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

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 [5–7]. Proximity-induced magnetic effects have been investigated in 2D semiconductors on graphene in heterostructures with ferromagnetic semiconductors [8] and magnetic oxides [9–16]. 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].

To create significant proximity-induced magnetic interaction in graphene, the use of a magnetic insulator with perpendicular magnetic anisotropy is desired. Additionally, for a good interface, atomically-flat layered 2D material-based van der Waals heterostructures (vdWh) are ideal [1–4]. Recently, 2D magnetic materials were successfully prepared via exfoliation down to the monolayer limit, showing intrinsic long-range Heisenberg ferromagnetic order [17–19] that is tunable by application of a gate voltage [20–22]. Additionally, giant tunneling magnetoresistance, spin filtering and magnon-assisted tunneling phenomenon have been demonstrated using such 2D magnetic materials [23–27]. Recently, heterostructures of such 2D magnetic materials with 2D semiconductors [8], topological insulators [28], semimetals [29] and graphene [27] have also been investigated. Theoretical predictions indicate that heterostructures of 2D magnetic insulators with graphene are expected to produce a large exchange splitting in the graphene layer, enabling the emergence of a topological quantum phase [30–32].

Here, we use van der Waals heterostructures of graphene with the ferromagnetic insulator Cr₂Ge₂Te₆ (CGT) having a perpendicular magnetic anisotropy to demonstrate a proximity-induced magnetic exchange interaction, which is revealed by the temperature-dependent 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-of-plane proximity-induced magnetism induced in graphene is a crucial step towards realizing more exotic electronic states in 2D material heterostructures.

The van der Waals heterostructures are prepared by dry-transferring CGT flakes ($\sim 30$ nm in thickness) onto chemical vapor deposited (CVD) graphene on a SiO₂/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 $\sim 6.9\,\mathring{\rm A}$ (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 $\Delta {{E}_{{\rm ex}}}$ (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–Weiss law $\frac{1}{\chi }=\frac{{{(T-Tc)}^{\gamma }}}{C}$ (inset in figure 1(e)), values of the transition temperatures of ~65 K ($\gamma =1$) and ~204 K ($\gamma \approx 1.6$) were obtained. The former shows a more distinct magnetization enhancement with deceasing temperature. The magnetic moment m of the high temperature (${{T}_{{\rm c}}}\sim 204\,{\rm K}$) 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.

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Magnetic proximity effect in graphene-Cr₂Ge₂Te₆ 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/TiO₂ 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 proximity-induced exchange interaction by employing spin transport and Hanle precession measurements. The insulating behavior of CGT (two-terminal resistance $\sim 60$ ${\rm M }\Omega$) allows charge carriers to flow mostly in the graphene layer with a field-effect mobility of ~2400 cm² V⁻¹ s⁻¹ in the heterostructure channel (supplement figure S4).

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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 (${{B}_{\bot }}$), 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 ${{B}_{\bot }}$ [38], the spin lifetime ${{\tau }_{{\rm s}}}=244\pm 32$ ps, diffusion coefficient ${{D}_{{\rm s}}}=0.019\pm 0.005$ m² s⁻¹ and diffusion length $\lambda =2.1\pm 0.4$ 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)).

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The presence of Hanle peak shifts indicates that the proximity-induced exchange field in graphene persists above the Curie temperature for bulk CGT [28] ($\sim 65$ 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 $T>{{T}_{{\rm c}}}$ of bulk CGT and decays with increasing temperature, while being completely absent at temperatures above 165 K. Fitting the symmetric component of the Hanle signal with the solution of the Bloch equation for spin diffusion in a homogeneous channel gives values of the in-plane spin lifetimes τ_ǁ in the range of 90–280 ps; the comparably large spread of values results due to a large number of free fitting parameters (see supplementary note 4). However, most fits resulting in reasonable spin transport parameters yielded an exchange field on the order of a few 10s of mT.

