Two-dimensional ferromagnetism detected by proximity-coupled quantum Hall effect of graphene

The recent discovery of a two-dimensional van der Waals magnet has paved the way for an enhanced understanding of two-dimensional magnetic systems. The development of appropriate heterostructures in this emerging class of materials is required as the next step towards applications. Here, we report on the electrical transport in monolayer graphene coupled with the two-dimensional ferromagnet Cr2Ge2Te6 (CGT). Graphene that forms an interface with CGT is electron-doped owing to charge transfer. The temperature-dependent resistance of graphene/CGT undergoes a nontrivial sudden change near the Curie temperature (Tc) of CGT. Apart from this, the behavior of various transport parameters also differs before and after Tc. Moreover, the contribution of the magnetization of CGT to the enhanced magnetic flux density leads to the critical evolution of the quantum Hall state. These results imply that graphene in the graphene/CGT hybrid structure can be utilized to electrically monitor the magnetic phase transition of the adjacent CGT layer.

In particular, studies on the magnetic proximity effect were carried out only for thin films because two-dimensional (2D) magnetism was expected to be absent due to thermal fluctuation, according to the Mermin-Wagner theorem 24 . However, various 2D magnetic materials (Cr 2 Ge 2 Te 6 , CrI 3 , Fe 3 GeTe 2 , etc.) were recently reported such that abundant proximity-induced phenomena, both fundamental and practical, are anticipated [25][26][27][28][29][30] . Among these magnetic materials, Cr 2 Ge 2 Te 6 (CGT) offers advantages that include facile exfoliation, stability in the air, and an insulating nature, which enable the investigation of the electrical properties of a van der Waals (vdW) heterostructure such as those of the graphene/2D magnetic material. Monitoring the electrical properties of a graphene/2D magnet is of significance for two reasons. The first is the induction of spin-related transport in graphene for spintronic applications 13,15,19,[31][32][33][34][35] . The second, which is less well known, is that it allows the phase transition of a 2D magnet to be monitored 21 . Given that only magnetic properties such as magnetization can be studied in magnetic insulators, the fact that graphene can detect changes in adjacent 2D magnets provides a versatile route for investigating the phase transition.
Here, we report on the modification of the properties of graphene resulting from the magnetic-proximity effect of CGT. Prior to studying graphene/CGT, we characterized the electrical properties of pristine CGT using a graphene electrode to show that the results are consistent with those of previous studies. Then we examined the graphene/CGT to determine the influence of CGT on graphene, which exhibits many proximity-induced phenomena, including electron doping owing to charge transfer and the nontrivial temperature dependence of the transport properties related to the phase transition in CGT. The ability to detect changes in its environmental surroundings renders the graphene field-effect transistor a platform for studying various phases in magnetic insulators.

RESULTS
Device fabrication and characterization of pristine CGT and graphene/CGT The left panel of Fig. 1a exhibits a conceptual schematic of graphene/CGT heterostructure on h-BN, where the magnetization of CGT couples with graphene. The right panel of Fig. 1a shows a schematic representation (upper panels) and optical images (lower panels) of the graphene/CGT device (Device #1, D1). The device structure comprises exfoliated monolayer graphene placed on the bottom h-BN flake, which is followed by the transfer of the CGT and the top h-BN layers. Two types of graphene, patterned in the shapes of (i) two electrodes and (ii) a Hall-bar structure shown in Fig. 1a, were adopted to investigate the electrical properties of pristine CGT and graphene/CGT, respectively. It should be noted that the graphene and the CGT flakes were weakly coupled in our experiment, which may have resulted from the short-term exposure to air during the transfer of exfoliated CGT flakes (see Supplementary Fig. 1). Despite the weak coupling, as we show in the following results, the magnetic phase transition in CGT was sensitively monitored through the electrical transport in graphene, including the quantum Hall phenomena.
