Abstract
Recently discovered relativistic spin torques induced by a lateral current at a ferromagnet/paramagnet interface are a candidate spintronic technology for a new generation of electrically controlled magnetic memory devices. The focus of our work is to experimentally disentangle the perceived two model physical mechanisms of the relativistic spin torques, one driven by the spinHall effect and the other one by the inverse spingalvanic effect. Here, we show a vector analysis of the torques in a prepared epitaxial transitionmetal ferromagnet/semiconductorparamagnet singlecrystal structure by means of the allelectrical ferromagnetic resonance technique. By choice of our structure in which the semiconductor paramagnet has a Dresselhaus crystal inversion asymmetry, the system is favourable for separating the torques due to the inverse spingalvanic effect and spinHall effect mechanisms into the fieldlike and antidampinglike components, respectively. Since they contribute to distinct symmetry torque components, the two microscopic mechanisms do not compete but complement each other in our system.
Introduction
The two considered microscopic origins of the relativistic spin torques observed at a ferromagnet/paramagnet interface^{1,2} have the following basic characteristics: in one picture, a spin current generated in the paramagnet via the relativistic spinHall effect^{3} (SHE) is absorbed in the ferromagnet and induces the spin transfer torque^{4} (STT). In the other picture, a nonequilibrium spindensity is generated via the relativistic inverse spingalvanic effect^{5} (ISGE) and induces the spin–orbit torque^{6,7,8} (SOT) in the ferromagnet. From the early observations in paramagnetic semiconductors, SHE and ISGE are known as companion phenomena that can both allow for electrically aligning spins in the same structure^{9,10,11}. It is therefore both challenging and desirable for our basic physical understanding of the spin torques at the ferromagnet/paramagnet interface to experimentally disentangle the SHE and ISGE contributions.
The splitting of the two microscopic mechanisms between the fieldlike and the antidampinglike torque components has not been previously achieved for several conceptual reasons. The original theoretical proposals^{12,13,14} and experimental observations^{10,11,15,16} of the ISGE were made in paramagnets with no ferromagnetic component in the structure. The corresponding nonequilibrium spin density, generated in the ISGE by inversionasymmetry terms in the relativistic Hamiltonian, has naturally no dependence on magnetization. Hence, in the context of magnetic semiconductors^{6,8,17,18} or ferromagnet/paramagnet structures^{1,7,19,20,21}, the ISGE may be expected to yield only the fieldlike component of the torque ~M × ζ, where the vector ζ is independent of the magnetization vector M (see Fig. 1a). However, when carriers experience both the spin–orbit coupling and magnetic exchange coupling, the inversion asymmetry can generate a nonequilibrium spin density component of extrinsic, scatteringrelated^{22,23} or intrinsic Berrycurvature^{24,25,26} origin, which is magnetization dependent and yields an antidampinglike torque ~M × (M × ζ). Experiments in (Ga,Mn)As confirmed the presence of the ISGEbased mechanism^{8,17,18} and demonstrated that the fieldlike and the Berrycurvature antidampinglike SOT components can have comparable magnitudes^{25}.
The STT is dominated by the antidampinglike component^{4} in weakly spin–orbitcoupled ferromagnets with τ_{ex}≪τ_{s}, where τ_{ex} is the precession time of the carrier spins in the exchange field of the ferromagnet and τ_{s} is the spin lifetime in the ferromagnet. This, in principle, applies also to the case when the spin current is injected to the ferromagnet from a paramagnet via the SHE (see Fig. 1b). However, at finite τ_{s}, the STT also acquires a fieldlike component^{4}. Experiments in W/Hf/CoFeB structures confirmed the presence of the SHEbased mechanism in the observed torques and showed that the SHE–STT can have both antidampinglike and fieldlike components of comparable magnitudes^{27}.
