Control of Spin Precession in a Spin-Injected Field Effect Transistor

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Science  18 Sep 2009:
Vol. 325, Issue 5947, pp. 1515-1518
DOI: 10.1126/science.1173667


Spintronics increases the functionality of information processing while seeking to overcome some of the limitations of conventional electronics. The spin-injected field effect transistor, a lateral semiconducting channel with two ferromagnetic electrodes, lies at the foundation of spintronics research. We demonstrated a spin-injected field effect transistor in a high-mobility InAs heterostructure with empirically calibrated electrical injection and detection of ballistic spin-polarized electrons. We observed and fit to theory an oscillatory channel conductance as a function of monotonically increasing gate voltage.

Many types of spintronic devices have been proposed, investigated, and developed. However, the spin-injected field effect transistor (spin FET), which lies at the heart of spintronics, has yet to be realized. Proposed by Datta and Das (1), the demonstration of a spin FET involves spin injection and detection using a ferromagnetic source and drain. However, a special feature of the spin FET is the periodic modulation of source-drain conductance as controlled by gate voltage–induced precession of the injected spins. Electrical spin injection and detection have been demonstrated in a variety of semiconductors (26). Carrier spin precession has been induced by using an external magnetic field and detecting the Hanle effect, a Lorentzian-shaped magnetoresistance caused by precessional dephasing of diffusing spins, in materials with relatively small spin-orbit interaction such as GaAs and Si (35). However, modulating the channel conductance by using an electric field to induce spin precession has remained elusive. A material with large spin-orbit interaction will not permit the observation of the Hanle effect, yet this type of material is necessary for gate voltage–induced spin precession. These two phenomena are mutually exclusive within any single material. We used a high-mobility InAs heterostructure with strong intrinsic spin-orbit interaction α, and we measured the nonlocal channel conductance (5, 6) rather than the direct source-drain conductance suggested by Datta and Das. Conventional lateral spin valve techniques measured the population of ballistic spins. Shubnikov–de Haas (SdH) experiments provided an independent measurement of the dependence of the spin-orbit interaction on gate voltage. Apart from a small phase shift, the oscillatory conductance that we measured fits to theory (1) with no adjustable parameters. The temperature dependence indicates that the modulation is only observed when the injected electrons have ballistic trajectories to the detector.

A conventional lateral spin valve device (Fig. 1A) is a convenient structure to investigate spin injection and detection for several reasons. First, the ferromagnetic (FM) electrodes have a uniaxial shape anisotropy that can create binary magnetization states along the y axis, ±My. A small external magnetic field applied along the y axis (Ba) can create conditions with the injector (source) and detector (drain) magnetizations parallel or antiparallel, resulting in relatively high or low spin-dependent voltages at the detector (2, 7, 8). Second, a small channel length, L, between injector and detector can be defined lithographically. Third, in the “nonlocal” configuration (512), the bias current is grounded at one end of the sample, there is no charge current in the vicinity of the spin detector, background effects are minimized, and the signal-to-noise ratio is maximized. Spin-polarized carriers with ballistic trajectories along the +x and −x directions are injected with equal probability.

Fig. 1

Lateral gated spin valve device with an external magnetic field (Ba = 0.5 T) applied along the y axis (A) and x axis (B). In (A), the magnetizations of the FM electrodes are shown oriented along the y axis. The injected spin-polarized electrons are oriented along the y axis and do not precess under the influence of the Rashba field BRy. (B) shows the electrons injected with spin orientation along the x axis, perpendicular to BRy, and they precess under the influence of the effective field. (C) Scanning electron micrograph of the device. For clarity, the image was taken before depositing the gate oxide and electrode. (D) Observation of oscillatory conductance from injector to detector with T = 1.8 K. Gate-controlled spin precession occurs in configuration (B) (black trace) and not in configuration (A) (red trace). The green and blue traces represent data from a control sample that has a ferromagnetic injector but a nonmagnetic detector. The channel length is L = 1.65 μm and the bias current is I = 1 mA. The plots are shifted for clarity. (E) Conventional, nonlocal, lateral spin valve magnetoresistance measurement using configuration (A) at T = 1.8 K. The black and red lines correspond to field sweep-up and -down, respectively. The pairs of arrows indicate the magnetization alignments of the two FM electrodes, either parallel or antiparallel.