We characterized the electrical properties of pristine CGT (located across two graphene electrodes, marked as region (i)) in Fig. 1b, c. The inset in Fig. 1b shows that the graphene-CGTgraphene series resistance is ohmic in the two-probe (2P) configuration. The transfer characteristic curve of CGT in Fig. 1b exhibits p-type semiconductor behavior at room temperature [36][37][38] . Figure 1c indicates the temperature-dependent resistance with back-gate voltage (V bg ) of 0 V, showing nonmetallic behavior in the low-temperature regime. The magnitude of R 2p is of the order of 10 6 Ω near room temperature and increases to 10 12 Ω at the lowest temperature of 2 K. The thermal activation energy gap, estimated from the relation R 2p ∝exp(E a ⁄2k B T), where k B is Boltzmann's constant, is E a~0 .42 eV according to the linear fitting of the Arrhenius plot in the inset in Fig. 1c. The order of magnitude of this gap is the same as the previously reported values of~0.2 eV 39 and~0.8 eV 40 . From the viewpoint of graphene/CGT to be discussed below, the charge transport of CGT can be ignored owing to its extremely high resistance compared with that of graphene.
A more significant result is observed for the temperaturedependent resistance (R xx vs. T) of the graphene/CGT device (region (ii), where CGT is located on top of the graphene Hall bar), in Fig. 1d. The temperature dependence of R xx shows kink-like behavior near the temperature of 60 K, which corresponds to the Curie temperature (T c~6 1 K) of CGT for the ferromagnetic transition 25 . In general, phonon scattering (in the metallic regime, dR xx /dT > 0) and thermal activation (in the insulating regime, dR xx / dT < 0) were extensively discussed in a review on the transport of pristine graphene 41 . However, their common feature is that R xx vs. T changes smoothly rather than abruptly. Therefore, the peculiar change near 60 K in Fig. 1d for the graphene/CGT device can be attributed to extrinsic effects: the magnetic-phase transition of CGT in this case.

Charge transfer between graphene and CGT
We also observed n-type doping in the graphene underneath the CGT above T c as shown in Fig. 2. Schematic illustrations of two different device configurations (type A and B) are presented in Fig. 2a, c, respectively. For type A, which corresponds to samples D1 and D2, graphene was patterned in the shape of a Hall bar and partially covered by the CGT flake in the region of its internal voltage probes. The resistance of the sample was measured in two different ways. The first is the 2P configuration using the probes at both ends of the sample (as marked with red lines in Fig. 2a), where the measured resistance (R 2p ) is the addition of the resistance of both pristine graphene, and that of graphene/CGT connected in series. The other involved the use of the four-probe (4P) configuration to measure the resistance value (R xx ) of graphene/CGT only, because the voltage probes are entirely covered by the CGT flake. Figure 2b shows the transfer-characteristic curves of sample D1 at 80 K. The 2P measurement indicates that R 2p exhibits two distinct peaks at V bg = −11 V and 3 V, indicating that two types of graphene channel with different carrier density are connected in series 42 . However, R xx in the 4P measurement exhibits a single peak at V bg = −11 V, yielding the electrical property of only graphene/CGT. The well-matched peaks at V bg = −11 V in both data curves surely correspond to the Dirac point (V DP ) of graphene/CGT. The observation that V DP of graphene/CGT is more negative than that of pristine graphene reveals that electron doping occurred as a result of charge transfer between graphene and CGT. This electron doping effect is repeatedly observed in a different device configuration, type B shown in Fig. 2c, where many R 2p electrode pairs are formed in the same sample, and one of them is covered by CGT. The sample D3 gives V DP = 2 V for graphene/CGT and V DP = 12 V for pristine graphene as in Fig. 2d. In addition to samples D1 and D3, other samples, D2 (type A) and D4 (type B), also exhibit reproducible electron doping effects as summarized in Supplementary Table 1. Moreover, all of these devices exhibit a similar electron doping level of~7.58 × 10 11 cm −2 as an average density. This feature may be related to the charge transfer originating from the difference in the work function between graphene and CGT 43 .