In the commonly studied polycrystalline transitionmetal ferromagnet/heavymetal paramagnet samples, the dependence of the torques on the angle of the driving inplane current also does not provide the direct means to disentangle the two microscopic origins. The lowestorder inversionasymmetry spin–orbit terms in the Hamiltonian have the Rashba form (see Fig. 1c) for which the vector ζ is in the plane parallel to the interface and perpendicular to the current, independent of the current direction. The same applies to the spin polarization of the SHE spin current propagating from the paramagnet to the ferromagnet. The M and ζ functional form of the fieldlike and antidampinglike SHE–STTs is the same as of the corresponding SOT components. In the observed lowestorder torque terms in Pt/Co and Ta/CoFeB structures^{28}, the ISGEbased and the SHEbased mechanism remained, therefore, indistinguishable. The simultaneous observation of higherorder torque terms in these samples pointed to SOTs due to structural inversionasymmetry terms beyond the basic Rashba model. From the Ta thickness dependence measurements in the Ta/CoFeB structure, it was concluded that in these samples both the ISGEbased and the SHEbased mechanisms contributed to both the fieldlike and the antidampinglike torques^{29}.
The SHE and ISGE were originally discovered in III–V semiconductors^{9,10,11,15,16} but for maximizing the relativistic spin torques in common transitionmetal ferromagnets, it turned out to be more suitable to interface them with the highly conductive heavymetal paramagnets such as Pt, Ta or W^{1,2,27,28,29}. To clearly separate the two microscopic origins of the torques, returning to III–V semiconductor paramagnets is instrumental as the leading inversionasymmetric term is played by the broken inversion symmetry in the crystal structure. Independent of the interface, holes in the strained zincblende lattice of a III–V semiconductor experience a linearinwavevector Dresselhaus spin–orbit coupling. The ISGE of the corresponding symmetry (see Fig. 1d) generated in the semiconductor should induce a SOT in an adjacent ferromagnetic film with ζ perpendicular to the current for current along [110] or crystal axes of the semiconductor, while ζ should be parallel to the current for the [100] or [010] current directions.
In the following, we measure the relativistic spin torques in a single crystal Fe (2 nm)/(Ga,Mn)As (20 nm) bilayer using an electrically induced and detected ferromagnetic resonance (FMR) technique^{18,30} (for growth details see Methods). We dope the GaAs host with ~3% of substitutional Mn_{Ga} acceptors to increase the semiconductor conductivity, while not providing a sizeable exchange splitting within the semiconductor at room temperature. From magnetization angle dependence measurements of the FMR voltages, we find the fieldlike and antidamping torques have similar magnitudes. By measuring devices where the current is along different crystal directions of the semiconductor, we show that the ISGE with a characteristic Dresselhaus symmetry induces only the fieldlike torque in the adjacent Fe, whereas the SHE spin current, generated inside the paramagnetic pdoped GaAs layer, is absorbed in the weakly spin–orbitcoupled Fe in the form of the antidampinglike STT. Therefore in this bilayer, we show that the ISGE and SHE mechanisms are separated into distinct symmetry components of the currentinduced torque.
Results
Electricallyinduced FMR measurements
Currentinduced torques were measured in patterned bars of width 10μm and length 200μm using an allelectrical FMR technique (see Fig. 2a). In this method, a microwave current flowing in the device induces FMR when the externally applied magnetic field matches the resonant condition. The resonance of the Fe magnetization is detected in the d.c. voltage induced across the bar, V_{d.c.}. This is due to the homodyne mixing of the microwave current with the oscillating component of magnetoresistance caused by the magnetization precession. In these measurements, we increase the microwave current coupled into the sample, with a typical resistance of 8 kΩ, using an impedance matching network^{30} (see Methods and Supplementary Note 1).
