Abstract
There has been considerable interest in exploiting the spin degrees of freedom of electrons for potential information storage and computing technologies. Topological insulators (TIs), a class of quantum materials, have special gapless edge/surface states, where the spin polarization of the Dirac fermions is locked to the momentum direction. This spin–momentum locking property gives rise to very interesting spindependent physical phenomena such as the Edelstein and inverse Edelstein effects. However, the spin injection in pure surface states of TI is very challenging because of the coexistence of the highly conducting bulk states. Here, we experimentally demonstrate the spin injection and observe the inverse Edelstein effect in the surface states of a topological Kondo insulator, SmB_{6}. At low temperatures when only surface carriers are present, a clear spin signal is observed. Furthermore, the magnetic field angle dependence of the spin signal is consistent with spin–momentum locking property of surface states of SmB_{6}.
Introduction
Spintronics aims to use the spin degrees of freedom for information technologies^{1,2,3}. The injection of spinpolarized carriers into twodimensional quantum materials, including graphene and the surface states of topological insulators (TIs), is particularly interesting^{4,5}. Different from graphene showing weak spin–orbit coupling and long spin lifetimes^{6,7,8,9}, the surface states of TI exhibit very large spin–orbit coupling^{10,11,12,13}. Even more interestingly, the spin and the momentum directions are strongly coupled to each other in the surface states of TI^{4,10,11,12,13,14}. Since the observation of the spin–momentum locking properties with scanning tunneling microscopy and spinangleresolved photoemission spectroscopy (spinARPES)^{15,16}, a great deal of effort has been made to demonstrate various unique effects associated with this property, such as large spin polarization currents and large spin–orbit torque in the Bi_{2}Se_{3}based threedimensional TI^{17,18,19,20,21,22,23,24,25}. However, a major obstacle to the clean demonstration of the Edelstein/inverse Edelstein effects for the spin–momentum locked surface states is the presence of unavoidable bulk carriers which dominate the conduction in these Bi_{2}Se_{3}based threedimensional TI^{19,26}. Recently, SmB_{6}, a Kondo insulator, has been found to be a new type of TI based on transport measurements and ARPES^{27,28,29,30,31,32,33,34,35}. At temperatures below ∼3 K, the bulk states are insulating, and only surface carriers contribute to the conduction, as demonstrated by the previous surface Hall measurements^{30,31}.
Here, we report the spin injection into the surface states using the spin pumping and the observation of the inverse Edelstein effect in this topological Kondo insulator (TKI). The temperature and magnetic field angle dependences of the spin voltage are consistent with the spin–momentum locking properties of the surface states, which have been shown to be topological in previous studies^{29}.
Results
Spin injection into the surface states of SmB_{6}
The spin injection experiment is performed using Ni_{80}Fe_{20} (Py) as the spin injector, which is deposited onto the (001) surface of the SmB_{6} single crystals, as shown in Fig. 1a (see the ‘Methods’ for details). When the ferromagnetic resonance condition for Py is fulfilled under certain magnetic fields and microwave frequencies, the precessing magnetization launches a spin current, which enters the adjacent nonmagnetic SmB_{6} layer. This technique is called spin pumping, which has been widely used to measure the spin to charge conversion in various materials, including metals, semiconductors and graphene and so on^{36,37,38,39,40,41,42,43}. In our measurements, we use a radio frequency (RF) signal generator to provide the microwave power and standard lockin technique for better sensitivity and signaltonoise ratio (see the ‘Methods’ for details). Figure 1b shows the schematic drawing of energy dispersion relationship of the surface states at the Fermi level for both and Г points. The resistance of the SmB_{6} device is measured from 300 to ∼0.8 K, as shown in Fig. 1c. Clearly, the resistance saturates blow ∼3 K, which indicates that the surface states are dominant and the bulk states do not contribute to conduction. As the temperature increases, the resistance decreases quite rapidly, owing to a large number of the activated bulk carriers as the temperature increases.