In a two-dimensional electron gas (2DEG) channel with strong spin-orbit interaction, the structural asymmetry provides an intrinsic electric field along the z axis, Ez,0, where the subscripts denote the z direction and zero gate voltage. In the rest frame of a carrier moving with a weakly relativistic Fermi velocity, vFx ~ c/300, with c the speed of light, electric field Ez,0 transforms as an effective magnetic field BRy,0, which is called the Rashba field (13). The Rashba field is perpendicular to the directions of the carrier velocity and the electric field. In Fig. 1, BRy,0 is along the y axis and has no effect on carriers that are injected with spin polarization also along the y axis (Fig. 1A). Datta and Das predicted, however, that carriers injected with spin polarization along the x axis would precess under the influence of BRy,0, a condition that occurs when the magnetization of the injector is oriented along the x axis (Fig. 1B). The magnitude of Ez can be modulated by a variable gate voltage VG, the magnitude of the Rashba field changes, BRy is proportional to Ez, and the precession rate therefore changes as a function of VG. When the detector is also a FM electrode with magnetization along the x axis and carriers have ballistic trajectories from injector to detector, the channel conductance of the structure in Fig. 1B is predicted to oscillate periodically as a function of monotonically increasing gate voltage, because the detector voltage will be high when a detected spin has its orientation parallel with that of the detector and the detector voltage will be low when the spin is antiparallel (1). This is a relativistic electric field analog of Larmor waves (14). Whereas Larmor waves may be detected in superposition with a diffusive resonance feature, the spin-orbit interaction in a spin FET is so large that spin orientation is randomized after only a few scattering events, and the diffusive analog (the Hanle effect) is not observed [supporting online material (SOM) text S1].

Our devices consist of two Ni81Fe19 electrodes on top of an InAs high–electron mobility transistor (HEMT) channel and a gate electrode (15). The InAs HEMT (6, 16) was grown by molecular beam epitaxy on a semi-insulating InP (100) substrate. The single quantum well, which functions as a 2DEG channel, has a depth of 35.5 nm from the top surface. The carrier density and mobility of the 2DEG are nS = 1.8 × 1012 to 2.8 × 1012 cm−2 and μ = 50,000 to 60,000 cm2 V−1 s−1 at temperature T = 1.8 K, respectively. The channel, defined by a mesa etch, is oriented with x along the <110> direction and has a width w = 8 μm. The two FM electrodes were fabricated with electron beam lithography and lift-off and have lateral dimensions of 0.4 × 80 μm and 0.5 × 40 μm (Fig. 1C). Samples were made with FM electrode spacings of L = 1.25 and 1.65 μm, measured center to center.

An example of the oscillatory conductance modulation is shown in Fig. 1D. An external magnetic field, Ba = 0.5 T, was applied to fix the magnetization orientations of the FM electrodes in a chosen direction, thereby determining the axis of spin injection and detection. The nonlocal channel conductance was measured as a function of gate voltage for the range −3 ≤ VG ≤ 3 V. The red trace presents data for field Bay applied along the y axis (Fig. 1A). The orientation of injected spins along the y axis is parallel to the Rashba field. There was no spin precession and no modulation of voltage recorded by the detector. For the data represented by the black trace, the external field Bax = 0.5 T was large enough to overcome the shape anisotropy of the FM electrodes. The magnetization orientations of injector and detector are along the +x direction (Fig. 1B), and the injected spin orientation is perpendicular to the Rashba field. The spin precession varies as a function of gate voltage, and an oscillation of detected voltage as a function of VG was observed. The range of gate voltage is sufficiently large that more than one full cycle of voltage oscillation was recorded.

Control experiments were performed to further confirm that the voltage oscillation originated from the detection of spin precession in the channel. The devices used as controls were made with the same geometry and lithographic processing but with the FM detector replaced by a nonmagnetic electrode composed of an In (50 nm)/Au (30 nm) film. Identical transport measurements were made, but no voltage modulation was observed, regardless of the direction of the external field (blue and green traces in Fig. 1D).

A set of experiments was performed to enable quantitative analysis and detailed comparison with theory. Data from a conventional lateral spin valve measurement (5, 6, 812) are shown in Fig. 1E. In the absence of an external magnetic field, the magnetizations of the injector and detector have bistable states along the ±y axis because of their shape anisotropy, and they have slightly different coercivities because of the different aspect ratios. With VG = 0 and constant bias current I = 1 mA, a small magnetic field was swept along the y axis, the magnetization alignment of FM electrodes changed between parallel and antiparallel configurations, and the detector voltage V was high or low, respectively. The characteristic dips seen in the data were observed for Ba > 0, when the field sweep was from negative to positive (black trace), and for Ba < 0, when the field sweep was from positive to negative (red trace). The spacing L between the injector and the detector is less than a carrier mean free path, l, and measurements are dominated by ballistic transport effects. There is no formal theory for the magnitude of the lateral spin valve effect for ballistic carriers. Instead, this conventional lateral spin valve measurement provides a calibration for the amplitude of the voltage oscillation in Fig. 1D, because the mechanism for spin-dependent voltage is the same for both experiments. The magnitude of the dips, A ≡ ΔV = 6 ± 0.2 μV, is the same as the amplitude of the oscillatory voltage shown in Fig. 1D, ΔV = 6 ± 0.5 μV, and this empirically measured amplitude A was used for the quantitative fits.