For a series of external magnetic field directions in the plane of the sample, FMR sweeps were recorded using a microwave frequency of close to 16 GHz. From the magnetization angle dependence of the resonance field, we obtained the magnetization amplitude value of μ_{0}M_{s}=1.85±0.03 T, which is close to the literature value of 1.7 T for Fe^{31}, and we found an inplane uniaxial anisotropy of μ_{0}H_{U}=0.101±0.001 T, which is typical for thin films of Fe grown on GaAs^{32}. By solving the Landau–Lifshitz–Gilbert equation for a small currentinduced excitation field, (h_{x}, h_{y}, h_{z})e^{jωt}, V_{d.c.} is found to be comprised of symmetric and antisymmetric Lorentzian functions with coefficients V_{sym} and V_{asy}, respectively. Here h_{x} is the excitation field component parallel to the current and h_{y} is the component perpendicular to the current. h_{z} is the component perpendicular to the plane of the bilayer. The coefficients depend on the angle, θ, of the magnetization vector relative to the current and are given by
Here, V_{mix} is the sensitivity of the mixing detection and is given by , where I_{0} (e^{jωt}, 0, 0) is the microwave current in the device and ΔR is the coefficient of the anisotropic magnetoresistance of the sample. A_{yy} and A_{yz} are the diagonal and offdiagonal components of the a.c. magnetic susceptibility, which depend on the magnetic anisotropies and Gilbert damping of the sample. In our devices, ΔR is typically 17 Ω which, assuming Fe carries the majority of the current in the bilayer, is consistent in sign and magnitude with literature values of 0.2% anisotropic magnetoresistance in Fe^{33}. We estimate the proportion of total bilayer current in the Fe layer to be 79% by resistance measurements of Hall bars before and after removing the Fe and capping Al (see Supplementary Note 2).
FMR measurements were made using devices patterned in four crystal directions. The microwave power for all devices, incident on the impedance matching network, was 24 dBm. For each angle, the resonances were fitted by symmetric and antisymmetric Lorentzian functions. A typical curve is shown in Fig. 2b. The inplane uniaxial magnetic anisotropy of Fe implies that, in general, the magnetization does not lie along the external field. The actual magnetization angles and uniaxial anisotropy are selfconsistently calculated from the dependence of the resonant field on the external magnetic field angle^{34}. This also allows the susceptibilities, A_{yz} and A_{yy}, to be calculated. The magnetization angle dependence of V_{sym}/A_{yz} and V_{asy}/A_{yy} is plotted in Fig. 2c for a bar patterned in the [010] crystal direction. The full expression for the angle dependence of the fitted data is given in Supplementary Note 3.
Validity of FMR analysis
Our analysis of the currentinduced torques using equation (1) is not necessarily valid if the torques do not act in phase with the microwave current. In comparison with electrically detected FMR measurements where the microwave current is capacitively or inductively coupled into the sample^{35}, we do not expect a phaseshift between the microwave current and induced fields as the current is conducted ohmically. Nevertheless, we might worry that some part of our microwave resonator circuit leads to a phase shift. To test this, we repeated our measurements with a [100] device over a frequency range (11.8–14.4 GHz) using a microstrip resonator with a fundamental frequency close to 13 GHz (Fig. 3a). If there were some frequencydependent phase shift, we would expect the lineshape to oscillate between an antisymmetric and symmetric Lorentzian over this frequency range. However, the ratio of V_{sym} to V_{asy} remains constant in this frequency range to within experimental error (Fig. 3b), confirming that our analysis is correct.
Analysis of the currentinduced torques
As shown in Fig. 4a, the inplane currentinduced field depends strongly on the crystal direction of the current and can be well fitted by the Dresselhaus symmetry ISGE field, h^{ISGE}~(cos 2φ_{[100]}, −sin 2φ_{[100]}, 0), where φ_{[100]} is the angle between the current and the [100] crystal direction. This is the expected symmetry of the currentinduced nonequilibrium spin polarization of carriers in the semiconductor due to the inversionasymmetric crystal structure of the strained zincblende lattice of (Ga,Mn)As. The interface exchange coupling of these polarized carriers with the adjacent Fe moments induces the fieldlike SOT in Fe with the Dresselhaus symmetry. We note that other torque terms with the symmetry common to the Rashba ISGE, the fieldlike component of the SHE–STT or the torque due to an Oersted field have only a minor contribution to the total measured fieldlike torque.