Critical behavior due to proximity coupling By focusing on the ferromagnetic phase of CGT below T c~6 1 K, we observe a clear change in the transport parameters of graphene/CGT, which are collectively shown in Fig. 3. The V bgdependent longitudinal resistance curves of sample D1 at 80 K and 2 K are presented in Fig. 3a. At 80 K, R xx undergoes no hysteresis when the V bg sweep direction is reversed, whereas hysteresis is observed at 2 K. The ΔV DP data, defined as the difference between V DP values in the opposite V bg sweep directions, are plotted as a function of temperature in the upper panel of Fig. 3e. Hysteresis (represented by ΔV DP ≠ 0) exists in the temperature region below 60 K, but disappears (with ΔV DP = 0) at temperatures above 60 K. The inset shows the raw data of V DP that were used for estimating ΔV DP . Hysteresis in the R xx vs. V bg transfer curves is usually ascribed to the effect of charge traps near the channel, where the trapping and releasing processes are controlled by the gate bias 44 . Even though the energy trap can be deepened as the temperature decreases, the sudden emergence of hysteresis near 60 K cannot be easily understood without a correlation with the ferromagnetic phase transition of CGT. Furthermore, similar hysteresis is observed in the quantum Hall (QH) state at the temperature of 2 K and magnetic field of 14T as in Fig. 3b. The fact that charge traps usually induce strong Coulomb scattering and hinder the appearance of clear QH states seems to suggest that the charge traps are spatially apart from the graphene channel in this graphene/CGT device.
We also confirmed the coupling between graphene and CGT located in close proximity by investigating the magneto-transport properties of the graphene/CGT device. Figure. 3c, d show graphs of R xx and R xy vs. μ 0 H of sample D1 at various temperatures between 2 K and 150 K, respectively, where μ 0 is the vacuum permeability and H is the magnetic field strength. The QH states of monolayer graphene, corresponding to the quantized Hall resistance of h⁄2e 2 and h⁄6e 2 , in which h is Planck's constant and e is the charge element, exist in the low-temperature regime. However, unlike the general QH feature of pristine graphene where the positions of QH plateaus or R xx peaks are fixed for a given V bg 45,46 , the position of the R xx peak of the graphene/CGT device in Fig. 3c shifts towards the high-magnetic field regime as the temperature decreases from 60 K (orange dot) to 2 K (black dot). This tendency is confirmed in the second panel of Fig. 3e, which shows the temperature dependency of the R xx peak. Interestingly, the R xx peak does not shift markedly at temperatures above 60 K.
The Hall carrier density (n Hall ) is obtained from the slope of the R xy data curves, i.e., dR xy /d(μ 0 H), at low magnetic fields (between −1 T and 1 T) in Fig. 3d. As shown in the third panel of Fig. 3e, the temperature dependency of n Hall changes abruptly near 60 K. In addition, the temperature-dependent mobility (μ) was also estimated with V bg = 0 V on the basis of the Drude model (σ = μne) and is plotted in the fourth panel of Fig. 3e, where σ and n were obtained from the measured R xx (Fig. 1d) and n Hall (Fig. 3e), respectively. All the transport parameters in Fig. 3e exhibit critical changes near 60 K, which is in good agreement with the magnetic-phase transition of CGT at T c . The consistency of the critical behavior of μ(T) with the magnetic phase transition also implies that it is affected by the magnetic-proximity effect and consequently becomes a relevant indicator for the phase transition.
We conducted a more in-depth analysis by examining the correlation among the transport parameters in Fig. 3e. Because the position of the R xx peak for a given QH state is connected with the carrier density (n) and the magnetic field (H) from basic QH physics, we deliberately considered these two factors simultaneously by adopting the concept of a filling factor ν, defined as ν = nh/(eμ 0 H). Figure 4a, b present the graph of R xx and R xy vs. the inverse of the filling factor (ν −1 ) at different temperatures. The R xx peak shift is clearly suppressed at low temperatures in Fig. 4a. Furthermore, the linearity of R xy in weak magnetic fields is scaled with ν −1 irrespective of the temperature (Fig. 4b). These results indicate that the shifts of μ 0 H peak and n Hall in the second and the third panel of Fig. 3e have the same physical origin, which is the variation in the temperature-dependent carrier density under the influence of the ferromagnetic phase transition of CGT at its Curie temperature (T c~6 1 K) 25 .
