All-electrical time-resolved spin generation and spin manipulation in n-InGaAs
We demonstrate all-electrical spin generation and subsequent manipulation by two successive electric field pulses in an n-InGaAs heterostructure in a time-resolved experiment at zero external magnetic field. The first electric field pulse along the crystal axis creates a current induced spin polarization (CISP) which is oriented in the plane of the sample. The subsequent electric field pulse along  generates a perpendicular magnetic field pulse leading to a coherent precession of this spin polarization with 2-dimensional electrical control over the final spin orientation. Spin precession is probed by time-resolved Faraday rotation. We determine the build-up time of CISP during the first field pulse and extract the spin dephasing time and internal magnetic field strength during the spin manipulation pulse.
pacs:72.25.Pn, 78.47.D-, 85.75.-d
Spin-orbit interaction in bulk semiconductors and semiconductor nanostructures provides a variety of useful applications in spintronic devices and can fulfill basic tasks such as electrical initialization, manipulation and detection of electron spin polarizations or spin currents Wolf et al. (2001); Dyakonov (2008); Awschalom and Samarth (2009). A charge current in a semiconductor structure can either lead to a homogeneous electron spin polarization (current-induced spin polarization (CISP)) Edelstein (1990); Kato et al. (2004a); Sih et al. (2005); Stern et al. (2006); Koehl et al. (2009) or can result in a spin accumulation transverse to the current direction by spin dependent scattering (spin Hall effect) Hirsch (1999); Zhang (2000); Kato et al. (2004b); Sih et al. (2005); Wunderlich et al. (2005); Garlid et al. (2010); Hernandez et al. (2013). Electron spin states can be manipulated by Larmor precession about an effective magnetic field which can be controlled through SO interaction either by static electric fields Kato et al. (2004c, 2005); Meier et al. (2007); Norman et al. (2010) or by electric field pulses providing an additional degree of freedom Kuhlen et al. (2012). Finally, spin sensitive electrical readout has been demonstrated by the spin-galvanic effect Ganichev et al. (2002). All previous time-resolved experiments on spin initialization and spin manipulation combine time-resolved electrical with ultrafast optical techniques. All-electrical time-resolved experiments on spin initialization and subsequent spin manipulation are still pending.
In this Letter, we demonstrate that pulsed CISP can be combined with coherent spin manipulation by SO-induced local magnetic field pulses (LMFP) in one time-resolved experiment which allows to achieve all-electrical two-dimensional directional and temporal control of an electron spin polarization in n-InGaAs. The first electric field pulse is applied along the crystal axis to create an in-plane spin polarization by CISP. The second electric field pulse along the  crystal axis triggers a LMFP which leads to coherent Larmor precession of the spin polarization. Time-resolved Faraday rotation (TRFR) is used to probe spin precession during the manipulation pulse (Fig. 1(a)). By changing the width and amplitude of both CISP and LMF pulses we achieve all-electrical control over the initial spin polarization, the direction of the Larmor precession and the final spin orientation. Furthermore, the experiment allows a time-resolved detection of the CISP build-up time, the determination of the spin dephasing time and the strength of the LMFP during the spin manipulation pulse.
The sample is a 500 nm thick InGaAs epilayer doped with Si yielding a room temperature carrier density of cm which allows for long spin dephasing times Dzhioev et al. (2002); Kikkawa and Awschalom (1998); Schmalbuch et al. (2010). The epilayer was grown on a semi-insulating (001) GaAs wafer by molecular beam epitaxy and capped by a 100 nm thick layer of undoped GaAs. The n-InGaAs layer was patterned into a cross-shaped mesa by optical lithography and wet etching (Fig. 1(a)). Annealed Au/Ge/Ni electrodes yield ohmic contacts to its center square (200 m 200 m) which provides optical access for spin detection. Each of the four contact pads is connected to a signal line of a coplanar wave-guide. The sample is connected to a dual channel pulse-pattern generator Kuhlen et al. (2012) and cooled to K in a magneto-optical cryostat Suppl ().
The experiment consists of three basic steps (see Fig. 1(a)): (1) generation of an in plane spin polarization along the -direction by an electric field pulse along the -direction (CISP pulse), (2) coherent spin manipulation by a second electric field pulse along the -direction which launches a LMF pulse with the magnetic field oriented along the -direction and (3) optical detection of the out-of-plane component of the spin polarization along the -direction by measuring time-resolved Faraday rotation of a linearly polarized probe pulse. This sample orientation was chosen as it provides strong CISP in -direction (step 1) Kato et al. (2004a) and, at the same time, large electric field-induced internal magnetic fields in -direction Kato et al. (2004c) which are used for spin manipulation (step 2).