To highlight that carriers in the semiconductor layer are responsible for the Dresselhaus symmetry ISGE field, we compare Fig. 4a with previous measurements in which the inplane currentinduced fields were measured in a bare (Ga,Mn)As epilayer^{25} without the Fe film. To observe the corresponding SOT in this sample, a larger concentration of magnetic Mn moments was used, and the measurements were performed at low temperatures where the Mn moments are ferromagnetic in equilibrium. Instead of the interfacial exchange coupling to Fe, the currentinduced nonequilibrium spin polarization of carriers in the semiconductor due to the Dresselhaus symmetry ISGE is exchangecoupled directly to the ferromagnetic moments on which it exerts the fieldlike SOT. In both the Fe/(Ga,Mn)As and the (Ga,Mn)As samples the same crystalsymmetry fieldlike SOT is observed, which confirms their common Dresselhaus ISGE origin.
In contrast to the inplane field, the outofplane currentinduced field is independent of the crystal direction of the current but depends on the magnetization angle. It is dominated by a term h^{SHE}~M × y (y is the direction transverse to the current), which generates the antidampinglike torque. As shown in Fig. 4b, the amplitudes of the fieldlike and antidampinglike torques are comparable in our Fe/(Ga,Mn)As structure. The underlying microscopic mechanism of the antidamping component can only be of the SHE–STT origin. The experimental error shown in Fig. 4b is greater than any crystaldependent variation in the spinHall angle.
In previous measurements in the bare (Ga,Mn)As epilayer^{25}, the antidampinglike SOT was dominated by the counterpart microscopic mechanism to the Dresselhaus ISGE. This Dresselhaussymmetry antidampinglike SOT is clearly missing in our measured data. It is suppressed in our Fe/(Ga,Mn)As structure by design, because carriers in the semiconductor are not sufficiently magnetized at equilibrium due to the low Mn moment density and high temperature of the experiment. In principle, one might also consider that the spin accumulation induced by the Dresselhaus ISGE could cause a diffusive spin current to flow into the ferromagnet and exert an antidampinglike STT. This would have the Dresselhaus symmetry that is, however, not seen in our antidampinglike torque data.
A Rashbasymmetry antidampinglike SOT due to the carriers in the Fe experiencing the inversion asymmetry of the interface could in principle also explain the symmetry of our data; however, we do note the lack of a corresponding strong Rashbasymmetry fieldlike SOT. This antidamping SOT would have the same symmetry as the antidamping SHE–STT. This possibility is, however, ruled out by our control experiment in which we perform electrically detected FMR in a similar molecular beam epitaxygrown Fe (1 nm)/insulating GaAs structure at room temperature. In this case, we do not observe the antidamping torque in the rectification effect, despite the sample possessing a similar magnetoresistance ratio (~0.2%) to our Fe/(Ga,Mn)As. This is consistent with the carriers being removed from the semiconductor, which eliminates the SHE source of the spin current. We note that also consistently with the absence of carriers in the semiconductor in the Fe/insulating GaAs structure, we do not observe the Dresselhaussymmetry fieldlike SOT in this control sample.
Determining the magnitudes of the ISGE and SHE
To calibrate the microwave current in the sample we used a bolometric technique (see Supplementary Fig. 1 and Supplementary Note 4). Using this calibration, we estimate amplitudes of μ_{0}h^{ISGE}/J_{GaAs}=16±10 μT per 10^{6} A cm^{−2} and μ_{0}h^{SHE}/J_{GaAs}=20±9 μT per 10^{6} A cm^{−2}. The error is found from the statistical variation of all of the devices measured. To verify the bolometric calibration, we also perform an additional check with a single device by measuring the change in Qfactor of the microstrip resonator loaded with and without a sample (see Supplementary Figs 2 and 3 and Supplementary Note 5). This calibration yields values of μ_{0}h^{ISGE}/J_{GaAs}=37 μT per 10^{6} A cm^{−2} and μ_{0}h^{SHE}/J_{GaAs}=47 μT per 10^{6} A cm^{−2}, close to the values of the bolometric technique.