Furthermore, Fig. 4b reveals the evolution of additional QH states in relation with the phase transition of CGT. More specifically, R xy is entirely linear at the high temperature of 150 K until it encounters the ν = 2 QH plateau, but it deviates from that linearity as the temperature decreases. Finally, R xy becomes quantized with the value of h/6e 2 corresponding to the ν = 6 QH state. For the quantitative analysis, we differentiated R xy with respect to ν −1 in Fig. 4c to verify the formation of the ν = 6 QH plateau (i.e., dR xy /dν −1 → 0 as indicated in Fig. 4e for the conventional QH effect), and plotted the dR xy /dν −1 values for ν = 6 as a function of temperature in Fig. 4d. Noticeably, dR xy /dν −1 is almost constant above T c , but its magnitude starts to decrease as the temperature is lowered below T c until it becomes dR xy /dν −1 0 to form the clear ν = 6 QH state at low temperatures. This change can be interpreted concerning the magnetization in CGT coming into existence below T c . A comparison of the evolution of the ν = 6 QH state as a function of temperature in Fig. 4c with the other results in Figs. 1d and 3e show that all the transitions begin to occur near 60 K, which corresponds to the magnetic transition temperature of CGT. The total magnetic field, which, strictly speaking, is the magnetic flux density defined by B = μ 0 (H+M) where M is the magnetization, is abruptly boosted by the ferromagnetic transition in CGT. This correspondence of the sudden change in n Hall and the evolution of the ν = 6 QH state is also observed in the other sample D2 (Supplementary Fig. 3). Other possibilities, such as parallel conduction through CGT, can be excluded by the typical temperature dependence of the QH effect as a function of ν. In addition, the result that the value of n Hall increases with decreasing temperature precludes the contribution of thermal activation in CGT.

DISCUSSION
The essential observation in this work is that gate hysteresis is strongly correlated with the ferromagnetic phase transition of CGT. There are mainly two origins for gate hysteresis of graphene FET: charge trapping and capacitive gating 47 . The two mechanisms give distinct hysteresis direction with V bg , indicating that charge trapping is responsible for our case. Depending on charge trapping agents such as defect sites in graphene/substrate or adsorbate, the temperature dependence of gate hysteresis is distinguished [48][49][50][51] . Because our pristine graphene in the device D1 has no significant temperature-dependent hysteresis, we can rule out the aforementioned origins. We also show in Supplementary  Fig. 6 the back-gate voltage sweep data at room temperature of many other pristine graphene devices on SiO 2 and on h-BN/SiO 2 substrates. The non-hysteresis of the devices confirms that no extrinsic sources for the hysteresis are involved during the fabrication process in our experiment. As a result, the hysteresis can be utilized as a sensitive probe in this study. Furthermore, the critical occurrence of the gate hysteresis implies that ferromagnetic phase transition of CGT layer is indeed the origin for the gate hysteresis. Even though the microscopic mechanism for the spinmediated trapping needs further theoretical work, signatures such as anomalous Hall effect (AHE) and exchange-induced state (ν = 4) could exhibit its spin-related nature. Namely, even though the unclearly-defined CGT layers at the interface between graphene and CGT were formed as shown in Supplementary Fig. 1 of the TEM side-view image, we observed induced AHE feature and spinpolarized state for D1 as shown in Supplementary Figs. 7 and 8, respectively. Based on the discussion, we should emphasize that gate hysteresis becomes an appropriate parameter to detect phase transition of adjacent CGT layer, which can be expanded to other magnetic phases.
In addition to gate hysteresis, the other transport parameters can be employed to probe magnetic phase transition of ferromagnetic CGT; especially, T c can be estimated by the electrical way. In fact, the seminal study for the magnetic proximity effect of graphene/CGT heterostructure has been Fig. 3 Probing phase transition of CGT using temperature-dependent transport of D1. a R xx vs. V bg with 0 T at 80 K (black) and 2 K (red). b R xx vs. V bg with 2 K and 14 T, depending on sweeping direction. N indicates the Landau level index and ΔV peak is the difference in the peak position for each N. c, d Temperature-dependent R xx and R xy vs. μ 0 H with V bg = 0 V. e Temperature dependence of the extracted transport parameter ΔV DP , which is obtained from the difference of V DP for forward-(black squares) and backward-(red circles) gate sweeping in the inset. The black-dotted line is to guide the eye. μ 0 H peak corresponds to the local maxima depicted by the dots in (c). Hall carrier density n Hall is extracted by linear fitting from −1 T to 1 T of R xy vs. μ 0 H in (d). Mobility μ is calculated using the Drude model, where R xx in Fig. 1d and n Hall in Fig. 3e are adopted.
