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Magnetic proximity in a van der Waals heterostructure of magnetic insulator and graphene

Engineering 2D material heterostructures by combining the best of different materials in one ultimate unit can offer a plethora of opportunities in condensed matter physics. Here, in the van der Waals heterostructures of the ferromagnetic insulator Cr2Ge2Te6 and graphene, our observations indicate an out-of-plane proximity-induced ferromagnetic exchange interaction in graphene. The perpendicular magnetic anisotropy of Cr2Ge2Te6 results in significant modification of the spin transport and precession in graphene, which can be ascribed to the proximity-induced exchange interaction. Furthermore, the observation of a larger lifetime for perpendicular spins in comparison to the in-plane counterpart suggests the creation of a proximity-induced anisotropic spin texture in graphene. Our experimental results and density functional theory calculations open up opportunities for the realization of proximity-induced magnetic interactions and spin filters in 2D material heterostructures and can form the basic building blocks for future spintronic and topological quantum devices.


Introduction
Topological quantum states of matter and spintronics have considerable interest in the field of condensed matter physics for applications in low-power electronics without the application of an external magnetic field [1,2]. The generation of magnetic exchange interaction and strong spin-orbit coupling in two-dimensional (2D) Dirac materials such as graphene is expected to result in the emergence of quantum anomalous Hall state and topologically protected chiral spin textures [3,4]. Graphene, having excellent charge and spin transport properties, is a suitable atomically-thin 2D material to create proximity-induced effects when placed in heterostructures with other functional materials [5][6][7]. Proximity-induced magnetic effects have been investigated in 2D semiconductors on graphene in heterostructures with ferromagnetic semiconductors [8] and magnetic oxides [9][10][11][12][13][14][15][16]. However, there are severe challenges in producing a sizable out-of-plane exchange interaction in magnetic oxide-graphene structures due to the in-plane magnetic anisotropy of the oxide-based magnetic insulators used so far with graphene [13].
Here, we use van der Waals heterostructures of graphene with the ferromagnetic insulator Cr 2 Ge 2 Te 6 (CGT) having a perpendicular magnetic anisotropy to demonstrate a proximity-induced magnetic exchange interaction, which is revealed by the temperaturedependent splitting of Hanle spin precession signals. The observed anisotropic spin relaxation indicates a possible nontrivial spin texture imprinted in graphene by proximity to CGT. The demonstration of out-ofplane proximity-induced magnetism induced in graphene is a crucial step towards realizing more exotic electronic states in 2D material heterostructures.

Results
The van der Waals heterostructures are prepared by dry-transferring CGT flakes (∼ 30 nm in thickness) onto chemical vapor deposited (CVD) graphene on a SiO 2 /n-Si substrate in a cleanroom environment within one minute after exfoliation. The atomic structure of the CGT flakes consists of van der Waals layers of Cr atoms sandwiched by Te and Ge atoms with an interlayer distance of ∼ 6.9Å (figure 1(a)) [33,34]. The choice of CGT is motivated by its layered structure, insulating behavior [30,35], and perpendicular magnetic anisotropy [17]. CGT is expected to induce a magnetic exchange interaction in graphene, splitting the spin-degenerate graphene bands by a characteristic exchange ∆E ex ( figure 1(b)). The Raman spectrum of the CGT flake in a heterostructure with graphene is shown in figure 1(c). It contains the phonon mode at 108 cm −1 , which is characteristic of a CGT flake with more than one layer [36]. We do not observe any broad peak at 121 cm −1 , characteristic of an oxidized CGT surface (supplement figure S1 (stacks.iop.org/TDM/7/015026/mmedia)) after long exposure to the ambient atmosphere, indicating absence of substantial oxidation in freshly cleaved CGT flakes. The Raman spectrum of the CVD deposited graphene channel (figure 1(c)) contains a 2D peak (2642 cm −1 ) of stronger intensity than the G peak (1600 cm −1 ), indicating monolayer thickness of graphene [37]. Magnetic characterization of the bulk CGT crystal by SQUID magnetometry shows perpendicular magnetic anisotropy of the material ( figure 1(d)). From the temperature dependence of the magnetization of the bulk CGT crystal under a perpendicularly applied magnetic field of 100 mT (figure 1(e)), one can observe two magnetic ordering temperatures. By fitting the inverse magnetic susceptibility according to the Curie- figure 1(e)), values of the transition temperatures of ~65 K (γ = 1) and ~204 K (γ ≈ 1.6) were obtained. The former shows a more distinct magnetization enhancement with deceasing temperature. The magnetic moment m of the high temperature (T c ∼ 204 K) phase is, however, two orders of magnitude smaller than that of the main magnetic phase (T c ~ 65 K). The presence of a magnetic transition at higher temperature (figure 1(e) and supplement figure S2) could be due to imperfections in the lattice structure or an extra magnetic phase leading to a magnetic transition at higher temperature in the regions of the material with broken stoichiometry and lattice defects.