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 in-plane 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-of-plane direction, different amplitudes of the signal are observed for the corresponding magnetic field ranges (figure 4(c)). Therefore, the in-plane spin lifetime ${{\tau }_{||}}$ is estimated from low B_⊥-field Hanle data, while the out-of-plane spin lifetime ${{\tau }_{\bot }}$ is extracted from large out-of-plane B_⊥-field measurements. As shown in figure 4(d), in the graphene-CGT heterostructure the spin signal magnitudes at B_⊥  =  0 for in-plane spins ($\Delta R_{{\rm NL}}^{||}$) and at B_⊥  =  2.5 T for spins perpendicular to plane ($\Delta R_{{\rm NL}}^{\bot }$) show strong anisotropy, with $\Delta R_{{\rm NL}}^{\bot }>\Delta R_{{\rm NL}}^{||}$ and with a ratio $\Delta R_{{\rm NL}}^{\bot }/\Delta R_{{\rm NL}}^{||}\sim 10$. The spin lifetime anisotropy $\newcommand{\e}{{\rm e}} r\equiv {{\tau }_{\bot }}/{{\tau }_{||}}$ is obtained from $\Delta R_{{\rm NL}}^{\bot }/\Delta R_{{\rm NL}}^{||}=\sqrt{r}{{e}^{-(L/{{\lambda }_{||}})(\frac{1}{\sqrt{r}}-1)}}$, where L is the channel length and ${{\lambda }_{||}}$ is the spin diffusion length for in-plane spins [43]. From this expression we find a strong anisotropy, with ${{\tau }_{\bot }}$ being 3.9 times the value of ${{\tau }_{||}}\sim 150$ 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$\pm 0.01$ in figure 4(e)).

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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 (${{\lambda }_{{\rm VZ}}}$) generates an out-of-plane spin texture that, in the presence of strong inter-valley scattering (${{\tau }_{{\rm iv}}}$), 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 ${{\lambda }_{{\rm R}}}$  =  0.253 meV and ${{\lambda }_{{\rm VZ}}}$  =  0.113 meV. Assuming ${{\tau }_{{\rm iv}}}=\left(5-10 \right){{\tau }_{{\rm p}}}$, where $\tau_{\rm p}$ is the momentum scattering time, we obtain an anisotropy of the order $r={{\left({{\lambda }_{{\rm VZ}}}/{{\lambda }_{{\rm R}}} \right)}^{2}}\left({{\tau }_{{\rm iv}}}/{{\tau }_{{\rm p}}} \right)+1/2=1.5{{\rm \text {--}}}2.5$.

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 $\left(r\approx 1.002 \right)$ 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(b) points to at least some contribution of exchange fluctuations, while the anisotropy measurement in figure 4(d) can be explained by either of the mechanisms.

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-of-plane 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 [30–32]. This holds great potential for applications in spintronics and low-power quantum electronics.

Device fabrication and measurement

DFT simulations

Authors from Chalmers, ICN2, and University of Regensburg acknowledge funding from the European Union's Horizon 2020 research and innovation programme under Grant agreement no. 785219 (Graphene Flagship Core 2). The authors at Chalmers acknowledge financial support from EU FlagEra project (from Swedish Research Council VR No. 2015-06813), Swedish Research Council VR project Grants (No. 2016-03658), Graphene center and the AoA Nano program at Chalmers University of Technology. We acknowledge Dr Ron Jansen for useful discussions about proximity-induced exchange and stray Hall effects in the heterostructures. We acknowledge help from Bing Zhao in our group and staff at Nanofabrication laboratory and Quantum device laboratory for useful discussions and help in fabrication and measurements of devices. ICN2 is funded by the CERCA Programme/Generalitat de Catalunya and is supported by the Severo Ochoa program from Spanish MINECO (Grant No. SEV-2017-0706). M. Vila acknowledges funding from 'La Caixa' Foundation.

SPD and BK conceived the idea and designed the experiments. BK fabricated and measured the devices. AWC, MV, SR performed the simulations. KZ and JF performed the theoretical calculations. DK, AMH, AD helped in device fabrication and measurements. PS performed SQUID magnetic characterization of bulk CGT crystal. BK, AWC, MV, KZ, JF, SR, SPD contributed in analysis of the data, compiled the figures and wrote the manuscript. All authors gave input on interpretation of the data and contributed in writing of the manuscript. SPD supervised and managed the project.

The authors declare no competing financial interests.