Large and tunable magnetoresistance in van der Waals ferromagnet/semiconductor junctions

Magnetic tunnel junctions (MTJs) with conventional bulk ferromagnets separated by a nonmagnetic insulating layer are key building blocks in spintronics for magnetic sensors and memory. A radically different approach of using atomically-thin van der Waals (vdW) materials in MTJs is expected to boost their figure of merit, the tunneling magnetoresistance (TMR), while relaxing the lattice-matching requirements from the epitaxial growth and supporting high-quality integration of dissimilar materials with atomically-sharp interfaces. We report TMR up to 192% at 10 K in all-vdW Fe3GeTe2/GaSe/Fe3GeTe2 MTJs. Remarkably, instead of the usual insulating spacer, this large TMR is realized with a vdW semiconductor GaSe. Integration of semiconductors into the MTJs offers energy-band-tunability, bias dependence, magnetic proximity effects, and spin-dependent optical-selection rules. We demonstrate that not only the magnitude of the TMR is tuned by the semiconductor thickness but also the TMR sign can be reversed by varying the bias voltages, enabling modulation of highly spin-polarized carriers in vdW semiconductors.

gate-tunable magnetic proximity effects in Co/graphene lateral spin valves 15 .
In this work, we demonstrate a surprisingly large and tunable TMR of up to 192% in all-vdW Fe3GeTe2/GaSe/Fe3GeTe2 MTJs with a semiconducting GaSe spacer separating two Fe3GeTe2 (FGT) ferromagnets.This realization greatly expands materials design opportunities for semiconductor spintronics that are unavailable to MTJs with insulators 16,17 , including applications in artificial neural networks 18,19 and spin-lasers 20 .To our knowledge, this TMR significantly exceeds the largest reported value in any MTJ with a semiconductor spacer 21 .
The sketch of the MTJ devices is plotted in Fig. 1a, where the two FGT electrodes sandwich a GaSe layer and an hBN layer covers the whole junction to avoid oxidation.An outof-plane magnetic field B controls the magnetization alignment of the FGT electrodes.The devices (A, B, C, D, E, F and G) with different GaSe-layer thicknesses were fabricated using mechanical exfoliation and dry transfer method (See Methods), where the GaSe-layer thicknesses were determined by atomic force microscope (AFM) for device A, B, C, D, E, F and G are about 5.5, 6.5, 7.3, 8.2, 9.2, 10.0 and 15.6 nm, respectively (Supplementary Fig. 1).
From the optical image of all the fabricated devices, the active junction overlap areas A < 20 μm 2 , which are comparable to the typical magnetic domain sizes in FGT flakes 22 .
We first investigate the current-voltage (I-Vbias) characteristics under applied perpendicular B = -0.4T to ensure the parallel-magnetization configuration of the two FGT.To directly compare different devices, the normalized nonlinear current density-voltage J-Vbias curves at 10 K for devices A to G are shown in Fig. 1b, where the nonlinear behavior of devices A and B with a thinner GaSe layer shows in a larger current range (inset of Fig. 1b).The nonlinear J-Vbias characteristics reveal the existence of the tunneling-barrier between GaSe and FGTs.The band alignment at the FGT/GaSe interface obtained by fitting the Fowler-Nordheim tunneling plots 23 also reveals that the maximum tunneling-barrier of electrons is up to 0.83 eV (Supplementary Fig. 2).We next examine the TMR.Upon sweeping the out-of-plane B, the devices A-F show two distinct parallel (RP) and antiparallel resistance (RAP) states (Supplementary Fig. 3).Among them, at bias of 10 mV, the RP and RAP of device D are 122.25 kΩ and 357.52 kΩ, respectively (Fig. 1c).The corresponding TMR = (RAP -RP)/RP is 192.4%, which is the highest among the reported TMR devices with a semiconducting tunnel barrier 24,25 .The thickness of GaSe-layer dependence of the measured maximum TMR ratio is shown in Fig. 1d, which first increases from 83.1% (device A) and 133.5% (device B) and 180.2% (device C) to 192.4% (device D) and then decreases to 182.3% (device E) and 121.7% (device F), and finally vanishes (devices G) with increasing the thickness of GaSe-layer.The zero-bias resistance-area product (RA) of the devices for both the parallel and antiparallel states increases approximately exponentially with increasing the GaSe thickness, suggesting that the transport mechanism is dominated by tunneling (inset of Fig. 1d) 26 .The large TMR and nonlinear J-V curve indicate that the GaSe spacer serves as a good tunneling-barrier.The maximum TMR at low bias is found in the device with GaSe of 8.2 nm, and the internal physical mechanism can be explained as follows.On one hand, the spin filtering effect of GaSe gets weaker when the thickness is reduced, resulting in the decrease of TMR 2 .On the other hand, with further increase of the spacer thickness, the TMR decreases and, eventually, vanishes in device G with 15.6-nm-thick GaSe, where the tunneling through extrinsic defects could become important and eventually exceed the spinrelaxation length of GaSe 27,28 .This experimental result suggests we can further improve TMR by optimizing the thickness of the semiconductor spacer layer.To investigate TMR(Vbias) for devices with different GaSe thickness, we measured the R-B curves.As shown in Fig. 2a-b, the positive TMRs decrease with Vbias.Negative TMRs of -12.3% and -30.5% for devices A and D are obtained at 1.2 V and 0.9 V, respectively.This salient sign inversion of TMR is found in all the devices A-F.The number of sign reversals of TMR can be tuned, from single to multiple, with increasing the GaSe thickness.To better understand the variation of TMR with bias, as shown in Fig. 2c, we measured the I-Vbias curves of the devices in parallel and antiparallel states respectively.The nonlinear I-Vbias curves for devices B, D and E show very different trends in parallel and antiparallel states, which allow us to derive bias-dependent TMR for these devices (Fig. 2d).The obtained TMR value matches well to that extracted from the R-B curves (Fig. 2a-b and Supplementary Figs.4-5), indicating the influence of the Zeeman effect on TMR is negligible.The symmetric bias-dependent current and TMR suggest the symmetrical FGT/GaSe interfaces in these devices.