Magnetic proximity effect in graphene-Cr 2 Ge 2 Te 6 heterostructures
The device schematic and an optical microscope image of a nanofabricated device consisting of a graphene-CGT heterostructure channel are shown in figures 2(a) and (b) (see methods for details about the device fabrication process). The ferromagnetic tunnel contacts of Co/TiO 2 on graphene are used for injection and detection of the spin-polarized current in the heterostructure channel, with three-terminal contact resistances of 3-6 kΩ at room temperature (supplement figure S3). In such graphene-CGT heterostructure devices, we probe the proximityinduced exchange interaction by employing spin transport and Hanle precession measurements. The insulating behavior of CGT (two-terminal resistance ∼ 60 MΩ) allows charge carriers to flow mostly in the graphene layer with a field-effect mobility of ~2400 cm 2 V −1 s −1 in the heterostructure channel (supplement figure S4).
First, spin-valve and Hanle precession measurements were carried out at room temperature (300 K), well above the T c of CGT, to check the functionality of the heterostructure devices in a nonlocal (NL) configuration (see figure 2(a)). A NL spin resistance change ΔR NL = ΔV NL /I ≈ 5.5 mΩ was measured at 300 K while sweeping the in-plane magnetic field (B ǁ ) along the easy axis of the Co contacts in a device with channel length L = 6.9 µm (figure 2(c)). Next, Hanle measurements were conducted in the NL configuration but with an out-of-plane applied magnetic field (B ⊥ ), which causes in-plane Larmor precession of spins as they propagate through the heterostructure channel. Such measurements at room temperature (figure 2(d)) for both up and down magnetic field sweeps showed conventional Hanle signals without any special features [38]. By fitting the data with the solution of the Bloch equation that describes spin dynamics in the channel with an applied B ⊥ [38], the spin lifetime τ s = 244 ± 32 ps, diffusion coefficient D s = 0.019 ± 0.005 m 2 s −1 and diffusion length λ = 2.1 ± 0.4 µm were obtained.
At low temperatures (50 K), below the Curie point of CGT (figure 2(e)), one can notice two distinctive features of the measured Hanle signal: a shift of the two Hanle peaks with respect to each other and asymmetry of the Hanle peak. Such observations are indicative of  an out-of-plane magnetism induced in the graphene by proximity to CGT. These features are also seen in simulations (figure 2(f) and supplementary note 1) obtained from the solution of the Bloch equation that considers a magnetic exchange interaction in graphene due to the influence of the CGT flake [39]. The CGT flake can induce ferromagnetism in the underlying graphene via the exchange field B ex , which adds to the external magnetic field, B ⊥ → B ⊥ + B ex + B s , and thus modifies the Hanle spin precession signal in the heterostructure channel. While the stray fields B s do contribute to the spin precession in the channel in a similar way as B ex , the observed Hanle signals are mainly shaped by the contributions from externally applied and exchange fields (see supplementary note 2). The peak splitting between the two Hanle sweeps can then originate from hysteretic behavior [20] of the proximity-induced magnetic exchange fields in graphene. This alters the position of the Hanle peak corresponding to zero total field, which, due to hysteresis, is obtained at different values of the applied magnetic field depending on the sweep direction.
Meanwhile, the asymmetry of the Hanle peak arises from the spatial inhomogeneity of the proximity-induced exchange field; a finite graphene-CGT interfacial region leads to an asymmetry, while CGT covering the entire graphene flake would result in a symmetric Hanle curve (see supplementary note 1). Since hysteresis gives opposite shifts of the exchange field depending on the sweep direction, this is reflected in the opposite asymmetry of the measured Hanle signals (figures 2(e) and (f)). The measurements in the two devices with different CGT/graphene channel overlaps by the CGT flake confirm decreased asymmetry with increased channel overlap (supplementary note 3), which is in agreement with simulation results (supplementary note 1).
To further elucidate the proximity-induced magnetic interaction in graphene-CGT heterostructures, the Hanle spin precession measurements were performed at several different temperatures in a systematic manner ( figure 3(a)). The measured data reveal a rapid decrease of the nonlocal spin signal amplitude (R NL ) with increasing temperature in comparison to the temperature dependence of pristine graphene (figure 3(b)) [38], followed by a saturation of the signal above the curie temperature of the CGT. The rapid spin signal amplitude decay with temperature in the range of T < T c , compared to pristine graphene [38], can be attributed to fluctuating proximity-induced magnetic exchange fields due to random fluctuations of the magnetization of the CGT flake, which become more pronounced approaching the magnetic ordering temperature of CGT [15]. Such fluctuations cause random changes of the proximity-induced exchange field and, hence, the effective field that acts on the propagating spins, leading to enhanced spin relaxation [40,41]. Furthermore, the separation between the peaks for opposite Hanle sweeps vanishes at elevated temperatures ( figure 3(c)).
The presence of Hanle peak shifts indicates that the proximity-induced exchange field in graphene persists above the Curie temperature for bulk CGT [28] (∼ 65 K) up to at least 100 K. Additionally, one can deconvolute the measured Hanle signal into symmetric and asymmetric components, where the latter contains information on additional rotation of spins in the channel [42] with respect to normal precession caused by the applied perpendicular magnetic field. Such rotation can originate e.g. from the modified spin texture of graphene under the CGT flake caused by the proximity to the latter. From figures 3(d) and (e) one can see that the asymmetric contribution to the signal also vanishes with increasing temperature in a comparable way as in figure 3(c). This suggests the same origin for peak splitting and asymmetry-both can arise from the proximity-induced exchange field in the graphene channel under the flake, which persists at T > T c of bulk CGT and decays with increasing temperature, while being completely absent at temperatures above 165 K.

