Abstract
The generation, manipulation and detection of spinpolarized electrons in lowdimensional semiconductors are at the heart of spintronics. Pure spin currents, that is, fluxes of magnetization without charge current, are quite attractive in this respect. A paradigmatic example is the spin Hall effect, where an electrical current drives a transverse spin current and causes a nonequilibrium spin accumulation observed near the sample boundary^{1,2}. Here we provide evidence for an another effect causing spin currents which is fundamentally different from the spin Hall effect. In contrast to the spin Hall effect, it does not require an electric current to flow: without bias the spin separation is achieved by spindependent scattering of electrons in media with suitable symmetry. We show, by freecarrier absorption of terahertz (THz) radiation, that spin currents flow in a wide range of temperatures. Moreover, the experimental results provide evidence that simple electron gas heating by any means is already sufficient to yield spin separation due to spindependent energyrelaxation processes.
Main
Scattering of electrons involves a transition from a state with wavevector k to a state with wavevector k′ which is usually considered to be spinindependent. However, in gyrotropic media, for example, GaAs quantum wells (QWs) or heterojunctions, spin–orbit interaction adds an asymmetric spindependent term to the scattering probability. The asymmetric spindependent scattering matrix element is linear in wavevector k and the Pauli spin matrices σ (note, that in fact all terms odd in k, including kcubic terms, may also contribute to spindependent asymmetric scattering). Microscopically, this term is caused by structural inversion asymmetry (SIA) and/or bulk inversion asymmetry. Although the asymmetry of electron scattering can cause spin currents to flow, it does not modify the energy spectrum.
A process actuating spin separation is illustrated in Fig. 1a and involves Drude absorption of radiation. Drude absorption is caused by indirect intraband optical transitions and includes a momentum transfer from phonons or impurities to electrons to satisfy momentum conservation. Figure 1a shows the process of Drude absorption via virtual states for a spinup subband (s=+1/2, left panel) and a spindown subband (s=−1/2, right panel) of a QW containing a twodimensional electron gas (2DEG). Vertical arrows indicate optical transitions from the initial state k_{x}=0, whereas the horizontal arrows describe an elastic scattering event to a final state with either positive or negative electron wavevector k′_{x}. Although, for simplicity, we have only drawn transitions starting from k_{x}=0, the argument holds for arbitrary k_{x}. Owing to the spin dependence of scattering, transitions to positive and negative k′_{x} states occur with different probabilities. This is indicated by horizontal arrows of different thickness. As the asymmetric part of electron scattering is proportional to components of [σ×k′], probabilities for scattering to positive or negative k′_{x} are inverted for spindown and spinup subbands (note that we assumed k_{x}=0, and the presence of SIA alone). Similarly, relaxation of excited carriers is also asymmetric as is shown in Fig. 1b. As the latter mechanism only causes a polarizationindependent background signal in the experiments discussed below, the discussion will first focus on the mechanism shown in Fig. 1a.
The asymmetry causes an imbalance in the distribution of photoexcited carriers for s=±1/2 subbands between positive and negative k′_{x} states. This in turn yields electron flows i_{±1/2} within each spin subband^{3}. However, the charge currents, j_{+}=ei_{1/2} and j_{−}=ei_{−1/2}, where e is the electron charge, have opposite directions because i_{+1/2}=−i_{−1/2} and therefore cancel each other. Nevertheless, a spin current J_{spin}=(1/2)(i_{+1/2}−i_{−1/2}) is generated because electrons with spinup and spindown move in opposite directions. This leads to a spatial spin separation and spin accumulation at the edges of the sample.
By applying a magnetic field that polarizes spins, the spin current is detected as charge current. In a spinpolarized system, the two fluxes i_{±1/2}, which are proportional to the spinup and spindown free carrier densities, n_{±1/2}, cease compensating each other and yield a net electric current where S=(1/2)(n_{+1/2}−n_{−1/2})/(n_{+1/2}+n_{−1/2}) is the magnitude of the average spin. An external magnetic field, B, results in different populations of the two spin subbands due to the Zeeman effect. In equilibrium, the average spin is given by Here g is the electron effective g factor, μ_{B} is the Bohr magneton, is the characteristic electron energy being equal to the Fermi energy ɛ_{F}, or to the thermal energy k_{B}T, for a degenerate or a nondegenerate 2DEG, respectively.