Figure 1d shows the typical magnetic field dependence of the spin voltage measured at 1.7 K with three representative microwave frequencies of 8.3, 9.4 and 10.1 GHz, respectively. We first confirm that the magnetic fields, at which we observe the voltage signals, are the same as the resonance magnetic fields (H_{res}) of the Py under the same microwave frequencies (Supplementary Fig. 1 and Supplementary Note 1). It is noticed that there are mainly three contributions to the voltages, namely the voltage due to the spin pumping and inverse Edelstein effect (V_{SP}), the voltage due to the Seebeck effect from the microwave heating (V_{SE}) and the anomalous Hall effect (V_{AHE}) of the Py. Due to their different symmetries as a function of the magnetic field, we can obtain the voltage amplitudes of all these three contributions by fitting the magnetic field dependence of the voltage with the following equation (Supplementary Fig. 2 and Supplementary Note 2).
where V_{S} and V_{AS} are the voltage amplitudes for the symmetric and antisymmetric Lorentzian shapes, respectively, and ΔH is the halfline width. The V_{SP} exhibits a positive sign for positive magnetic fields and the positive sign of the spintocharge conversion in the surface states of the SmB_{6} is theoretically expected from the counterclockwise spin textures for the electron band of the topological surface states^{18,42}. The counterclockwise spin textures have been shown by both spinARPES measurements and DFT calculations^{34,44}. After the determination of H_{res} and ΔH for all applied microwave frequencies, we obtain the effective magnetization (M_{eff}) and the Gilbert damping constant for the Py layer. Our results show that M_{eff} is 781±16 e.m.u. cm^{−3}, which is obtained using the Kittel formula shown below^{45}:
where γ is the geomagnetic ratio. From the slope of the linearly fitted curve of the halfline width versus microwave frequency at 1.7 K, we calculate the Gilbert damping constant of the Py on SmB_{6} to be 0.0166±0.0006 (Supplementary Fig. 3).
The microwave power dependence of the spin voltage is shown in Fig. 2a measured at 1.7 K and with the microwave frequency of 10.1 GHz. The measured resonance peak increases as the microwave power increases. Following the same fitting procedure (Supplementary Note 2), we obtain the power dependence of V_{SP} and V_{SE}. Both V_{SP} and V_{SE} show a linear relationship with the microwave power, as shown in Fig. 2b,c.
Temperature dependence of the spin voltage
As mentioned earlier, the surface states of SmB_{6} dominate the transport as the bulk carriers freeze out below ∼3 K; above ∼3 K, the contribution from the bulk states is thermally activated. When a spin current enters the spin–momentum locked surface states, an electric field is resulted due to the inverse Edelstein effect, which is measured as a spin voltage. To investigate how the spin voltage evolves as the surface states emerge and become dominant, we perform the measurements from ∼0.8 to 10 K. Below ∼0.8 K, it is difficult to stabilize the temperature due to the microwave heating. Figure 3a shows the typical measurements of the voltage as a function of the magnetic field with the microwave power of 100 mW and frequency of 10.1 GHz at 0.84, 1.66, 2.1, 2.3 and 10 K, respectively. At 0.8 K, when only spin–momentum locked surface states exist, the spin signal is ∼42 nV. This value is relatively small compared with previous studies on Bi_{1.5}Sb_{0.5}Te_{1.7}Se_{1.3} and αSn (refs 18, 42), which could be related to the spin pumping efficiency and/or the spintocharge conversion efficiency and needs further studies (Supplementary Note 3). The spin voltage steadily decreases as the temperature increases, and when the temperature reaches 10 K, no voltage can be detected. The resistance of the SmB_{6} from 10 to ~0.8 K is shown in Fig. 3b, indicating that the bulk states start to contribute to the total conductance between 2 and 3 K. From 3 to 5 K, the conduction due to the bulk carriers quickly increases, resulting in a 100fold decrease in the total resistance. This feature is consistent with the previous surface conductance and Hall measurements, indicating the nearly pure surface states contributing to the conduction^{30,31}. The temperature dependence of the V_{SP} is summarized in Fig. 3c. V_{SP} shows little temperature dependence below ∼2.2 K. At temperatures above ∼2.2 K, V_{SP} steadily decreases as the temperature increases. The temperature dependences of both V_{SP} and the resistance strongly support that the spin signal originates from the spin–momentum locked surface states. When the spin polarization is generated in the surface states, an inplane electrical voltage is produced in the direction perpendicular to the spin directions, due to the inverse Edelstein effect. As the temperature further increases, more bulk carriers are activated and the spin voltage is greatly suppressed. This is very interesting, for the bulk states should have strong spin–orbit coupling as well and therefore ordinary inverse spin Hall effect from bulk states could give rise to a finite voltage. However, we do not observe any voltage signal at high temperatures.