Anisotropic spin relaxation in graphene-CGT insulator heterostructures
The proximity-induced exchange interactions in the graphene-based heterostructures can also result in spin relaxation anisotropy. Here we observe spin relaxation anisotropy in graphene-CGT heterostructures by employing the same NL Hanle measurement configuration. However, here the field sweep range is broader, allowing the injection and detection of both in-plane and out-of-plane spins in different field ranges. In-plane spins are injected and detected at low field values when the contacts are magnetized inplane at magnetic fields B ⊥ < 0.4 T ( figure 4(a)). With increasing out-of-plane field the magnetization of the contacts starts to rotate to the out-of-plane direction, reaching saturation at B ⊥ > 2 T ( figure 4(b)). When spins relax with different rates in the in-plane or out-ofplane direction, different amplitudes of the signal are observed for the corresponding magnetic field ranges ( figure 4(c)). Therefore, the in-plane spin lifetime τ || is estimated from low B ⊥ -field Hanle data, while the out-of-plane spin lifetime τ ⊥ is extracted from large out-of-plane B ⊥ -field measurements. As shown in figure 4(d) , where L is the channel length and λ || is the spin diffusion length for in-plane spins [43]. From this expression we find a strong anisotropy, with τ ⊥ being 3.9 times the value of τ || ∼ 150 ps (assuming homogeneous channel characteristics). Such observations are in contrast with the isotropic spin relaxation in pristine graphene channels, which have a value of r close to 1 (0.94±0.01 in figure 4(e)).
The observed anisotropic spin relaxation in graphene-CGT heterostructures could occur, for example, if spin relaxation is dominated by the so-called valley-Zeeman spin-orbit coupling (SOC), similar to the case of graphene on transition metal dichalcogenides [44,45]. Valley-Zeeman SOC (λ VZ ) generates an outof-plane spin texture that, in the presence of strong inter-valley scattering (τ iv ), quickly relaxes the in-plane spins and results in large anisotropy. To determine the type and magnitude of SOC induced in graphene by CGT, we perform density functional theory (DFT) simulations of the graphene-CGT heterostructure (see methods and supplementary note 5). By evaluating the band splitting at both K and K′ valleys, we obtain a Rashba SOC λ R = 0.253 meV and λ VZ = 0.113 meV. Assuming τ iv = (5 − 10) τ p , where τ p is the momentum scattering time, we obtain an anisotropy of the order r = (λ VZ /λ R ) 2 τ iv /τ p + 1/2 = 1.5-2.5.
While SOC can induce a spin lifetime anisotropy r > 1, the temperature dependence of the spin signal in figure 3(b) suggests that magnetic exchange fluctuations are playing a role in the spin relaxation. In this scenario, an apparent spin relaxation anisotropy can also emerge. In case of the exchange fluctuation mechanism the spins are dephased by the fluctuations, but if magnetic field is applied the fluctuations are suppressed. This is different for spins parallel and perpendicular to the applied magnetic field, which results in an increase of anisotropy with increasing out-of-plane magnetic field B ⊥ . Assuming that exchange fluctuations are the sole source of spin relaxation in the graphene-CGT devices, we find that the spin relaxation is nearly completely isotropic (r ≈ 1.002) at B ⊥ = 0 and becomes anisotropic with increasing values of B ⊥ (see supplementary note 6). This analysis indicates that if the spin relaxation is dominated by exchange fluctuations, the large anisotropy seen in figure 4(d) can be driven by the external field B ⊥ and may not be intrinsic to the graphene/CGT interface. This is because the perpendicular proximity-induced exchange field B ex , while sufficiently large to see in Hanle measurements, is not large enough to suppress exchange fluctuations in graphene. It is still unclear whether spin relaxation is dominated by SOC, exchange fluctuations, or a combination of the two. However, considering that according to DFT calculations the exchange splitting is expected to be an order of magnitude stronger than SOC (see discussion for supplement figure S10), one can expect the origin of the experimentally observed anisotropy of spin relaxation to be mainly caused by the exchange fluctuations. Figure 3

