurements of the damping modulation in the system, which will be a topic of our future research. Fitting the dependence in Fig. 3b with the latter half of Eq. (7), we extracted a value (4.02 ± 0.995) × 1015 cm−2 for the intrinsic spin-mixing conductance G↑↓. The spin diffusion length was simultaneously obtained from the fit as λs = 6.3 nm. The high value of G↑↓ and the nonmonotonic change in the damping parameter both indicate spin current injection into the BSTS. For completeness, we also fitted the data in Fig. 3b using the ballistic transport model of Eq. (3), obtaining G↑↓ = (1.19 ± 0.006) × 1015 cm−2 and λs = 7.2 nm. Using Eq. (5), the spin-flip probability ϵ in these heterostructures was calculated to be 13.4%. This high value of ϵ »1.0 × 10−2 was a direct manifestation of strong spin-orbit coupling of heavy metallic Bi, which makes the Bi-based alloy a good spin sink52,53. Using ϵ = 0.134 and the values of G↑↓ and λs extracted from the fit using Eq. (7), the spin backflow factor β was calculated to be 5.9 × 10−16 cm2 for the 25 nm-thick BSTS layer. Based on the form of Eq. (4), β is higher for lower thicknesses and asymptotically approaches its lower limit when t »λs. However, even at very high thicknesses, β does not reduce to zero due to the finite contribution of the material-dependent quantity ϵ. On the other hand, the exponential form for the backflow factor implicit in Eq. (3) is applicable in the ballistic limit when the thickness of the film is less than the mean free path54. The effective spin-mixing conductance Geff includes the presence of the spin backflow and was determined using Eq. (6) to be (1.19 ± 0.295) × 1015 cm−2 for t = 25 nm, approximately a factor of three smaller than G↑↓. The inclusion of a nonnegligible spin backflow led to a larger value of \({G}_{\uparrow \downarrow }\) relative to Geff derived using spin diffusion theory compared to the estimate using the ballistic model. The variation of Geff calculated in this manner for different thicknesses of BSTS are shown in Fig. S2 of the Supplementary Information.

Fig. 3: Extraction of the intrinsic and effective spin-mixing conductance and the spin diffusion length.
figure 3

a Precessional Kerr rotation data for the Sub/BSTS(t)/CoFeB(5 nm)/SiO2(3 nm) samples at an external field of 1.7 kOe. b Modulation of the damping parameter with the BSTS layer thickness. The solid line shows fitting with a spin pumping model to extract the intrinsic spin-mixing conductance and spin diffusion length. c Precessional Kerr rotation data for the Sub/BSTS(25 nm)/CoFeB(d)/SiO2(3 nm) samples. d Modulation of the damping parameter with the CoFeB layer thickness. The solid line shows the fitting considering spin pumping (SP) and two-magnon scattering (TMS) for extracting the effective spin-mixing conductance.

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We next aimed to determine the value of the effective spin-mixing conductance Geff directly from experiment by modeling the FM layer thickness-dependent damping modulation. For this purpose, we chose a BSTS thickness of 25 nm »λs where the BSTS-thickness dependence of the damping saturates such that the effect of varying the CoFeB layer thickness could be eliminated. The precessional data taken at a 1.7 kOe saturating magnetic field for the Sub/BSTS(25 nm)/CoFeB(d)/SiO2(3 nm) samples are given in Fig. 3 (c), where d was varied from 2 to 10 nm. The damping was found to show a sharp increase with the inverse of the CoFeB layer thickness, consistent with the presence of a strong spin pumping effect in our systems. The observed dependence was fitted with the sum of linear and quadratic scaling with the inverse of CoFeB thickness provided in Eq. (8), arising from spin pumping and two-magnon scattering effects, respectively. From the fit, the values of effective spin-mixing conductance Geff and βTMS were found to be (1.19 ± 0.034) × 1015 cm−2 and (1.03 ± 0.116) × 10−16 cm2, respectively, while the intrinsic Gilbert damping α0 was found to be 0.0084. Subsequently, the spin pumping and TMS contributions to the total damping modulation from its intrinsic value were isolated using Eq. (8). The TMS contribution was found to increase with decreasing CoFeB thickness, consistent with the higher average roughness values at lower film thickness, as determined from the AFM measurements (Table 1). The finite βTMS value present in these heterostructures is not surprising due to the PLD growth of BSTS. Improving the structural quality of the interface should lead to more efficient spin transmission and a lower percentage of TMS. Regardless, as shown in Fig. 4a, spin pumping emerged as the dominant mechanism underlying the damping modulation in our case, even at the lowest CoFeB thickness studied.

Fig. 4: Isolation of the spin pumping and two magnon scattering effects and variation of damping with the Cu spacer layer thickness.
figure 4

a Fraction of the damping modulation arising due to pure spin pumping (SP) and two-magnon scattering (TMS) as a function of the CoFeB thickness d. b Precessional Kerr rotation data for the Sub/BSTS(25 nm)/Cu(tCu nm)/CoFeB(5 nm)/SiO2(3 nm) samples at an external field of 1.7 kOe.