T.K. Chau et al. performed in terms of the Hanle spin precession experiment. Different from the nonlocal measurement configuration, we used local transport configuration and obtained a similar estimation for the magnetic phase transition of CGT. Consequently, a complementary understanding of the magnetic proximity in graphene/ CGT heterostructure can be achieved with previous nonlocal transport 35 .
In summary, we investigated the electrical transport properties of graphene under proximate coupling with a 2D ferromagnetic insulator, CGT, by forming a graphene/CGT heterostructure. Graphene is an appropriate contact electrode, making it feasible to measure the transport in pristine CGT. And the graphene/CGT heterostructure is suitable to detect the phase transition of CGT from its conductance variation. We found various pieces of evidence of successful proximity effects as discussed above. Furthermore, we observed the sudden emergence of an additional QH state, which can be attributed to additional magnetic flux density due to the magnetization of CGT. These results imply that graphene can sense the magnetic phase transition that occurs in adjacent CGT near T c . Unlike many previous experiments regarding magnetic property measurements 25,36,37 , the graphene transistor has the ability to detect electrical changes associated with magnetic phase-transition phenomena as a result of the proximity effect of the magnetic insulator. We foresee graphenebased vdW heterostructures to become an electrical platform for exploring various phases in magnetic insulators.

Device fabrication
Graphene/CGT heterostructures were fabricated on a heavily p-doped silicon substrate, with a 300-nm-thick SiO 2 insulating layer, as follows. First, h-BN flakes, with thicknesses in the range 20-40 nm, were exfoliated directly on the SiO 2 /Si substrate. Monolayer graphene was obtained via mechanical exfoliation on the PMMA/PVA/SiO 2 /Si substrate, where poly (methyl methacrylate) (PMMA) and poly(vinyl alcohol) (PVA) is coated and then transferred onto the h-BN/SiO 2 /Si substrate. Subsequently, the graphene was etched by oxygen plasma (3 mTorr and 30 W) for D1 and D2 to construct the Hall-bar structure and the graphene electrode. Metalelectrode patterning was performed using electron-beam lithography, followed by Cr/Au (5/50 nm) evaporation under high-vacuum conditions (~10 -6 Torr). The graphene device on h-BN was annealed in forming gas (H 2 , Ar) at 300°C for 4 h to remove contamination on the graphene surface. Second, CGT, with a thickness of a few tens of nanometers, was transferred onto the graphene devices. CGT flake was exfoliated from the single crystal (HQ grapheme, Netherland) and immediately transferred to avoid oxidation at the interface. Finally, a thick h-BN layer was placed on top of the device soon after transferring the CGT, to prevent oxidization of the latter.

Device characterization
We recorded the Raman spectra with a 532-nm laser under ambient conditions (Renishaw Inc., UK). The TEM cross-sectional experiment was carried out using a high-resolution TEM (JEM ARM 200 F, JEOL, Japan). The DC electrical characteristics of the pristine CGT (and graphene), and graphene/CGT were analyzed under high vacuum (~10 -6 Torr) in a cryostat (Physical Property Measurement System (PPMS), Quantum Design Inc., USA) with a semiconductor parameter analyzer (4200SCS, Keithley Instruments Inc., USA). We gently annealed the devices at 400 K for approximately 2 h in high vacuum (approximately 10 -6 Torr) before the electrical measurements.

DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request. Fig. 4 Scaling of R xx and R xy in terms of ν -1 and magnetization-enhanced magnetic flux density (D1). a, b R xx and R xy vs. ν −1 (=μ 0 He/nh) with respect to temperature. The gray shaded area indicates the region in which ν = 6, where the typical temperature-dependent QH effect is observed. R xx shows a fixed dip and R xy crosses near ν = 6, at a different temperature, in the gray region. Higher filling factors of 10 and 14 are indicated by red arrows. c Slope of R xy vs. ν −1 (i.e. dR xy /dν −1 ) near ν = 6 from 150 to 2 K. d Plot of temperature-dependent dR xy /dν −1 at ν = 6. e Schematic of R xx and R xy vs. ν −1 for typical QHE of graphene with respect to temperature. At filling factor ν, R xy evolves from linear (red) to plateau (blue) with decreasing temperature. At intermediate temperatures, R xy deviates slightly from linearity near ν (green).