Spin-momentum locking and spin-orbit torques in magnetic nano-heterojunctions composed of Weyl semimetal WTe2

Spin–orbit torque has recently been intensively investigated for the purposes of manipulating the magnetization in magnetic nano-devices and understanding fundamental physics. Therefore, the search for novel materials or material combinations that exhibit a strong enough spin-torque effect has become one of the top priorities in this field of spintronics. Weyl semimetal, a new topological material that features open Fermi arc with strong spin–orbit coupling and spin–momentum locking effect, is naturally expected to exhibit an enhanced spin-torque effect in magnetic nano-devices. Here we observe a significantly enhanced spin conductivity, which is associated with the field-like torque at low temperatures. The enhancement is obtained in the b-axis WTe2/Py bilayers of nano-devices but not observed in the a-axis of WTe2/Py nano-devices, which can be ascribed to the enhanced spin accumulation by the spin–momentum locking effect of the Fermi arcs of the Weyl semimetal WTe2.


Reviewer #2 (Remarks to the Author):
It is an interesting work and addresses a key topic. The field of Weyl semimetals has recently experienced a surge in all sorts of theoretical and experimental activities since the original proposal on the existence of Weyl points and Fermi arcs states in iridate materials. However, most work up to date has been done to detect Fermi arcs themselves and study chiral anomaly effect, two most striking features of Weyl semimetals, but the topological nature of the Fermi arcs states suggests their genuine applications in surface transport phenomena (as is the case of the topological insulators), something that is only beginning to appear. Therefore the present manuscript is important, timely, and potentially interesting to a broad physics community. However, the authors need to pay attention to the following points before the decision on publication is made: First, spin -momentum locking in topological insulators follows directly from the Hamiltonian of the surface state written in the form H=v [k * ez] *Sigma. There is no such Hamiltonian for the arc states, hence there is no spin momentum locking per se. On general ground, one can only expect that the spins along the arc should wind from one Weyl point to another Weyl point since the arc connect the points of opposite chirality. This has to be clearly explained in the manuscript and calling this effect "locking" is confusing. Second, the spin accumulation in topological insulators was studied theoretically in great detail in a recent Nature Communications 7, 10878 (2016) where the transfer of spin through the bulk has been emphasized as the primary mechanism of the spin accumulation. The authors here assume that it is a single surface phenomenon but bulk boundary correspondence, the genuine feature of topological systems seems to be missing in such assumption. The authors should discuss this point in greater details. Third, surface transport properties have been studied recently in a series of works [Phys. Rev. B 93, 235127 (2016), Phys. Rev. B 97, 085142 (2018)]. As the authors study a 2D transport in their system, and highlight rather high values for spin conductivity, it would be good to see a discussion in relation to the theoretical insights brought by these recent studies.
the resistance hysteresis feature in the samples with thickness thinner than 7.0 nm, although we measured several thin WTe 2 devices with thickness ranging from 4.0 to 7.0 nm. Figures R1-R3 gives the electrical detection of spin momentum locking in 10.0 nm thick WTe 2 device. Figure R1 shows the electrical detection of surface states with different measurement configurations, in which a DC current of 20 μA was applied. Except for the case of  To further demonstrate the spin-momentum locking effect in topological Fermi arc, we varied the strength of dc currents applied to the same sample (t=10.0 nm) with both dc current (I dc ) and magnetic field (H) along b-axis, as shown in Figure R2a. Figure R2b summarizes the dependence of the voltage difference between the high-and low-resistance states on the DC current. The nearly linear dependence of voltage difference on DC currents is in good agreement with that in Figure 3e in main text. The relative large error bars in 10.0 nm thick sample should be related closely to the fact that the thickness of 10 nm is near the critical thickness that Weyl semimetal states and topological Fermi arcs are gradually vanishing.   Figure R4.
And the results presented in Figure R5 show that the critical temperature that hysteresis behavior (I dc =20 μA) vanishes increased near 15-20 K, compared to the critical temperature of   text. Nevertheless, the different interfaces in heterojunctions will account for the difference in both spin momentum locking and spin orbit torques. We will discuss it below.
We added the new data into Supplementary Figures 19 and 20. Fig. 3f and Fig. 5c are not consistent for the similar thicknesses (23 nm vs. 20 nm). For the spin-momentum locking measurements, the signal is observed below 20 K, indicating the anisotropy below 20 K. However, in Fig. 5c, the strong anisotropy is observed below 150 K, and there is a slightly downward turn from ~10 K to ~ 2K.