Magnetic field angle dependence of the spin voltage
To further confirm the spin injection and detection in the surface states of the TKI, SmB_{6}, we study the inplane and outofplane spin polarization injection by changing the magnetic field direction. Figure 4a shows the typical results of the magnetic fielddependent voltages at 1.7 K with a microwave power of 200 mW and frequency of 10.1 GHz for the angles between the magnetic field and the Py electrode (shown in the inset figure), θ_{H}, equal to 0°, 63°, 76°, 83° and 86.5°. As θ_{H} increases, the resonance magnetic field increases accordingly, and in the meantime, the spin signal shows a decrease. At 86.5°, the spindependent voltage becomes vanishingly small. The H_{res} and ΔH as a function of θ_{H} are shown in Fig. 4b,c, which are consistent with the previous measurement of the ferromagnetic resonance of Py under different magnetic field directions^{37,46}. This further confirms that the measured spin voltage indeed arises from the precession of the Py magnetization.
Discussion
It is particularly interesting that only inplane spin polarization injection generates an electric field, whereas the outofplane spin polarization injection does not show this effect. This observation could be attributed to the spin–momentum locking properties of the surface states of the TKI, as illustrated in Fig. 5a,b. For the inplane spin polarization injection along the x direction, the Fermi surface shifts along the y direction, and Δk_{y} indicates the total shift due to the spin injection and the inverse Edelstein effect, as shown in Fig. 5a. On the other hand, for the outofplane spin polarization injection, there is no net effect of spin injection as the spins of the surface states lie inplane and are locked perpendicular to the momentum directions, as shown in Fig. 5b. Finally, we calculate the Py magnetization angle, θ_{M}, from the θ_{H} dependence of the resonance magnetic field (Supplementary Fig. 4) based on the 0 and 90 degrees data and the following equation^{37}.
where M_{S} is the saturated magnetization. It is clearly seen that V_{SP} almost vanishes as θ_{M} approaches 90 degrees (Fig. 5c), which is also consistent with the spin–momentum locking properties of the surface states of the TKI, as discussed above and illustrated in Fig. 5a,b. The complete understanding of the V_{SP} as a function of the θ_{M} needs future theoretical studies to quantitatively calculate how much the Fermi surface shift as a result of the inverse Edelstein effect of the spin polarization injection (Supplementary Fig. 5 and Note 4).
Our experimental results strongly support the demonstration of spin injection and the observation of the inverse Edelstein effect in the surface states of SmB_{6}. The temperature and magnetization angle dependences, as well as the sign of the spintocharge conversion are well consistent with spin–momentum locking properties of the surface states, which have been shown to be topological with the counterclockwise spin textures for the electron bands in previous studies^{29,34,44}. Since the detailed spin textures of the Rashba surface states have not been reported yet, it is premature to exclude any contribution from the Rashbasplit surface states at the current stage. To fully understand this, further studies, including the detailed spin textures from spinARPES measurements of the Rashba surface states and the quantitative theoretical calculations of the contributions from topological and Rashba surface states, are needed. Our observation could lead to future studies of the role of strong correlation in TKIs for spintronics and highly efficient spin current generation in the surface states of TIs via the materials design and engineering.
