Electron spin resonance in a proximity-coupled MoS₂/graphene van der Waals heterostructure Open Access

Proximity causes interaction—naturally, this basic rule also holds for nanoscale junctions made of van der Waals (vdW) materials.^1,2 By now, it is possible to assemble a large number of different vdW materials in order to tailor a system with specific properties, thus bringing together the best of “many worlds.” In particular, hexagonal boron nitride (h-BN) has been used to encapsulate vdW materials, enhancing the electronic properties of graphene (Gr) as well as different transition metal dichalcogenides (TMDCs).^1,2 For MoS₂ and WS₂, this has been studied in p–n junctions via excitons³ and in twisted homo-bilayers,^4,5 which show correlated electronic phases. MoS₂ and Gr are heavily studied systems individually. While Gr is a semi-metal, MoS₂ is a semiconductor (intrinsically typically n-doped) with large spin–orbit coupling (SOC), where the carrier density and thus its conductivity can be tuned by means of a gate voltage. The mobility and conductivity of MoS₂, however, are limited predominantly due to the rough interface and the SiO₂ substrates. In addition, it forms Schottky contacts with most metals, so that the fabrication of Ohmic contacts is a challenge.⁶ On the other hand, Gr is well studied as a Dirac metal with high charge carrier conductivity and mobility,⁷ but its device performance has been limited due to the lack of a bandgap and relatively small intrinsic SOC of the order of only 40 µeV.^8–11 Enhancing the SOC with TMDCs in close proximity is thus a way to marry the benefits of the properties of both materials.

Graphene can be employed as an Ohmic contact (or conductive backbone) material for MoS₂.^12,13 It is assumed that valley-Zeeman and Rashba-SOC are induced in Gr-on-TMDCs via the proximity effect.^14–18 Furthermore, it was suggested that the bandgap of MoS₂ could be tuned in Gr/MoS₂ heterostructures.¹⁹ This induced SOC is expected to be up to two orders of magnitude higher than the intrinsic value of Gr. In accordance with this, proximity induced SOC has been reported in a few experimental studies for heterostructures of Gr/WS₂,^20,21 Gr/WSe₂,¹⁸ and Gr/MoS₂.^18,22 Proximity induced spin lifetime anisotropy has also been explored in Gr/TMDC(MoSe₂).^23,24 So far, the signatures of induced SOC have been observed via magneto-transport embedded in weak anti-localization (WAL)^18,21 measurements, or via the spin Hall effect,^20,22 in Coulomb-drag effect studies,²⁵ and in the modulation of the Schottky barrier height.²⁶ Among these, only a couple of studies reported the electron transport behavior in Gr-on-MoS₂ at low temperatures.^18,25 A direct measurement of the g-factor on such a hybrid system has not been performed until today. Here, the premise is that the g-factor for free electrons is well-known with a value of 2.0023.^27,28 Any deviation is an indication of SOC in the system. In previous resistively detected electron spin resonance (ESR) measurements on single-layer and multi-layer Gr, a g-factor, parallel to the c axis of (1.952 ± 0.002), was determined for Gr-on-SiO₂.²⁹ 

Here, we report on a detailed resistively detected ESR traced in magneto-transport of Gr-on-MoS₂ (or in short GroMoS) samples in direct comparison with standard Gr-on-SiO₂ (or GroSi). The four-point measurements of the electrical resistance of the device are carried out at 1.5 K, as shown in the schematic architecture in Fig. 1(a). In order to couple an ESR signal, a Hertzian resonator coil is placed in the vicinity of the sample for microwave irradiation, which will be discussed in the following.²⁹ The magnetic field component of the microwave (B_ν) has to be perpendicular to the external magnetic field (B).³⁰ The magnetic moment of the electron precesses around the direction of B, while a resonant B_ν tips the magnetic moment into the plane, i.e., perpendicular direction to B. In terms of energy, the spin energy level splits with B, while B_ν causes spin flips when the frequency matches the splitting, according to the equation hν = gμ_BB. These resonant spin flips are observed as a change in the resistance attributed to spin energy being transferred to mobile electrons and momentum randomization of electrons.^31–33 

We use standard magneto-transport measurements to detect ESR, evaluate the charge transfer between the layers, and determine the doping density. We are able to report on the deviation of the g-factor (g∥c axis) of Gr from its intrinsic value in the heterostructure signaling that the SOC is altered by the close proximity of the MoS₂ layer.