Comment 2: 2) The critical temperatures between
These are certainly inconsistent with each other.
Reply: Thank you for your comment to improve our manuscript. As we observed and discussed above, the critical temperatures that hysteresis behavior vanishes are 7-10 K, 12-15 K and 15- First of all, we have to point out that the interfaces in the samples used to measure two effects are different, i.e. two interfaces in the sample of ferromagnet-insulator-Weyl used in spin momentum locking measurements, and one interface in the sample of ferromagnet-Weyl used in spin-orbit torques measurements. The effective spin polarization detected by ferromagnet and ferromagnet/insulator should be different. 1 Only when the thickness of the tunnel barrier is thick enough, the spin polarization by ferromagnet/insulator will approach the bulk spin polarization of ferromagnet. 1 Normally, the effective spin polarization in ferromagnet/insulator is smaller than that in bulk ferromagnet. Therefore, the critical temperature obtained in spin momentum locking experiment using a device of WTe 2 /Al 2 O 3 should be smaller than that obtained from the spin orbit torque measurement using a WTe 2 /Py device for the thick tunneling barrier lay of Al 2 O 3 (3 nm).
Second, during the device fabrication process, there are two more E-beam lithography (EBL) steps in making the devices used in spin momentum locking detection than in making the devices used in spin orbit torques measurements. Particularly, the WTe 2 /Al 2 O 3 layer has to be exposed to the e-beam lithography photoresist (PMMA). The quality of WTe 2 crystal might be deteriorated by the fabrication process, which might consequently damage the robust of topological Fermi arc states. Therefore, in comparison the critical temperature observed in the spin orbit torques measurements, the decrease of critical temperature observe in the measurements of spin momentum locking should be expected.
Most importantly, with the increase of WTe 2 thickness, the critical temperature in spin momentum locking detection increases from 7-10 K (10.0 nm) to 15-20 K (28.0 nm). This tendency agrees well with the observation in spin orbit torques measurements ( Figure 5 in main text).
As to the downward turn in spin conductivity, we believe that the slight downward turn in the temperature dependent spin conductivity (b-axis) from ~10 K to ~ 2K should be ascribed to the experimental error and fitting error (extraction of field like torque).Obviously, the fitting error bar of the data (b-axis) at 10 K in Figure 5c is relatively larger than that in other cases.
The reason for small discrepancy of critical temperature in both experiments is added in line 22 page 18 in main text and Supplementary note 2.  This carrier density in our WTe 2 flakes is almost twice that of the n-type carrier density of bulk WTe 2 reported previously. 4 The higher bulk carrier density of electrons in our very thin plates of several tens nanometers can be understood as following. In the large, single crystalline WTe 2 bulk, both low density of electrons and holes contribute nearly equally to the electrical conduction for its semimetal characteristics. 5 With decreasing the thickness of WTe 2 to the nm level, the Fermi level will shift upward near the Weyl point. 2 Consequently The dominated carrier changes to n-type and much more electrons (could be doubled) will be involved into the electrical transport.
To estimate the surface carrier density, we need to calculate from the Weyl orbit quantum oscillation in Figure 1 shown in main text, which is consist of two topological Fermi arcs and two bulk chiral Landau levels. According to Figure 1b,  According to our previous quantum oscillation analysis, 2 the Fermi velocity is The ratio of surface conduction to total conduction is, therefore, ). This case is opposite to the relative large surface state conduction in topological insulators. 6 Nevertheless, the 2D surface conduction in WTe 2 /Py can be obviously enhanced due to the formation of Rashba interface, as shown in Figures 1c and 1d in main text.
The discussion on surface state conduction and bulk conduction was added into the supplementary note 3. Have the authors ruled out those possibilities?
Reply: Thank you for your suggestion to exclude the fringe field effect and other spurious effect.
According to the work reported by E. K. de Vries, they could observe the voltage hysteresis loop not only for the case that the magnetization is perpendicular to the DC current but also for the one that magnetization is parallel to the DC current. They attributed to their observation to the fringe field induced by the asymmetry of these triangular features of Bi 2 Se 3 grain edges. 8 This asymmetric fringe magnetic field along z direction will also give rise to a Hall-like voltage loop, as shown in Figure R7. However, this case can be excluded as the origin in our case for following reasons.
First of all, topological insulator Bi 2 Se 3 tends to grow as a triangle, as shown in Figure R8a.
There are a great number of triangle shape grain edges, which will give rise to the fringe magnetic field when B i2 Se 3 is next to ferromagnetic layer. However, our mechanically exfoliated WTe 2 is quite flat without this asymmetric edge. Figure R8b gives a typical optical image of our exfoliated WTe 2 . Moreover, we have etched our WTe 2 into rectangle ribbons during the fabrication, and the region with terraces is removed by Ar during the device fabrication.
[Redacted: (Fig. 6)  In Pengke Li's work (PRB 93, 220404R 2016), they observed a nonlocal voltage hysteresis in the topological trivial metal (Au) based heterojunctions. In this work, the author did not explain clearly the physical origin of the observations. 9 Their voltage difference between two resistance states indeed shows significant temperature dependence, however, the anomalous Hall effect of CoFe should not exhibit so strong temperature dependence for the temperature below 50 K, because of the high Curie temperature of CoFe alloy. Therefore, they just rule out the spurious effect, such as, anomalous Hall effect of CoFe. Meanwhile, the strong temperature dependence in our observation (Figure 3f) also should exclude the possibility of anomalous Hall effect as the origin of our observations.
[Redacted: (Fig. 1a)  the spin direction tied with the momentum k, showing a spin texture in k space. In our work and in literature, the terminology "spin-momentum locking" refers to this kind of behavior.
As the referee mentioned, this concept has been widely discussed for topological insulators Thus, we think the usage of the terminology "spin-momentum locking" here is consistent with its usage in literature and is appropriate. Following the referee's suggestion, in the revised manuscript, we have cited the two relevant references mentioned above, and added the following explanation to clarify the issue. Please find them in page 8 line 10.  Fig.2(b)." Reply: We thank the referee for the valuable suggestion and for bringing into our attention these interesting theoretical works. In Phys. Rev. B 93, 235127 (2016), the authors found that the scattering between the Fermi arc surface states and bulk states for a Weyl semimetal leads to dissipation in the transport. In Phys. Rev. B 97, 085142 (2018), the authors found that such scattering strongly depends on the shape of the Fermi arc. The straight arc geometry is very disorder tolerant. These conclusions are quite interesting and relevant to our work.
Following the referee's suggestion, in revision, we have cited the mentioned works and added the following discussion in page 19 line 5.
"It has been shown that several factors could affect the transport of the Fermi arc states.
For example, the scattering between the Fermi arc surface states and bulk states for a Weyl semimetal would lead to dissipation in the transport. 4 In addition, such scattering has sensitive dependence on the arc geometry. 5