To demonstrate the existence of spin currents due to asymmetric scattering we carry out the following experiments. Drude absorption is achieved using linearly polarized terahertz radiation directed along the growth direction of (001)oriented heterostructures. The equilibrium spin polarization is obtained by an inplane magnetic field B, which shifts the two parabolas of Fig. 1a vertically by ±gμ_{B}B/2. The photocurrent is measured both perpendicular and parallel to the magnetic field. Our setup excludes other effects known to cause photocurrents: because linearly polarized radiation is used, all helicitydependent spin photocurrents, such as the spingalvanic effect^{4} and the circular photogalvanic effect^{5}, are absent. In addition, photon drag and the linear photogalvanic effect are forbidden by symmetry for normal incidence on (001) heterostructures^{6}.
The experiments are carried out on both (001)oriented ntype GaAs/AlGaAs and InAs/AlGaSb twodimensional structures grown by molecular beam epitaxy. The parameters of the samples are given in Table 1. Two pairs of ohmic contacts at the centre of the sample edges and lying along the and y∥[110] directions have been prepared to measure the photocurrent (see Fig. 2b, inset). A highpower THz laser has been used to deliver 100 ns pulses with radiation power P up to 1 kW. Several wavelengths between 77 and 496 μm have been selected using NH_{3},D_{2}O and CH_{3}F as active media^{6}. The samples are irradiated under normal incidence. The THz radiation causes indirect optical transitions within the lowest sizequantized subband. In the experiment, the angle α between the polarization plane of the light and the x axis is varied (see Fig. 3, upper panel inset). The external magnetic field with a maximum strength of B=0.6 T is applied parallel to the heterojunction interface along the [110] direction. The photocurrent in unbiased devices is measured via the voltage drop across a 50 Ω load resistor in a closed circuit with a storage oscilloscope. The measured current pulses of 100 ns duration reflect the corresponding laser pulses.
Irradiation of the samples at B=0 does not lead—as expected—to any current. A photocurrent response is obtained only when B is applied. As described by equations (1) and (2) the current increases linearly with B_{y} due to the increasing spin polarization and changes sign on reversal of B. Corresponding data will be discussed below. The temperature and polarization dependences of the current were measured in all samples for two directions: along and perpendicular to the inplane magnetic field. Figure 2 shows the typical temperature dependence of the photocurrent. Although the photocurrent is constant at low temperatures, it decreases as 1/T at temperatures above 100 K. As we show below, the peculiar temperature dependence is direct evidence that the current is driven by the spin polarization given by equation (2).
Before we discuss the corresponding microscopic origin in more detail we present the polarization dependences of the current perpendicular (Fig. 3, upper panel) and parallel (Fig. 3, lower panel) to B_{y}. The polarization dependence of the current j can be fitted by j_{x}=j_{1}cos2α+j_{2} for the transverse geometry and by j_{y}=j_{3}sin 2α for the longitudinal geometry. The overall polarization dependences of the photocurrent remain the same, independent of temperature and wavelength. An increased wavelength at constant intensity only results in an increased signal strength. The wavelength dependence for both configurations is described by j∝λ^{2} for the wavelengths used (see Fig. 3, lower panel inset) and reflects the spectral behaviour of Drude absorption, η(ω)∝1/ω^{2} at ωτ_{p}≫1 (see ref. 7). Here η(ω) is the 2DEG’s absorbance at frequency ω and τ_{p} is the momentum relaxation time.
The fact that an offset j_{2} is only observed for the transverse geometry is in accordance with the phenomenological theory of magneticfieldinduced photocurrents^{8}. For normal incidence, the current components are described by where I and e are the light intensity and polarization vector, respectively. The parameters C_{1} to C_{3} are coefficients determined by the C_{2v} symmetry, relevant for (001)oriented structures. The polarizationindependent offset is described by the second term on the righthand side of equation (3) and is only present for the transverse geometry. The only visible consequence of this contribution is the offset of j_{x} in the upper panel of Fig. 3. The other terms on the righthand sides of equations (3) and (4) yield polarization dependences in full agreement with experiments.