We exfoliated few-layer MoS₂ on a 300 nm SiO₂/Si wafer and fabricated a Hall-bar of CVD-grown Gr (Graphenea Semiconductor S.L., Spain) on top.^29,34 A part of the Gr Hall-bar covers the MoS₂ sample, while the other part is directly placed on SiO₂, as shown in Fig. 1(b). The contacts were fabricated on top of the Gr on both regions using standard electron beam lithography techniques with Ti/Au (4/70 nm) metallization. Figure 1(b) shows the optical image of the device where the exfoliated MoS₂ flake is outlined by the purple dotted line as a guide to the eye. The reactive ion etching process for the Hall-bar fabrication (also etched the MoS₂ outside the defined region) ensures Ohmic contacts on Gr. The highly p-doped Si under a 300 nm thick SiO₂ dielectric was used as the gate electrode to tune the carrier concentration.

In order to characterize GroSi and GroMoS, we performed Raman spectroscopy with a standard 532 nm laser, as shown in Figs. 1(c) and 1(d). Figure 1(c) shows the peaks corresponding to MoS₂ where the in-plane (E¹_2g) and out-of-plane vibration peaks (A_1g) are observed at 383.8 and 408.6 cm⁻¹, respectively, only on the GroMoS. Clear G and 2D peaks of Gr are observed in both the regions in Fig. 1(d). We do not observe any significant D-peak, indicating that the quality of Gr has not been compromised. We observe that GroMoS shows a small upshift in the 2D peak position compared to GroSi. The observed upshift is consistent with the vdW interaction with the MoS₂ flake.³⁵ Atomic force microscopy (AFM) performed on the sample after the transport measurements reveals that the uniformity of the graphene layer on MoS₂ has not been compromised (see the supplementary material, Fig. S1). The thickness of the flakes measured by AFM is higher than those attributed to the moisture adsorption and thermal cycling.

The device was annealed after fabrication at 200 °C in vacuum of 10⁻⁴ mbar overnight to remove any excess moisture.³⁴ The sample was then cooled to 1.5 K in a helium bath cryostat without breaking the vacuum. All transport measurements shown are performed at 1.5 K with and without a perpendicular magnetic field. The results to be discussed further are measured in four-point lock-in configuration by passing an AC current across the probes marked as A and D (ground) of Fig. 1(a).

Figure 2(a) shows the longitudinal resistance of the device measured between probes B and C as a function of the applied back gate voltage (V_g). This measurement was performed over the whole Gr Hall-bar where one voltage probe is on GroSi and the other on GroMoS. The black and green dotted line traces show the forward and backward sweep, respectively, where a clear ambipolar behavior is observed, as expected in Gr. The solid traces are respective Lorentzian fits to the measured transresistance. The charge neutrality point (CNP) for the Gr is V_g ∼ 7 V. The doping of the graphene is appreciably small, and we do not observe a significant hysteresis, which would be indicative of reduced moisture on the sample.³⁴ 

As observed commonly for CVD-grown Gr, we find weak localization (WL) signatures as a result of the strong inter-valley scattering.³⁶ WL is observed for all gate voltages with the data close to the CNP shown in Fig. 2(b). The Hall resistance measured across probes B and E for different gate voltages is shown in Fig. 2(c). Note that this Hall measurement is performed in the GroSi region alone. The sign reversal of the slope between 7 and 8 V signals the change in the carrier type from holes to electrons at the CNP. We also observe a small WL peak in the Hall data from a small parasitic longitudinal component in the measurement. The Hall slope is plotted against the gate voltage in Fig. 2(d), where the sign change is most evident. The mobility of the Gr is estimated to be ∼500 cm² V⁻¹ s⁻¹. The poor mobility in the device could be a result of the grain boundaries and wrinkles in our samples as observed in the AFM image (supplementary material, Fig. S1).³⁷ 

The carrier density is calculated close to the CNP using a two-carrier model³⁸ (for details, see supplementary material S2) and plotted in Fig. 2(e) using the longitudinal and transverse resistances in Figs. 2(b) and 2(c), respectively. The blue open circles and red filled circles represent the holes and electrons, respectively. The blue and red lines are linear fits to the carrier density that is lowest around ∼ 8 V. We also note a small asymmetry in the change of carrier density with the gate voltage for the hole and the electron side. We attribute this to the GroMoS region in the device. A saturation of the electron carrier density has been observed previously in GroMoS devices as a result of the negative compressibility in the system.³⁹ 