Summary and outlook
In summary, the observed modulation of the spin transport signal demonstrates the existence of an exchange interaction in graphene proximity-coupled to the layered magnetic insulator CGT. This is revealed by the observation of nontrivial features in the measured nonlocal Hanle spin precession signals in the graphene-CGT channel. Namely, at low temperatures there is a hysteretic shift of the Hanle signal maxima for opposite magnetic field sweep directions, accompanied by a corresponding asymmetry in the Hanle signal. These features persist up to at least 100 K, above the T c of bulk CGT. Supporting simulations reveal that these features can be explained by out-ofplane magnetism induced in the graphene layer by CGT. Additionally, measurements of large spin lifetime anisotropy indicate that proximity coupling of the graphene channel to CGT can modify its spin texture. This anisotropy can arise from the magnetic exchange induced in the graphene, while DFT simulations suggest that spin-orbit coupling could also be playing a role. Looking ahead, the proximity-induced effects can be further tuned by tailoring the van der Waals gap between graphene and CGT [30], and by placing it on both sides of the graphene layer. These achievements are important for the realization of quantum states of matter characterized by edge states which are topologically protected from backscattering without the application of an external magnetic field, namely, the quantum anomalous Hall effect [30][31][32]. This holds great potential for applications in spintronics and low-power quantum electronics.

Device fabrication and measurement
To fabricate the devices, CVD graphene was wettransferred onto a Si/SiO 2 substrate (from Graphenea). After patterning the graphene into stripes of typical lateral width of 1-4 µm by photolithography and annealing in an Ar/H 2 atmosphere, 2D flakes (~30 nm thick) of the hexagonal ferromagnetic insulator Cr 2 Ge 2 Te 6 (from HQ Graphene), prepared by exfoliation method, were dry transferred immediately to reduce oxidation from air exposure. Suitable graphene-CGT heterostructure areas were chosen by optical microscope for further fabrication of ferromagnetic contacts by electron beam lithography and electron beam evaporation of metals (1 nm TiO 2 /65 nm Co). The magnetic field sweeps at different temperatures were carried out in a Quantum Design Physical Property Measurement System while electrical biases were applied and measured by an external Keithley 6221 current source and a Keithley 2182A nanovoltmeter, respectively.

DFT simulations
For calculation of the electronic structure and structural relaxation of graphene on CGT density functional theory (DFT) [46] was used within Quantum ESPRESSO [47] using a previously developed model ( [31]) with a k-point sampling of 6 × 6 × 1, a Hubbard parameter of U = 1 eV [17], an energy cutoff for charge density of 500 Ry, and a kinetic energy cutoff for wave functions of 60 Ry [48,49]. When SOC is included, we used the relativistic versions of the pseudopotentials. For the relaxation of the heterostructures, we added van der Waals corrections [50,51] and used a quasi-Newton algorithm based on a trust radius procedure. A vacuum gap of 20 Å was used to simulate quasi-2D systems. To determine the interlayer distances, the atoms of graphene were allowed to relax only in z direction (vertical to the layers) for determination of the interlayer distances, while the atoms of CGT were free to move in all directions until reaching a state when all components of all forces were reduced below 10 −3 [Ry/a 0 ] (a 0 is the Bohr radius). For more details, see [31].