The devices A (Supplementary Fig. 6) and B show similar bias-dependent behavior of TMR.Specifically, as shown in Fig. 2c, for device B, the measured current for the parallel state is higher than that for the antiparallel state for Vbias < 0.76 V, leading to a positive TMR.
However, beyond such Vbias, the measured current for the parallel state is lower than that for the antiparallel state, resulting in a negative TMR (Fig. 2d).With increasing the thickness of the GaSe spacer layer, we observed multiple sign changes of the TMR.As shown in Fig. 2c, the nonlinear I-Vbias curves of device D in parallel and antiparallel states show two crossovers, and similar behavior is also observed in device C (Supplementary Fig. 7).Correspondingly, in Fig. 2d, the TMR of device D first decreases monotonously and changes sign of around 0.58 V, and again around 1.27 V as the bias increases.With further increasing the GaSe thickness, as shown in Fig. 2c, the nonlinear I-Vbias curves reveal three crossovers for device E. In Fig. 2d, the TMR of device E first decreases monotonically and changes sign around 0.56 V, and then the TMR decreases in an oscillatory fashion as the bias increases.Similar three-sign changes of TMR behavior is also observed in device F (Supplementary Fig. 8).To understand the bias-dependent magnetotransport, the spin-resolved density of states (DOS) of FGT in the 3-layer-FGT/6-layer-GaSe/3-layer-FGT heterojunction were obtained using the first-principles calculations (see Supplementary Fig. 9).The calculated spin-resolved DOS of FGT electrode is shown in Fig. 3a.Assuming that tunneling is elastic and spinconserving, with its tunneling probability independent of the initial and final states 29 , the spindependent tunneling current at zero temperature can be expressed as 1,2,30  are the chemical potentials and spin-resolved DOS for the drain (or source) FGT, respectively (σ is the spin index), and μDμ(S) = eVbias (Fig. 3b).The tunneling currents in parallel and antiparallel configurations can thus be expressed as  The above calculation of the spin-dependent tunneling current assumed that the transmission probability is the same for all initial and final states.However, if tunneling is at least partially coherent, the transmission probability should be larger for states with transverse momenta close to those where the decay rate of the evanescent states in GaSe is the smallest.
Because the band gap in GaSe is indirect, this may occur away from the Gamma point.The efficiency of this transverse-momentum filtering increases with increasing thickness of the tunnel barrier 30 .
Because the interlayer dispersion of the vdW FGT states is weak, they are at a given   -c all pass through the same zero at all temperatures, verifying that the bias-dependent TMR in the devices is dominated by tunneling 23 .The extracted TMR at different temperatures at 10 mV for device D (Fig. 4d) and device B and E (Supplementary Fig. 10) show a decreasing trend, which can be attributed to the decrease of spin polarization with temperature.When Vbias is extremely small, approximately only the electrons at the EF take part in tunneling transport.For simplicity, assume the source and drain FGT electrodes have almost the same spin polarization.Then TMR can be defined as TMR = 2P 2 /(1-P 2 ), where P denote the spin polarization at the EF for the drain and source FGT electrode 1,2 .As shown in Fig. 4d, the P decreases with temperature and the maximum P at 10 K is up to 70%, which is about 4 times larger than that obtained in other 2D semiconductor-based MTJs 24 .The estimated temperature-dependence of the spin polarization can be fitted well by the Bloch's low, given by P = P0(1-αT 3/2 ), where P0 is the spin polarization at 0 K, α is a materials-dependent constant 32 .The fitting value of α is 1.26-1.40×10-4 K -3/2 , which is comparable to the previous reports 24,33 .
Our presented results, which demonstrate large and tunable TMR, substantiate an ambitious vision where all-vdW MTJs could replace various charge-based memory applications 5 , targeted to reach TMR~200% for commercial viability.Implementing such vdW MTJs is expected to rely on insulating 2D tunnel barrier 5 , just as it was shown with h-BN barrier in an all-vdW MTJ with, at that time, the largest low-temperature TMR~160% 33 and also supported by a very recent report of TMR ~300% 34 .However, since we observe the desired large TMR values even with a semiconductor spacer, the prospect for all-vdW spintronics becomes considerably broader than just memory applications and the resulting large spin polarization and spin-orbit coupling opens opportunities beyond magnetoresistive effects.For example, the measured sign reversal of the TMR with applied bias is consistent with the reversal of the carrier spin polarization and could enable desirable polarization modulation 20 .Our findings could integrate semiconductor based optoelectronics, microelectronics and spintronics together, and could also relevant to emerging cryogenic applications where proximity-modified semiconductors and MTJs provide a platform for fault-tolerant quantum computing 35 .