From the measured h^{SHE} in our Fe/(Ga,Mn)As structure we can infer the roomtemperature spinHall angle, θ_{SH}, in the paramagnetic (Ga,Mn)As using the expression based on the antidampinglike STT^{2},
Here it is assumed that the thickness of the semiconductor is much larger than its spin diffusion length (5.6 nm in pGaAs^{36}) and d_{Fe} is the thickness of the Fe layer. Equation (2) yields values of θ_{SH}=1.7±0.9% (bolometric calibration) and 4% (Qfactor calibration), similar to spinHall angles previously reported for carriers with a porbital character in GaAs^{36,37}. This agreement with previously measured spinHall angles is further evidence that the antidampinglike torque does not have a significant Rashbasymmetry SOT contribution. To check these spinHall values, we compare our torque efficiencies in terms of field per total current density with those of transition metal/ferromagnet bilayers. For instance, Garello et al.^{28} measured an antidampinglike torque of μ_{0}h/J=690 μT per 10^{6} A cm^{−2} in layers with 0.6 nm Co and 3 nm Pt and an equivalent spinHall angle of 16%. Although our spinHall angle is only 4–8 times smaller, the field per total current density is 85–170 times smaller because the total magnetic moment of our Fe layer is ~4 times higher than of the Co and ~80% of the total current is shunted through the Fe.
To conclude, we have experimentally disentangled the two archetype microscopic mechanisms that can drive relativistic currentinduced torques in ferromagnet/paramagnet structures. In our epitaxial Fe/(Ga,Mn)As bilayer we simultaneously observed ISGEbased and SHEbased torques of comparable amplitudes. Designed magnetizationangle and currentangle symmetries of our singlecrystal structure allowed us to split the two microscopic origins between the fieldlike and the antidampinglike torque components. Experimentally establishing the microscopic physics of the relativistic spin torques should stimulate both the fundamental and applied research of these intriguing and practical spintronic phenomena.
Methods
Thinfilm growth
To obtain measurable torques in a metalferromagnet/semiconductorparamagnet structure requires at least partially matched conductances of the semiconductor and metal layers, which we achieved by doping a GaAs host with ~3% of substitutional Mn_{Ga} acceptors. Mn allows us to achieve this exceptionally high chargedoping. The semiconductor (Ga,Mn)As layer of thickness 20 nm was deposited on a GaAs(001) substrate by molecular beam epitaxy at a temperature of 260 °C. The substrate temperature was then reduced to 0 °C, before depositing a 2nm Fe layer, plus a 2nm Al capping layer without breaking vacuum. In situ reflection highenergy electron diffraction and ex situ Xray reflectivity and diffraction measurements confirmed that the layers are single crystalline with subnm interface roughness.
Impedance matching
To improve the sensitivity of the FMR measurement, the sample is embedded in a microstrip resonator circuit^{30}, which acts to impedance match the ~8kΩ sample to the external 50Ω transmission line at the fundamental frequency (in this case ~8 GHz) or harmonic frequencies of the resonator (see Supplementary Note 1). To allow measurement of V_{d.c.}, the resonator contains an onboard biasT. In this experiment, FMR measurements are made at the the 2nd harmonic frequency of the resonator (~16 GHz).
Additional information
How to cite this article: Skinner, T. D. et al. Complementary spinHall and inverse spingalvanic effect torques in a ferromagnet/semiconductor bilayer. Nat. Commun. 6:6730 doi: 10.1038/ncomms7730 (2015).
References
 1
Miron, I. M. et al. Perpendicular switching of a single ferromagnetic layer induced by inplane current injection. Nature 476, 189–193 (2011) .