Methods
Materials growth
Highquality single crystalline SmB_{6} samples are grown using the conventional Alflux method. A mixture consisting of a Sm chunk (purity: 99.9%), Boron (purity: 99.99%) and Al powders (purity: 99.99%) with a ratio of 1:6:400 is heated at high temperatures in the circumstance with continuously flowing Ar gas to form SmB_{6} single crystals. Then the SmB_{6} samples are put into diluted HNO_{3} acid to remove the residual aluminum flux.
We choose the samples with large rectangular crystals of millimeters size and large (001) facet for spin injection experiment. A 20 nm thick Py electrode is deposited on the (001) surface of the SmB_{6} single crystal by radio frequency magnetron sputtering with a growth rate of 0.02 Å s^{−1}. To prevent the oxidation of Py, a capping layer of 3 nm Al is deposited in situ before taking the samples out.
Device fabrication
A shadow mask technique (size: ∼0.9 × 3 mm^{2}) is used to define the shape and position of the ferromagnetic electrode (Py/Al) on the (001) surface of the SmB_{6} crystal (size: ∼1 × 5 mm^{2}, thickness: ∼0.5 mm). Al wires are used to contact the two ends of SmB_{6} sample for the electrical voltage measurement.
Device measurement
The spin injection is performed using the spin pumping method and the spins are detected via the inverse Edelstein effect of the surface states of SmB_{6}. The microwave power is supplied by a signal generator (Anritsu LTD. MG3690C) modulated with a digital lockin amplifier (NF Co. LI5640) with the frequency of 373 Hz to enhance the sensitivity and signaltonoise ratio. The spin pumping measurement is performed by precessing the Py magnetization around its resonance conditions with a coplanar waveguide from 10 to ∼0.8 K in a Janis He3 system. The resistance of the SmB_{6} single crystal is measured using Keithley K2400 and K2002 in Quantum Design Physical Properties Measurement System (PPMS) from 300 to 10 K and in a Janis He3 system from 10 to ∼0.8 K.
Data availability
The authors declare that the data supporting the findings of this study are available within the paper and its Supplementary Information files.
Additional information
How to cite this article: Song, Q. et al. Spin injection and inverse Edelstein effect in the surface states of topological Kondo insulator SmB_{6}. Nat. Commun. 7, 13485 doi: 10.1038/ncomms13485 (2016).
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Acknowledgements
We acknowledge the fruitful discussions with Professor Fa Wang and the financial support from National Basic Research Programs of China (973 program Grant Nos. 2014CB920902, 2015CB921104 and 2013CB921903) and National Natural Science Foundation of China (NSFC Grant Nos. 11574006 and 11374020). D.Z., T.W. and X.H.C. acknowledge the financial support from the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB04040100). T.W. acknowledges Recruitment Program of Global Experts and CAS Hundred Talent Program. J.S. acknowledges the support by the DOE BES Award No. DEFG0207ER46351. W.H. acknowledges the support by the 1000 Talents Program for Young Scientists of China.
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Contributions
W.H. proposed and designed the experiment. Q.S. did the Py growth and fabricated the devices. Q.S. and J.M. performed the electrical measurements. J.M. and C.Z. developed the microwave techniques in the He3 refrigerator used for the measurements below 10 K in Professor Zhang’s group. Q.S. and W.H. analysed the data. D.Z., T.W. and X.H.C. provided the single crystalline SmB_{6} sample. W.H. wrote the manuscript. All the authors commented on the manuscript and contributed to its final version.
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Supplementary Figures 15, Supplementary Notes 14 and Supplementary References (PDF 2377 kb)
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Song, Q., Mi, J., Zhao, D. et al. Spin injection and inverse Edelstein effect in the surface states of topological Kondo insulator SmB_{6}. Nat Commun 7, 13485 (2016). https://doi.org/10.1038/ncomms13485
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DOI: https://doi.org/10.1038/ncomms13485
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