Fig. 1 |
Fig. 1 | Large TMR in the FGT/GaSe/FGT MTJ devices.a, The schematic diagram of the device and magnetotransport setup.The magnetic field (B) is applied in out-of-plane direction.b, Current density J versus applied bias Vbias for the devices with the GaSe thickness ranging from 5.5 to 15.6 nm (devices A-G) in parallel-magnetic configuration.The inset shows the J-Vbias curves of devices A and B in a larger bias range.c, Magnetic hysteresis of the resistance R loop for device D at Vbias = 10 mV, and the corresponding TMR is ~192.4%.Red and blue horizontal arrows show the sweeping directions of B. Black-vertical arrows denote the two FGTs' magnetization configurations.d, The measured maximum TMR ratios in the different devices at 10 mV.The inset shows the plotted zero-bias log(RA) is nearly linear with the number of GaSe layers in both parallel and antiparallel states.

Fig. 2 |
Fig. 2 | The bias-dependent TMR of the devices.a-b, The R-B curves at various positive bias for devices B and D. c, I-Vbias curves of devices B, D and E in parallel and antiparallel states, respectively.d, The corresponding TMR as a function of Vbias.The hollow symbols are extracted from the R-B curves.The temperature is fixed at 10 K.

Fig. 3 |
Fig. 3 | The simulation of spin-resolved DOS of FGT and bias-dependent TMR calculated by elastic tunneling model.a, The calculated spin-resolved DOS for both the up (blue line) and down (red) spins of the FGT in 3-layer-FGT/6-layer-GaSe/3-layer-FGT heterojunction.b, Schematic diagram of direct band-to-band spin-dependent tunneling under bias window Vbias (shaded area).Light blue and green arrows represent the tunneling direction of the electrons in parallel and antiparallel states, respectively.c, The calculated TMR as a function of Vbias by using the simple elastic tunneling formula.

Fig. 3c .
Fig.3c.With increasing bias, the calculated TMR rapidly drops, changes sign, and then oscillates in qualitative agreement with the measurements for devices E and F. Multiple sign changes of TMR with increasing bias have also been predicted theoretically for Fe/MoS2/Fe MTJ devices31 .As the thickness of GaSe spacer decreases, the number of TMR reversals decreases to two in devices C and D and only one in devices A and B. The possible physical mechanism of the thickness-dependent TMR reversals is explained as follows.
transverse momentum essentially quantized.An energy isosurface of a lead thus consist of one or more 1D Fermi contours.Coherent tunneling is only possible at the intersections of the isosurfaces of the two leads corresponding to the same electrochemical potential.At large barrier thickness, a strong enhancement of the tunneling current should occur when such crossing points fall close to the points of the smallest decay rate in GaSe.If such matching condition is satisfied at the given bias for initial and final states of the same or opposite spin, positive or negative TMR is expected, respectively.The relative importance of such matching should increase at larger barrier thickness as long as coherent tunneling persists.Thus, coherent tunneling may explain why additional sign changes of TMR as a function of bias are observed at larger GaSe thicknesses.

Fig. 4 |
Fig. 4 | The temperature-dependent TMR.a-c, TMR ratios of devices B, D and E measured at temperatures from 10 K to 190 K, respectively.e, The TMR and spin polarization of device D as a function of temperature at bias of 10 mV.The red line shows the fitting data by the Bloch's low 1 .

Figure S6 .
Figure S6.R-B curves of device A with 5.5-nm-thick GaSe-layer at various positive bias a) and negative bias b).c) I-Vbias curves of device A measured in parallel and antiparallel magnetic configurations, respectively.d) TMR of device A as a function of Vbias, which decreases with the increase of bias and becomes negative when the bias exceeds 1.20 V.The temperature is fixed at 10 K.

Figure S7 .
Figure S7.R-B curves of device C with 7.3-nm-thick GaSe-layer at various positive bias a) and negative bias b).c) I-Vbias curves of device C measured in parallel and antiparallel magnetic configurations, respectively.d) TMR of device C as a function of Vbias, which decreases with the increase of bias and becomes negative when the bias exceeds 0.60 V and then back to positive value when the bias exceeds 1.43 V.The temperature is fixed at 10 K.

Figure S8 .
Figure S8.a) I-Vbias curves of device F with 10-nm-thick GaSe-layer in parallel and antiparallel states, respectively.b) TMR versus Vbias of device D. The temperature is T = 10 K.