All experimental features, that is, the temperature and polarization dependences, are driven by the spin degree of freedom: for fixed polarization, the current is proportional to the frequencydependent absorbance η(ω), momentum relaxation time τ_{p}, light intensity I and average spin S: j∝η(ω)Iτ_{p}S. This type of expression for the temperature dependence is valid for fixed scattering mechanisms, for example, phonon or impurity scattering. To corroborate this claim and to obtain the polarization dependence microscopically, we calculated the magnetoinduced photocurrent for impurity scattering within the framework of a spindensity matrix. The scatteringasymmetryinduced contribution to the photocurrents is given by
Here v_{k}=ħk/m^{*} is the electron velocity, ħ is the reduced Planck constant, m^{*} is the effective electron mass, δf_{sk} is the fraction of the carrier distribution function stemming from optical transitions in the spin subband s, M_{sk,sk′} is the matrix element of the indirect optical transition, f_{sk} is the equilibrium distribution function, ɛ_{k}=ħ^{2}k^{2}/2m^{*} is the electron kinetic energy for inplane motion and s is an index enumerating subbands with spin states ±1/2 along the direction of the external magnetic field. To first order in spin–orbit interaction, the compound matrix element for the indirect optical transitions via impurity scattering has the form^{9} Here A=Ae is the vector potential of the electromagnetic wave, c is the speed of light and V_{kk′} is the scattering matrix element given by^{10} where the term V_{0} describes the conventional spinindependent scattering and the term proportional to the secondrank pseudotensor V_{αβ} yields the asymmetric spindependent contribution linear in k responsible for the effects described here. The first term on the righthand side of equation (6) describes transitions involving virtual intermediate states in the conduction band, whereas the second term corresponds to transitions via virtual intermediate states in the valence band.
For C_{2v} pointgroup symmetry there are only two nonzero components of the tensor V_{αβ}: V_{xy} and V_{yx}. By using equations (5)–(7), an expression for the electric current j can be derived. We consider the freecarrier absorption to be accompanied by electron scattering from shortrange static defects and assume therefore that the matrix element V_{0} and the coefficients V_{αβ} are wavevector independent. As in experiments, we consider linearly polarized light at normal incidence and an inplane magnetic field B_{y} resulting in an average spin S_{y}. Then, currents parallel and perpendicular to the magnetic field can be written as where the photon energy ħω is assumed to be smaller than the characteristic energy . Note that the polarizationindependent part of equation (3) is missing here as our theory does not contain the relaxation process (Fig. 1b), which is responsible for the background signal of j_{x} in the upper panel of Fig. 3.
Equations (8) and (9) contain the polarization dependence for transverse and longitudinal orientation, respectively, given by The observed polarization dependences are in full agreement with equations (8)–(10) (see fits in Fig. 3). Note that the polarization dependence of j_{x} and j_{y} is independent of temperature and wavelength. It is solely described by equations (3) and (4) and does not depend on the specific scattering mechanism of Drude absorption.
