Gate-tunable large magnetoresistance in an all-semiconductor spin valve device

A large spin-dependent and electric field-tunable magnetoresistance of a two-dimensional electron system is a key ingredient for the realization of many novel concepts for spin-based electronic devices. The low magnetoresistance observed during the last few decades in devices with lateral semiconducting transport channels between ferromagnetic source and drain contacts has been the main obstacle for realizing spin field effect transistor proposals. Here, we show both a large two-terminal magnetoresistance in a lateral spin valve device with a two-dimensional channel, with up to 80% resistance change, and tunability of the magnetoresistance by an electric gate. The enhanced magnetoresistance is due to finite electric field effects at the contact interface, which boost spin-to-charge conversion. The gating scheme that we use is based on switching between uni- and bidirectional spin diffusion, without resorting to spin–orbit coupling. Therefore, it can also be employed in materials with low spin–orbit coupling.


Supplementary Note 1. Device characterization.
In this Note, we present the results of basic characterization measurements of the nongated spin injection device, used for the experiments summarized in Figures 2 and 3.
Supplementary Figure 1 shows the layer sequence of the wafer used to fabricate devices (see Methods) and the SEM picture of one of our devices without a gate. The transport channel containing the 2DES is contacted by (Ga,Mn)As/GaAs Esaki diodes covered with an Au/Ti metal film which connects the degenerately p-doped (Ga,Mn)As to the contact pads, seen in the SEM picture. The widths of the FM electrodes are 500 nm, 700 nm, 1 µm and 2 µm, separated by (center to center) 3.6 µm, 3.85 µm and 4.5 µm, respectively. The two narrowest electrodes were used as source (S) and drain (D) in the two-terminal experiments described in the main text. The four potential probes seen to the right of FM contacts were used to determine charge transport parameters in magnetotransport measurements (see Supplementary Figure 3  From the extracted charge transport and spin transport parameters we calculate the channel spin resistance as RS G <T G < ) 57 Ω, with the channel cross-section ( UV, where U 10 μm is the width and t is the thickness of the 2DES channel. 5 We estimate the spin resistance of the tunnel contact as 9 WX *1 Y ) 14.5 kΩ. Both parameters determine the conditions for efficient spin injection and detection in a given system. According to the standard model, the maximum spin signal is observed when RS ≪ ≪ RS G Q ⁄ . 5,6 The left condition is clearly satisfied for our device, indicating that the device works in the tunneling regime, enabling efficient spin injection. The right condition is not fulfilled, as the ratio RS ) 250 ⁄ is two orders of magnitude too large. This means that the dwell time of electrons in the channel is much larger than the spin relaxation time. [4][5][6][7] These values are typical for all our devices and a large RS ⁄ ratio is typical for semiconductor-based spin devices. As a high interface resistance indicates also larger spin-independent contribution to the two-terminal resistance ^,I^-, it results in a low magnetoresistance ratio MR ∆ / ^.8-13

Supplementary Note 2. Magnetoresistance of the gated device.
In this Note, we present additional two-terminal local measurements on the gated sample, used for the gate-controlled experiments presented in Figure 4.

Supplementary Note 3. Influence of an electric field on the spin signal.
In this Note, we explain in detail how we constructed Figure 3. There we compared the measured 2T local signal Δ with values ∆ abc expected from standard theory without electric field effects, and with ∆ adc , for which electric field's effects have been included. As an example, we discuss the procedure for an injection current of 52 µA.
Supplementary Figure 6a displays the results of 2T local spin valve measurements with a positively biased source (S) contact. We measure a large SV signal Δ 60 mV, which we plot in Fig. 3  . Next, we show how to estimate Δ adc . We first decompose the signal as Δ adc n g Δ g,i ./ + n i Δ i,g ./ , where n g,i-is a factor representing the effect of the electric field on the signal component detected at the source (drain). We write this factor as n g n g ,Cn g ,CC-, where n g ,Cdescribes the effect of drift on spin transport in the channel 14

Supplementary Note 4. Spin diffusion calculation of ∆R in a confined geometry.
In this Note we estimate the effect of confinement on the two-terminal spin resistance in the limit of low electric fields. For simplicity, we assume symmetric tunnel junctions having the same values for spin injection efficiency B and contact resistance . We checked that this assumption does not influence the following conclusions. As ‰ ≪ RS ≪ holds for our devices (see Supplementary Note 1), we can estimate the 2T resistance change ∆ Š{ . in the open configuration from the standard diffusion equations: For a confined geometry the formalism of Jaffrès et al. 5 predicts a two-terminal resistance of for the charge-and spin transport parameters of our device. This corresponds to an enhancement factor of ∆ RŠ.‹ /∆ Š{ . 5.8, which is in good agreement with our low field experimental results (see Fig. 4b).

Supplementary Note 5. Gate control of the magnetoresistance.
In this Note, we show the results of gate-controlled magnetoresistance measurements by repeating the measurement shown in Fig. 4

Supplementary Note 7. Two-terminal local Hanle measurements.
In this Note we summarize the results of two-terminal Hanle measurements, i.e., measurements in an external out-of-plane magnetic field. Suppression of the measured signal in the field direction transverse to the injected spins, with the amplitude of the signal fully consistent with local spin valve signals, confirms the spin origin of the measured magnetoresistance. As we reported in our recent work on nonlocal Hanle experiments in 2DES samples 19 , Hanle curves are strongly affected by dynamic nuclear polarization (DNP) effects 20 , which lead to narrowing of the curves through the additional effective magnetic field acting on electron spin. These effects are particularly strong for large bias voltages, when large spin accumulation is induced in the channel. This makes quantitative analysis of the experimental data, particularly extraction of the spin relaxation times, very difficult. As we showed in Ref.
19, one can limit the influence of the DNP by performing AC low excitation measurements. We

Supplementary Note 8. Temperature dependence of the local spin valve signal.
In this Note we show two-terminal local spin valve signals measured at different temperatures.
The amplitude of the signal drops with temperature as we approach the Curie temperature of used (Ga,Mn)As layer, Tc=55 K. The SV pattern moves for higher temperatures towards B=0 as the coercive fields of the magnetic contacts decrease.

Supplementary Figure 12 | Temperature dependence of the 2T spin valve signal
Two-terminal local spin valve signal for a DC injection current of Iinj=+60 µA at different temperatures. Measurement performed on the same device as presented in Fig. 2.