As depicted in Fig. 1(a), both CISP and LMF pulses each consist of two separate voltage pulse trains of opposite sign ( for spin polarizing CISP pulse (step 1) and for spin manipulation LMF pulse (step 2)) which arrive simultaneously on opposing sides of the sample. Numerical simulations Meier (2007) show that a geometry with four electrodes can result in rather inhomogeneous electric field distributions. Using two pulses on opposing sides significantly reduces inhomogeneities of the electric field distribution along the InGaAs channel. It furthermore doubles the effective electric field in the center of the sample. The rise-time of the voltage pulses is approximately 100 ps as determined by time-domain reflectometry (not shown). For time-resolved spin detection (step 3), we use an optical pulse train (3 ps pulses) launched from a Ti:sapphire laser. It is synchronized with the pulse-pattern generator at its 80 MHz repetition frequency and has its energy tuned to the fundamental band edge of the InGaAs layer (1.41 eV) Kuhlen et al. (2012). Both the current-induced spin polarization pulses and the optical spin detection pulses are modulated for lock-in detection. Spin dephasing times have also independently been determined from all-optical TRFR measurements Schmalbuch et al. (2010). Thereto, we optically create the initial spin polarization along the -direction by circularly polarized laser pump pulses, which hit the sample under normal incidence (-direction) and use same optical detection scheme as above.
For time-resolved CISP (step 1) we apply voltage pulses along the x-axis ( direction) with a width of ps and an amplitude of of V which generates an initial in-plane electron spin polarization parallel to the y-axis ( direction, see Fig. 1(a)). Furthermore, we apply an external magnetic field along the x-axis, which is parallel to the electric field but perpendicular to . The time-evolution of the out-of-plane component of the resulting spin polarization is measured by TRFR at the center of the sample (Figs. 1(c) and (d)). Most strikingly, we observe several precessions of the spin polarization demonstrating that the voltage pulse triggers a spin polarization with a well-defined phase. Similar results have been obtained by pulsed CISP using a fast photoconductive switch for electrical excitation Kato et al. (2004a). At T, spins are oriented along the -direction yielding . Spin precession is observed for T. Changing the sign of inverts the direction of spin precession which results in a sign reversal of . The curves can be described as exponentially decaying oscillations with the Larmor frequency proportional to . We note that the initial spin orientation is defined by the CISP pulse while there is no control over the final spin orientation as the spin polarization precesses at all times about the static magnetic field.
In step 2 we turn off the external magnetic field and manipulate the spin polarization by LMF pulses only. The respective pulse sequence is depicted in Fig. 1(b). As above, we generate the initial in-plane spin polarization by a CISP pulse ( V, ns). As there is no external magnetic field, is not precessing during the CISP pulse but instead can reach a larger saturation polarization. A waiting time of ns after the CISP pulse ensures that a spin-independent background signal from the CISP pulse completely decays before subsequent spin manipulation. The incoming spin manipulation pulse with V and ns acts as an internal magnetic field pulse Kuhlen et al. (2012) with x (see Fig. 1(a)) and rotates out of it’s initial in-plane orientation towards the -direction yielding . Fig. 2 shows the time evolutions of for various pulse configurations. In Fig. 2(a), a positive CISP pulse with V generates a spin polarization which is oriented in the -direction. The LMF pulse will trigger spin precession in the plane during its entire pulse width ( ns). Apparently, the spin precession direction reverses when reversing the polarity of the manipulation pulse. This is expected as the direction of the internal magnetic field is reversed at the same time Kuhlen et al. (2012). We note that both spin manipulation pulses rotate the spin polarization by ( pulse) from the into the direction. This gives us a full all-electrical two-dimensional directional control over the spin polarization in the sample.
It is known that the initial spin polarization direction from CISP can be reversed by reversing the CISP voltage Kuhlen et al. (2012). For a negative CISP pulse, we therefore generate a spin polarization in the -direction (Fig. 2(b)). Consequently, the respective signs of reverses during spin manipulation. No spin precession signals are seen if either the CISP or the LMF pulse are turned off (Fig. 2(b)) as in one case no initial spin polarization is generated (green curve) and in the other case the spin polarization stays in-plane (black Curve) and thus cannot be detected by TRFR.
We next focus on the temporal dynamics of the CISP process. The build-up time of CISP has been measured by varying the pulse width of the CISP pulse from 500 ps to 7 ns with the amplitude set to V. After a waiting time of ns we apply a subsequent spin manipulation pulse with V and ns to probe the temporal evolution of the CISP polarization process. The resulting TRFR curves can be described by an exponentially decaying sine function
with amplitude (CISP), delay , where we set ns at the beginning of the spin manipulation pulse at which spin precession starts, spin dephasing time , Larmor frequency with being the Planck’s constant, 0.61 the electron g-factor which has independently been determined from time-resolved CISP and all-optical TRFR experiments and the initial phase of the in-plane spin polarization .