 2
Liu, L. et al. Spintorque switching with the giant spin hall effect of tantalum. Science 336, 555–558 (2012) .
 3
Jungwirth, T., Wunderlich, J. & Olejnk, K. Spin hall effect devices. Nat. Mater. 11, 382–390 (2012) .
 4
Ralph, D. & Stiles, M. D. Spin transfer torques. J. Magn. Magn. Mater. 320, 1190–1216 (2008) .
 5
Ivchenko, E. & Ganichev, S. in Spin Physics in Semiconductors (ed Dyakonov, M. I.) Ch. 9 Springer (2008) .
 6
Bernevig, B. A. & Vafek, O. Piezomagnetoelectric effects in pdoped semiconductors. Phys. Rev. B 72, 033203 (2005) .
 7
Manchon, A. & Zhang, S. Theory of nonequilibrium intrinsic spin torque in a single nanomagnet. Phys. Rev. B 78, 212405 (2008) .
 8
Chernyshov, A. et al. Evidence for reversible control of magnetization in a ferromagnetic material by means of spinorbit magnetic field. Nat. Phys. 5, 656–659 (2009) .
 9
Kato, Y. K., Myers, R. C., Gossard, A. C. & Awschalom, D. D. Observation of the spin Hall effect in semiconductors. Science 306, 1910–1913 (2004) .
 10
Kato, Y., Myers, R. C., Gossard, A. C. & Awschalom, D. D. Current induced electron spin polarization in strained semiconductors. Phys. Rev. Lett. 93, 176601 (2004) .
 11
Wunderlich, J., Kaestner, B., Sinova, J. & Jungwirth, T. Experimental observation of the spin Hall effect in a two dimensional spinorbit coupled semiconductor system. Phys. Rev. Lett. 94, 047204 (2005) .
 12
Aronov, A. G. & LyandaGeller, Y. B. Nuclear electric resonance and orientation of carrier spins by an electric field. JETP Lett. 50, 431 (1989) .
 13
Edelstein, V. M. Spin polarization of conduction electrons induced by electric current in twodimensional asymmetric electron systems. Solid State Commun. 73, 233–235 (1990) .
 14
Mal'shukov, A. G. & Chao, K. A. Optoelectric spin injection in semiconductor heterostructures without a ferromagnet. Phys. Rev. B 65, 241308 (2002) .
 15
Silov, A. Y. et al. Currentinduced spin polarization at a single heterojunction. Appl. Phys. Lett. 85, 5929–5931 (2004) .
 16
Ganichev, S. D. et al. Can an electric current orient spins in quantum wells? Preprint at http://arxiv.org/abs/condmat/0403641 (2004) .
 17
Endo, M., Matsukura, F. & Ohno, H. Current induced effective magnetic field and magnetization reversal in uniaxial anisotropy (Ga,Mn)As. Appl. Phys. Lett. 97, 222501 (2010) .
 18
Fang, D. et al. Spinorbit driven ferromagnetic resonance: a nanoscale magnetic characterisation technique. Nat. Nanotechnol. 6, 413–417 (2011) .
 19
Miron, I. M. et al. Currentdriven spin torque induced by the Rashba effect in a ferromagnetic metal layer. Nat. Mater. 9, 230–234 (2010) .
 20
Pi, U. H. et al. Tilting of the spin orientation induced by Rashba effect in ferromagnetic metal layer. Appl. Phys. Lett. 97, 162507 (2010) .
 21
Suzuki, T. et al. Currentinduced effective field in perpendicularly magnetized Ta/CoFeB/MgO wire. Appl. Phys. Lett. 98, 142505 (2011) .
 22
Pesin, D. A. & MacDonald, A. H. Quantum kinetic theory of currentinduced torques in rashba ferromagnets. Phys. Rev. B 86, 014416 (2012) .
 23
Wang, X. & Manchon, A. Diffusive spin dynamics in ferromagnetic thin films with a Rashba interaction. Phys. Rev. Lett. 108, 117201 (2012) .