Next, the spin-orbit coupling strength α was measured as a function of gate voltage. SdH oscillations (17, 18) were measured at a variety of gate voltage values, beat patterns were observed (Fig. 2A), and α(VG) was deduced (SOM text S2). The changing nodal position of the beat pattern (arrows in Fig. 2A) shows that the gate voltage strongly affects the spin-orbit coupling of carriers in the InAs single-quantum well. The magnitude of α(VG) is strongly dependent on VG for the range −3 ≤ VG ≤ 1 V (Fig. 2B). The effect of the gate voltage is enhanced for the negative VG because of nonlinear bending of the quantum well. The dependence of α on VG is weak for the positive range 1 ≤ VG ≤ 3 V. Although magneto-intersubband scattering may also cause an oscillatory magnetoresistance (19, 20), this mechanism can be excluded from an interpretation of our data by using a detailed analysis of the Fourier transforms of the SdH oscillations (SOM text S3). Because the gate voltage might be expected to change the carrier concentration in the channel, the voltage-dependent concentration n(VG) was directly determined from Hall measurements. It shows negligible variation over the experimental range of VG (Fig. 2B). Having measured α(VG), the magnitude of the Rashba field is readily calculated from BRy = 2αkF/(gμB) (1), where kF and g are the Fermi wave vector and g factor, respectively, of the carriers in the channel, and μB = 9.27 × 10-24 J/T is the Bohr magneton. Using kF = 4.13 × 106 cm−1 and g = 15 (21), the field at zero gate voltage (Fig. 2B) has magnitude BRy = 8.5 T. Ba = 0.5 T is an order of magnitude smaller than BR and has a negligible effect on spin precession.

Fig. 2

Gate control of spin-orbit interaction at T = 1.8 K. (A) SdH oscillations as a function of gate voltage. The channel resistance Rxx is measured with a magnetic field, Ba, that is perpendicular to the 2DEG plane. (B) Spin-orbit interaction parameter α, deduced from (A), and carrier concentration nS, as functions of gate voltage. Because of the asymmetry of the quantum well structure, α is nonzero at VG = 0.

The theory of Datta and Das describes the transport of ballistic electrons in a 2DEG channel (SOM text S4). Allowing for an arbitrary phase shift ϕ, the expression for the detector voltage is V=Acos(2m*αL/2+ϕ) (1) The fit for the sample with L = 1.65 μm and m* = 0.05m0 (22),where m0 is 9.1 × 10-31 kg and is Planck’s constant divided by 2π, using the empirical values of α(VG) and A, is plotted in Fig. 3 as a solid line and shows excellent quantitative agreement with the data. The phase shift ϕ, believed to be a consequence of shielding near the metallic ferromagnetic electrodes, is the only adjustable fitting parameter. The data fit well for more than a full wavelength of oscillation, with a small weakness of the fit occurring for the regime where gate voltage modulation of α is weak, VG > 0 V.

Fig. 3

Gate voltage modulation of spin FETs having different channel lengths, with T = 1.8 K and I = 1 mA. The symbols indicate experimental data. The solid lines are the fits obtained from Eq. 1. Data are offset for clarity. Baseline voltages are 1.032 mV and 0.715 mV for L = 1.25 μm and 1.65 μm, respectively.

Because precessional phase accumulation is proportional to L, it follows that carriers in a device with shorter spacing L will require a larger range of α, and therefore a larger range of gate voltage VG to precess by π radians. A sample with L = 1.25 μm was fabricated and the data and fit are shown as the bottom trace in Fig. 3. The half period of oscillation is seen to increase from ΔVG = 1.24 V (L = 1.65 μm) to ΔVG = 1.53 V (L = 1.25 μm). Data with different values of L are fit successfully by Eq. 1 with no adjustable parameter other than a small phase shift.

The temperature dependence of the oscillatory voltage is shown in Fig. 4. Gate voltage modulation is clearly observed up to T = 40 K. From the Dyakonov-Kachorovski (23) and Dyakonov-Perel (24) mechanisms, the spin relaxation rate 1/τs scales as TE12τp in a narrow quantum well such as ours. Here E1 is the confinement energy of the quantum well and τp is the momentum scattering time. In our experiments, τp is nearly proportional to 1/T, and therefore the additional spin relaxation at higher temperature is negligible (6). At high temperatures, however, inelastic scattering becomes more pronounced. Our measurements of the temperature dependence of the mean free path (SOM text S5) show that the conductance oscillation broadens and disappears in the same temperature range (T ≥ 40 K) where l becomes shorter and transport therefore changes from ballistic to diffusive. This temperature dependence is a further confirmation of theory (1).

Fig. 4

Temperature dependence of oscillatory conductance with L = 1.25 μm and I = 1 mA. As temperature increases, the mean free path decreases and transport characteristics change from ballistic to diffusive.

Two decades ago, Datta and Das proposed an experiment involving spin injection, detection, and spin precession caused by a gate voltage and special relativistic effects on ballistic electrons in a 2DEG. Separate aspects have been demonstrated individually (3, 5, 17). We have used the nonlocal lateral spin valve geometry to combine these aspects in a single experiment. The InAs single-quantum well used here is an ideal material, because a large spin-orbit interaction modulates a Rashba field by several teslas with a gate voltage range of a few volts.

Supporting Online Material

Materials and Methods

SOM Text

Figs. S1 to S5


References and Notes

  1. Materials and methods are available as supporting material on Science Online.
  2. This work was supported by the Korea Institute of Science and Technology Institutional Program.
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