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With the experimentally obtained G↑↓ and Geff, the interfacial spin transparency T of the BSTS/CoFeB interface was investigated. T shows a complex dependence on the spin-mixing conductance of an NM/FM interface as well as the spin diffusion length and resistivity of the NM layer. In the spin-Hall magnetoresistance framework, the finite thickness of the BSTS layer was taken into account63. Using the experimentally determined value of Geff = (1.19 ± 0.034) × 1015 cm−2 and the extracted values of the resistivity (Section III of the Supplementary Information) and the spin diffusion length λs = 6.3 nm, T was calculated from Eq. (9) to be a very high value of 0.9 in the so-called “perfect spin-sink” regime t »λs when the BSTS thickness dependence of the damping modulation saturates54, leading to a high effective spin-mixing conductance of the BSTS/CoFeB interface. Thus, high values of T are attainable in BSTS/FM systems, which provides another dimension to their applicability for pure spin-current-based spintronic devices30,62. The strong bulk SOC of the BSTS topological insulator allows easier spin current dissipation52, resulting in a high Geff value and a high interfacial spin transparency. In addition to the bulk SOC, the pumped spin current is greatly enhanced by the SOC of the surface17 which can contribute to the high value of Geff. In addition to high Geff, the high resistivity of BSTS also plays a role in enhancing the interface transparency. Appropriate choice of thickness and exploring the tunability of resistivity in these systems are key to identifying optimal conditions for maximizing the efficiency of spin transfer; these aspects need further exploration and will form the basis of future work.

Finally, a thin Cu spacer layer was introduced between the BSTS and CoFeB layers, and TR-MOKE measurements were performed as a control experiment. Cu has a small spin-orbit coupling, and hence, very little spin-flip scattering is expected at the Cu interfaces. At the same time, a long spin diffusion length in Cu implies that pure spin current generated by spin pumping can penetrate fully through the spacer. Time-resolved Kerr rotation data for the Sub/BSTS (25 nm)/Cu (tCu)/CoFeB (5 nm)/SiO2 (3 nm) thin films with 0 ≤ tCu ≤ 1 nm are presented in Fig. 4b. Negligible modulation of damping with the introduction and variation of the Cu spacer thus ruled out the presence of any significant SML effect in our heterostructures and established the dominance of spin pumping in the observed thickness-dependent damping modulation.

Discussion

We used an all-optical time-resolved magneto-optical Kerr effect technique to reveal a sizeable spin pumping effect and interfacial spin transparency in BiSbTe1.5Se1.5 (BSTS)/Co20Fe60B20(CoFeB) heterostructures. High-quality BSTS thin films were grown by pulsed laser deposition, which showed characteristic structural features and a typical bulk insulating character with resistance vs. temperature characteristics showing a signature of surface-dominated transport at temperatures as high as 66 K. The modulation of Gilbert damping with the thickness of the CoFeB layer and that of the BSTS underlayer were found to be indicative of an efficient spin pumping effect in these heterostructures, which were characterized by analyzing the variation in Gilbert damping with the respective thicknesses of the BSTS and CoFeB layers. We determined the intrinsic spin-mixing conductance G↑↓ of the interface to be (4.02 ± 0.995) × 1015 cm−2 and found the spin-diffusion length λs in BSTS to be 6.3 nm at room temperature, thus demonstrating optical detection of pure spin current injection into the BSTS layer. Analyzing the CoFeB-thickness-dependent variation in Gilbert damping, we found the effective spin-mixing conductance Geff to be (1.19 ± 0.034) × 1015 cm−2 and isolated the two-magnon scattering parameter βTMS, which was calculated to be (1.03 ± 0.116) × 10−16 cm2, thereby revealing spin pumping to be the dominant contributor to the damping modulation. The roles of other interfacial losses, such as spin memory loss, were found to be negligible in comparison to spin pumping in our heterostructures, as evidenced by the negligible modulation of damping upon insertion of a Cu spacer layer at the BSTS/CoFeB interface. Finally, we calculated the interfacial spin transparency T, which we found to be as high as ~0.9 (90%) in our heterostructures for a BSTS thickness of 25 nm. High interfacial spin transparency is imperative for the enhanced efficiency of spin transport, and the nearly ideal value we obtained in the BSTS/CoFeB heterostructures are of direct relevance for spin-orbitronic device applications. Our first demonstration of room-temperature spin injection in a highly resistive topological insulator could be useful for future studies involving the correlation of the spin pumping effect with the interesting properties of topological insulators in general; such as different spin-orbit coupling of surface and bulk, nonmonotonic variation of the resistivity with temperature, thickness-dependent phase transition from the topological to trivial insulating character, and the properties of BSTS in particular, such as high resistivity and tunable band structure by stoichiometry variation. Exploration of the effects of the resistivity and thickness of the topological insulator on the spin diffusion length, spin-mixing conductance and interfacial spin transparency, particularly as the thickness is sufficiently lowered to destroy the surface states and hence isolate the surface state contribution, will be important to identify optimal conditions for maximizing pure spin current transfer in next-generation topological spintronic devices.