We fit the data to Eq. 1 and plot the extracted amplitudes against (Fig. 3(a), red open squares). The observed exponential increases of shows that CISP results from a dynamical process with a build-up time of 1.82 ns. The build-up spin polarization reaches saturation when the build-up rate equals the subsequent spin dephasing rate.
We next determine the in-plane spin lifetime of the CISP by varying at fixed ns and ns. After the initial spin polarization is generated by the CISP pulse it is given the time to decay. The remaining spin polarization is measured afterwards by applying a subsequent LMF pulse which again rotates the spin polarization in the laser probe direction. The dependence of resulting on is seen in Fig. 3(a) (blue filled squares) and shows an exponential decay with a spin lifetime of 3.83 ns. This value is comparable to the out-of-plane spin lifetime of 3.53 ns measured in all-optical pump-probe experiments at mT (see also Fig. 4(d)). These results directly confirm the absence of any significant spin relaxation anisotropy between spin orientations along and in this type of heterostructures.
Finally, we vary the width of the spin manipulation pulse at fixed ns and ns. As the angle of the Larmor precession as well as the total precession time is proportional to the pulse width , we expect to control the final spin orientation by varying . Fig. 3(b) shows a sequence of TRFR measurements of the out-of-plane spin polarization for various pulse widths ranging from 1.15 to 3.55 ns. For the longest pulse width of 3.55 ns the curve is similar to Fig. 2 and again shows a rotation of the spin polarization. For shorter pulses follows the spin precession curve (black curve) during the LMF manipulation pulse. However, spin precession abruptly stops after the manipulation pulse has turned off. This is seen by an exponential decay thereafter. We note that the spin polarization is rotated by ( pulse) for ns, which is not corresponding to the maximum out-of-plane spin polarization because of relatively short spin lifetime. Along with the control over the initial spin polarization we obtain significant two-dimensional control over the final orientation of the spin polarization.
In all spin manipulation experiments shown in Figs. 2 and 3, the LMF pulse only allows for spin rotation by at most ( pulse). This seems to contradict with the time-resolved CISP results in Fig. 1(c) where multiple Larmor precession cycles are visible on much longer time-scales. Apparently, the LMF pulses not only triggers spin precession but also yields significant spin dephasing. We therefore now focus on the magnitude of and the spin dephasing time during coherent spin manipulation. Figs. 4(a) and (b) show during the spin manipulation pulse for different LMF pulse amplitudes . The pulse width is set to 7 ns for all measurements. It is obvious that spin precession becomes faster at higher voltages and changes its direction with the polarity of . A fit to all measurements by Eq. 1 allows to extract both voltage dependent spin dephasing times (red filled squares in Fig. 4(d)) and internal magnetic field strengths (red filled squares in Fig. 4(c))). Similar as in Ref. Kuhlen et al. (2012), we observe a linear dependence of on and a voltage induced spin dephasing which is seen by the strong decrease of in Fig. 4(d). The moderate internal magnetic field strength in combination with the short spin dephasing times are the reason that a spin manipulation over by a single pulse is not accessible in present devices. We emphasize, however, that the spin polarization can be rotated into arbitrary directions within the plane by using LMF pulses of both positive and negative polarity (see red and blue curve in Fig. 4(a)).
To explore whether the pulsed CISP excitation has any influence on the extracted and values, we have also determined the respective values from a separate set of TRFR measurements where we replace the electrical CISP pulses by circularly polarized laser pulses which are focused onto the sample under normal incidence and thus result in optical spin orientation parallel to the -direction. As in the all-electrical experiment we launch a spin manipulation pulse right after spin excitation. As the internal magnetic field direction is again perpendicular to the spin orientation, it will trigger Larmor precession. Both and are again determined from spin precession during the spin manipulation pulse and are included as black open squares in Figs. 4(c) and (d), respectively. The results from both measurement techniques are in rather good agreement. The error bar for respective values from optical excitation are larger as our mechanical delay line only covers a shorter time-window of 2.5 ns compared to our long electronic delay of 7 ns which has been used for pulsed CISP excitation.
In conclusion, we have demonstrated that all-electrical electron spin generation and manipulation by two subsequent electrical pulses is achievable in n-InGaAs. High degree of all-electrical temporal and directional control over both the initial and final spin orientation is shown. In addition, we measured the build-up time of CISP for the first time proving that CISP is a dynamical process. Furthermore, we extract internal magnetic fields and spin dephasing times which are identical to all-optical reference experiments demonstrating that pulsed electrical spin polarization, i.e. time-resolved CISP, does not affect these values. The excellent quantitative agreement between both techniques proves the applicability and flexibility of pulsed CISP for spintronic applications.
We gratefully acknowledge financial support from the DFG via FOR 912 (project BE 2441/6-2).
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