 24
Garate, I. & MacDonald, A. H. Influence of a transport current on magnetic anisotropy in gyrotropic ferromagnets. Phys. Rev. B 80, 134403 (2009) .
 25
Kurebayashi, H. et al. An antidamping spinorbit torque originating from the berry curvature. Nat. Nanotechnol. 9, 211–217 (2014) .
 26
Freimuth, F., Blügel, S. & Mokrousov, Y. Spinorbit torques in Co/Pt(111) and Mn/W(001) magnetic bilayers from first principles. Phys. Rev. B 90, 174423 (2014) .
 27
Pai, C. et al. Enhancement of perpendicular magnetic anisotropy and transmission of spinhalleffectinduced spin currents by a Hf spacer layer in W/Hf/CoFeB/MgO layer structures. Appl. Phys. Lett. 104, 082407 (2014) .
 28
Garello, K. et al. Symmetry and magnitude of spinorbit torques in ferromagnetic heterostructures. Nat. Nanotechnol. 8, 587–593 (2013) .
 29
Kim, J. et al. Layer thickness dependence of the currentinduced effective field vector in TaCoFeBMgO. Nat. Mater. 12, 240–245 (2013) .
 30
Fang, D. et al. Electrical excitation and detection of magnetic dynamics with impedance matching. Appl. Phys. Lett. 101, 182402 (2012) .
 31
Danan, H., Herr, A. & Meyer, A. J. P. New determinations of the saturation magnetization of nickel and iron. J. Appl. Phys. 39, 669–670 (1968) .
 32
Brockmann, M., Zolfl, M., Miethaner, S. & Bayreuther, G. Inplane volume and interface magnetic anisotropies in epitaxial Fe films on GaAs(001). J. Magn. Magn. Mater. 198199, 384–386 (1999) .
 33
McGuire, T. & Potter, R. Anisotropic magnetoresistance in ferromagnetic 3d alloys. IEEE Trans. Magn. 11, 1018–1038 (1975) .
 34
Ando, K. et al. Angular dependence of inverse spinHall effect induced by spin pumping investigated in a NiFe/Pt thin film. Phys. Rev. Lett. 78, 014413 (2008) .
 35
Harder, M., Cao, Z. X., Gui, Y. S., Fan, X. L. & Hu, C. M. Analysis of the line shape of electrically detected ferromagnetic resonance. Phys. Rev. B 84, 054423 (2011) .
 36
Chen, L., Matsukura, F. & Ohno, H. Directcurrent voltages in (Ga,Mn)As structures induced by ferromagnetic resonance. Nat. Commun. 4, 2055 (2013) .
 37
Okamoto, N. et al. Electric control of the spin hall effect by intervalley transitions. Nat. Mater. 13, 932–937 (2014) .
Acknowledgements
We acknowledge support from the EU European Research Council advanced grant no. 268066, from the Ministry of Education of the Czech Republic grant no. LM2011026, from the Grant Agency of the Czech Republic grant no. 1437427G and the Academy of Sciences of the Czech Republic Praemium Academiae. A.J.F. acknowledges support from a Hitachi research fellowship. H.K. acknowledges financial support from the Japan Science and Technology Agency.
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K.O., R.P.C., B.L.G. and H.K. grew the materials. K.O. and H.K. prepared the samples. T.D.S., L.K.C. and H.K. performed the experiments and T.D.S. analysed the data. T.D.S., T.J. and A.J.F. prepared the manuscript. T.D.S. and A.J.F. planned the project.
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Correspondence to T. D. Skinner or A. J. Ferguson.
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Supplementary Figures 13, Supplementary Table 1, Supplementary Notes 15 and Supplementary References (PDF 295 kb)
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Skinner, T., Olejník, K., Cunningham, L. et al. Complementary spinHall and inverse spingalvanic effect torques in a ferromagnet/semiconductor bilayer. Nat Commun 6, 6730 (2015). https://doi.org/10.1038/ncomms7730
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