Methods

Sample fabrication

Thin films of BSTS topological insulator were grown on SiO2-coated Si substrates using a pulsed laser deposition technique, wherein BSTS targets of nominal stoichiometry were ablated using a high-powered KrF excimer laser (Coherent Inc.) and deposited on an insulating Si (100) substrate coated with 300-nm-thick SiO2. Although films deposited by molecular beam epitaxy (MBE) are more frequently used in fundamental research, MBE is a time-consuming and expensive process presenting serious roadblocks for the integration with practical applications; additionally, the growth of Bi2-xSbxTe3-ySey topological insulators of controllable stoichiometry was not achieved by MBE41. However, we note that the topology of the surface states are protected irrespective of the lack of epitaxy, as the Dirac electrons propagate in the surface with a topological protection against any nonmagnetic defects, including grain boundaries. The sample thickness was controlled by monitoring the number of laser pulses used to ablate the target once the pulse energy, deposition pressure and substrate-to-target distance were fixed to optimize the plasma plume. Prior to the deposition, the chamber was evacuated to a base pressure of 3 × 10−5 Torr. Deposition was performed in a flowing argon (Ar) environment with an Ar pressure of 3.6 × 10−1 Torr at a substrate temperature of 240 °C. After deposition, the samples were annealed in an Ar atmosphere for 20 min, which aids in mobilizing the Se and Te atoms to their preferred low energy positions within the quintuple layers, greatly reducing residual bulk carriers49. The presence of Laue oscillations corresponding to the film thickness in the XRD pattern was testament to the high quality of PLD-grown polycrystalline samples, which was achieved by careful temperature control and use of an optimized in situ annealing temperature during the deposition process.

Subsequently, ferromagnetic CoFeB layers of different thicknesses were grown on top of the PLD-deposited BSTS by DC magnetron sputtering, followed by deposition of a 3-nm-thick protective capping layer of SiO2 by RF sputtering to protect it under ambient conditions and prevent it from damages due to high-power laser exposure during optical pump-probe measurements. CoFeB was deposited with a DC voltage of ~375 V, and SiO2 was deposited with an RF power of 50 W. For the Sub/BSTS (25 nm)/Cu (tCu)/CoFeB (5 nm)/SiO2 (3 nm) samples, the Cu-spacer layer was deposited at a DC voltage of ~340 V. All depositions were performed at 0.5 mTorr Ar pressure with a base pressure of 1.4 × 10−6 Torr. The deposition conditions were carefully optimized and identical for all the samples. A very low deposition rate of 0.2 Å/s was maintained for the deposition of all metallic films, and 0.1 Å/s for the SiO2 capping layer in order to achieve uniform deposition down to thicknesses ≤ 1 nm.

TR-MOKE measurements

Measurement of magnetization dynamics in all the thin film samples was carried out using a two-color TR-MOKE technique with a 400 nm pump beam and 800 nm probe beam with a pump-probe cross-correlation width of ~100 fs40. This all-optical technique facilitates the direct observation of the precessional oscillations in the pico- and nanosecond time domain. An amplified laser system (Libra, Coherent Inc.) employing a chirped-pulse regenerative amplification technique generates femtosecond laser pulses. The second harmonic of the amplified laser output (wavelength = 400 nm, pulse width > 40 fs, repetition rate = 1 kHz) was used for laser excitation of the ferromagnetic thin films. Meanwhile, the time-delayed fundamental beam (wavelength = 800 nm, pulse width = 40 fs, repetition rate = 1 kHz) was used to probe the ensuing magnetization dynamics. The delay time between the pump and probe pulses was externally controlled by a variable delay generator. A noncollinear pump-probe geometry was adopted in which the pump beam was focused to a spot size of 300 µm and was directed to be obliquely incident on the sample while the probe beam, with a spot size of 100 µm, was incident normal to the sample surface and carefully aligned to the center of the pump spot to detect the local magnetization changes from a uniformly irradiated part of the sample. The pump fluence was set to 10 mJ/cm2 and the probe fluence was set to 1 mJ/cm2 for all the measurements. Initially, the 800 nm probe beam was orthogonally polarized to the pump. After reflection from the sample surface, the Kerr-rotated probe beam was directed into a Si photodiode after passing through a Glan-Thompson polarizer adjusted to a small angle from extinction to minimize optical artifacts in the Kerr rotation signal. Digital signal processing lock-in amplifiers (Stanford Research Systems, SR830) provided phase-sensitive detection of the modulated signal. The reference signal for lock-in detection was provided by an optical chopper operating at 373 Hz placed in the pump path. All measurements were performed under a 1.7 kOe bias field applied at a 10°–15° tilt from the sample plane to saturate the magnetization of the samples. All experiments were carried out under ambient temperature and pressure conditions.