From a separate measurement on the GroMoS region (see the supplementary material, Fig. S2), we observe that the CNP is shifted to ∼−6 V, implying that MoS₂ is n-doping the Gr and thus a strong interaction between the systems is induced. We also observe jumps in the I–V characteristics taken from the GroMoS region as opposed to the whole sample, which is indicative of an exchange of electrons between the two layers (supplementary material, Fig. S3). We do not observe any ESR from this region, presumably as the cross section of the probed region is too small to induce a measurable signal.

Proximity induced SOC interactions between Gr and MoS₂ are reflected in the electronic g-factor, which we can experimentally address via ESR. Here, the magneto-resistance is measured across contacts B and C while simultaneously applying microwave radiation using a Hertzian coil antenna, as shown in the schematic in Fig. 1(a). The resonance signal is observed in the difference ΔR_xx of the magneto-transport measurements with and without radiation (dark), $ΔRxxB,hν=RxxB,hν−Rxx(B,dark)$⁠. The signal peak follows the resonance condition hν = gμ_BB corresponding to the Zeeman splitting for various microwave frequencies ν.⁴⁰ 

Figure 3(a) shows exemplary traces of ΔR_xx, measured at a gate voltage of 6.1 V, with ESR peaks highlighted by a dotted line as a guide to the eye. The smaller non-dispersive peak centered at B = 0 is an artifact from the temperature dependence of WL under non-resonant heating. The dense color-scale plot in Fig. 3(b) is a summary of all frequencies. The resonance region is marked with a magenta dashed line. Figure 3(c) shows a linear fit of the resonance, where the slope reflects the g-factor at 6.1 V. Similarly, we are now able to extract the g-factor for all other gate voltages around the CNP. The result of this g-factor analysis is plotted in Fig. 3(d) over the gate voltage range of interest. A detailed inspection results in an average value of 1.91 (red dashed line) as opposed to earlier reports on pure Gr, which reported a constant value of 1.952 ± 0.002, irrespective of the gate voltage.^10,29 We also calculated the spin lifetime using $τs=ℏ/2ΔE≅71.5±4$ ps, where ΔE = μ_BΔB is the Zeeman energy and ΔB is the half width of the ESR peaks.²⁹ This is comparable to the reported out-of-plane spin lifetime values for graphene and Gr/TMDC.^23,29 The half width (spin lifetime) is slightly smaller (larger) in comparison to that measured in GroSi reported by Lyon et al.²⁹ The graphene flake in our device lies partly over MoS₂. We believe this lowers the electron–hole puddles caused by the SiO₂ substrate, thereby increasing the spin lifetime.⁴¹ 

In contrast to former measurements, we observe a strong variation of the g-factor with gate voltage (i.e., carrier concentration). For positive V_g, the g-factor correction is twice as large as that for pure Gr,²⁹ which is consistent with the SOC enhancement via the proximity effect. As described by Gmitra and Fabian,¹⁶ a positive electric field induces a carrier transfer between graphene and MoS₂, where first principle calculations estimate a splitting of ∼1 meV. Hence, we can assume that the g-factor variation from 1.95 to 1.91 and its dependence on the gate voltage are proximity-induced, signaling the interaction with the MoS₂ layers. We stress that the measurement was carried out over a large strip of Gr covering SiO₂ as well as MoS₂. This “mixed” approach was necessary to improve the signal-to-noise ratio in ΔR_xx. We have not been able to obtain a recognizable ESR signal when the distance between the voltage probes is reduced. This, we assume, is due to the smaller number of spin flips owing to smaller area.

In conclusion, we can state that a clear ESR signal in the heterostructure of Gr/MoS₂ is traceable due to the interaction between the two systems. Variations of the g-factor indicate crosstalk of the strong spin–orbit coupled electrons of MoS₂ to the carriers in Gr as expected from theoretical calculations.^14–18 Enhanced SOC in Gr can potentially lead to topological phases, such as the quantum spin Hall effect.¹¹ Understanding the exact nature of this coupling will enable us to design spin-transfer devices with possibly extremely enhanced spin-relaxation times.