However, the different scattering mechanisms involved in Drude absorption are reflected in the temperature dependence of the photocurrent shown in Fig. 2. Although impurity scattering prevails at low temperatures, phonon scattering takes over for T>100 K and is then the dominant scattering mechanism^{11}. For temperatures up to ≈25 K the current is constant. As for Drude absorption, η(ω)∝n_{s}/τ_{p} at ωτ_{p}≫1 (see ref. 7) and at low temperatures S∝1/ɛ_{F}∝1/n_{s} (see equation (2)), the current j/I∝τ_{p}η(ω)S is constant and independent of τ_{p} and n_{s}. In further experiments we changed the carrier density at 4.2 K by visible and nearinfrared light. For sample 1, for example, the carrier density (mobility) increases from 1.3×10^{11} cm^{−2} (1.7×10^{6} cm^{2} V^{−1}s^{−1}) to 3.0×10^{11} cm^{−2} (4.1×10^{6} cm^{2} V^{−1}s^{−1}) after illumination at low T. Although both n_{s} and τ_{p} increase by a factor of 2, the photocurrent remains unchanged, thus confirming the above arguments. In addition, for T> 100 K the carrier density n_{s} is roughly constant but S is now sufficiently well described by the Boltzmann distribution and hence S∝1/k_{B}T, see equation (2). Therefore, the current j is proportional to n_{s}/T and becomes temperature dependent, concordant with experiment. Fits to the data at low and high T are shown as solid lines in Fig. 2. The unusual temperature dependence of j_{x} proves that the current is driven by the average spin (equations (1) and (2)). As shown in Fig. 2c, it is uncorrelated to the T dependence of the mobility, which dominates the resistance of our samples. In the intermediate range between 25 and 100 K, such simple analysis fails. There the scattering mechanism changes from impurity dominated to phonon dominated. This transition region has not yet been treated theoretically and is outside the scope of this letter.
The experiments, carried out on different samples, are summarized in Fig. 4. Using the setup shown in the upper panel in Fig. 3 for two fixed polarization directions, α=0^{∘} and 90^{∘}, we obtain a linear increase of the corresponding photocurrent, shown in the upper panel of Fig. 4. By subtracting and adding the currents of both polarizations, the coefficients j_{1} (polarizationdependent amplitude) and j_{2} (polarizationindependent background) can be extracted. Corresponding results of j_{1} (lower left panel) and j_{2} (lower right panel) for four different samples are shown. Owing to the larger g factor of sample 4 (InAs QW), causing larger average spin S, the currents are largest for this sample. The other three samples are GaAsbased heterostructures that differ in structural inversion asymmetry. Sample 1 is a heterojunction (see Table 1) which, owing to the triangular confinement potential, is expected to have the strongest SIA contribution. Samples 2 and 3 are QWs of the same width, asymmetrically and symmetrically modulation doped, with larger and smaller SIA strength, respectively. The fact that with decreasing strength of the SIA coupling coefficient (from samples 1–3) the currents become smaller is in excellent agreement with our picture of asymmetricscatteringdriven currents. The coupling strength constant controls the current via V_{αβ} in equations (8) and (9) and equivalent expressions for other scattering mechanisms: the larger the coupling strength, the larger the effect of asymmetric scattering.
Finally, we would like to address the role of spindependent relaxation, shown in Fig. 1b. The absorption of radiation leads to electron gas heating. Owing to the spindependent asymmetry of scattering, energy relaxation rates for positive and negative k_{x} are nonequal as indicated by bent arrows of different thickness and spin currents result. Like for Drude excitation, spin separation takes place and applying a magnetic field results in a net electric current. As indicated in Fig. 1a,b excitation and relaxationinduced currents flow in opposite directions. Experimentally this is observed for all samples: j_{1} and j_{2} for each sample have consistently opposite signs.
In summary, we emphasize that all central experimental features of the terahertz photocurrent, namely, magnetic field, temperature, mobility and concentration dependences provide evidence that the observed effect is solely determined by the spin degree of freedom. Furthermore, our observations suggest that heating the electron gas by any means (microwaves, voltage and so on) is sufficient to generate spin currents. Our results demonstrate that spindependent scattering provides a new tool for spin manipulation.
References
 1.
Kato, Y., Myers, R. C., Gossard, A. C. & Awschalom, D. D. Observation of the spin Hall effect in semiconductors. Science 306, 1910–1913 (2004).
 2.
Wunderlich, J., Kaestner, B., Sinova, J. & Jungwirth, T. Experimental observation of the spinHall effect in a twodimensional spinorbit coupled semiconductor system. Phys. Rev. Lett. 94, 047204 (2005).
 3.
Tarasenko, S. A. & Ivchenko, E. L. Pure spin photocurrents in lowdimensional structures. Pis’ma Zh. Eksp. Teor. Fiz. 81, 292–296 (2005) ibid. JETP Lett. 81, 231–235 (2005).
 4.
Ganichev, S. D. et al. Spingalvanic effect. Nature 417, 153–156 (2002).
 5.
Ganichev, S. D. et al. Conversion of spin into directed electric current in quantum wells. Phys. Rev. Lett. 86, 4358–4362 (2001).
 6.
Ganichev, S. D. & Prettl, W. Intense Terahertz Excitation of Semiconductors (Oxford Univ. Press, Oxford, 2006).
 7.
Seeger, K. Semiconductor Physics (Springer, Wien, 1997).
 8.
Bel’kov, V. V. et al. Magnetogyrotropic photogalvanic effects in semiconductor quantum wells. J. Phys. Condens. Matter 17, 3405–3428 (2005).
 9.
Tarasenko, S. A. Spin orientation of a twodimensional electron gas by a highfrequency electric field. Phys. Rev. B 73, 115317 (2006).
 10.
Ivchenko, E. L. & Pikus, G. E. Optical orientation of free carriers spins and photogalvanic effects in gyrotropic crystals. Izv. Akad. Nauk SSSR 47, 2369–2372 (1983) ibid. Bull. Acad. Sci. USSR 47, 81–84 (1983).
 11.
Kelly, M. J. LowDimensional Semiconductors (Clarendon, Oxford, 1995).
Acknowledgements
We would like to thank I. Gronwald for help in sample preparation. This work was supported by the DFG through Project GA501/5, Research Unit FOR370 and Collaborative Research Center SFB689, the RFBR and programs of the RAS. S.G. thanks the HBS and S.A.T. thanks the Foundation ‘Dynasty’–ICFPM and the President Grant for young scientists for support.
Author information
Affiliations
Fakultät Physik, Universität Regensburg, 93040 Regensburg, Germany
 Sergey D. Ganichev
 , Vasily V. Bel’kov
 , Sergey N. Danilov
 , Stephan Giglberger
 , Christoph Hoffmann
 , Dieter Weiss
 , Werner Wegscheider
 , Christian Gerl
 , Dieter Schuh
 , Joachim Stahl
 & Wilhelm Prettl
A. F. Ioffe PhysicoTechnical Institute, Russian Academy of Sciences, 194021 St Petersburg, Russia
 Vasily V. Bel’kov
 , Sergey A. Tarasenko
 & Eougenious L. Ivchenko
IMEC, Kapeldreef 75, B3001 Leuven, Belgium
 Jo De Boeck
 & Gustaaf Borghs
Authors
Search for Sergey D. Ganichev in:
Search for Vasily V. Bel’kov in:
Search for Sergey A. Tarasenko in:
Search for Sergey N. Danilov in:
Search for Stephan Giglberger in:
Search for Christoph Hoffmann in:
Search for Eougenious L. Ivchenko in:
Search for Dieter Weiss in:
Search for Werner Wegscheider in:
Search for Christian Gerl in:
Search for Dieter Schuh in:
Search for Joachim Stahl in:
Search for Jo De Boeck in:
Search for Gustaaf Borghs in:
Search for Wilhelm Prettl in:
Contributions
Project planning, model and writing: S.D.G., V.V.B., S.A.T., E.L.I., D.W., W.W., W.P.; experiments and data analysis: S.D.G., V.V.B., S.N.D., S.G., Ch.H.; sample growth and characterization: W.W., Ch.G., D.S., J.S., J.B., G.B.; theory: S.A.T., E.L.I.
Competing interests
The authors declare no competing financial interests.
Corresponding author
Correspondence to Sergey D. Ganichev.
Rights and permissions
To obtain permission to reuse content from this article visit RightsLink.
About this article
Further reading

Observation of anomalous linear photogalvanic effect and its dependence on wavelength in undoped InGaAs/AlGaAs multiple quantum well
Nanoscale Research Letters (2014)

Experimental observation of the optical spin–orbit torque
Nature Photonics (2013)

Observation of secondharmonic generation induced by pure spin currents
Nature Physics (2010)