2D Materials PAPER • OPEN ACCESS Magnetic proximity in a van der Waals heterostructure of magnetic insulator and graphene To cite this article: Bogdan Karpiak et al 2020 2D Mater. 7 015026 View the article online for updates and enhancements. This content was downloaded from IP address 158.109.11.194 on 20/12/2019 at 15:18 2D Mater. 7 (2020) 015026 https://doi.org/10.1088/2053-1583/ab5915 OPEN ACCESS PAPER Magnetic proximity in a van der Waals heterostructure of magnetic RECEIVED insulator and graphene 15 August 2019 RE VISED Bogdan Karpiak1 , Aron W Cummings2 , Klaus Zollner3 , Marc Vila2,4 , Dmitrii Khokhriakov1 , 23 October 2019 Anamul Md Hoque1 , André Dankert1, Peter Svedlindh5 , Jaroslav Fabian3, Stephan Roche2,6 ACCEP TED FOR PUBLICATION 19 November 2019 and Saroj P Dash1,7,8 1 PUBLISHED Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296, Göteborg, Sweden 2 11 December 2019 Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and The Barcelona Institute of Science and Technology, Campus UAB, Bellaterra, 08193 Barcelona, Spain 3 Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany Original content from 4 this work may be used Department of Physics, Universitat Autònoma de Barcelona, Campus UAB, Bellaterra, 08193 Barcelona, Spain 5 under the terms of the Division of Solid-State Physics, Department of Engineering Science, Uppsala University, Box 534, SE-75121 Uppsala, Sweden Creative Commons 6 ICREA—Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain Attribution 3.0 licence. 7 Graphene Center, Chalmers University of Technology, SE-41296, Göteborg, Sweden Any further distribution 8 Author to whom any correspondence should be addressed. of this work must maintain attribution E-mail: saroj.dash@chalmers.se to the author(s) and the title of the work, journal Keywords: graphene, 2D ferromagnet, van der Waals heterostructures, Cr2Ge2Te6, proximity effect, magnetism, spin anisotropy citation and DOI. Supplementary material for this article is available online Abstract 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 [5–7]. Proximity-induced magnetic effects have been investigated in 2D semiconductors on graphene in Topological quantum states of matter and spintronics heterostructures with ferromagnetic semiconductors have considerable interest in the field of condensed [8] and magnetic oxides [9–16]. However, there are matter physics for applications in low-power severe challenges in producing a sizable out-of-plane electronics without the application of an external exchange interaction in magnetic oxide-graphene magnetic field [1, 2]. The generation of magnetic structures due to the in-plane magnetic anisotropy of exchange interaction and strong spin–orbit coupling the oxide-based magnetic insulators used so far with in two-dimensional (2D) Dirac materials such as graphene [13]. graphene is expected to result in the emergence of To create significant proximity-induced mag- quantum anomalous Hall state and topologically netic interaction in graphene, the use of a magnetic protected chiral spin textures [3, 4]. Graphene, insulator with perpendicular magnetic anisotropy having excellent charge and spin transport is desired. Additionally, for a good interface, atom- properties, is a suitable atomically-thin 2D material ically-flat layered 2D material-based van der Waals to create proximity-induced effects when placed in heterostructures (vdWh) are ideal [1–4]. Recently, heterostructures with other functional materials 2D magnetic materials were successfully prepared © 2019 IOP Publishing Ltd 2D Mater. 7 (2020) 015026 B Karpiak et al via exfoliation down to the monolayer limit, show- perpendicular magnetic anisotropy of the material ing intrinsic long-range Heisenberg ferromagnetic (figure 1(d)). From the temperature dependence order [17–19] that is tunable by application of a gate of the magnetization of the bulk CGT crystal under voltage [20–22]. Additionally, giant tunneling magne- a perpendicularly applied magnetic field of 100 toresistance, spin filtering and magnon-assisted tun- mT (figure 1(e)), one can observe two magnetic neling phenomenon have been demonstrated using ordering temperatures. By fitting the inverse such 2D magnetic materials [23–27]. Recently, het- magnetic susceptibility according to the Curie– γ erostructures of such 2D magn­etic materials with 2D Weiss law χ1 = (T−Tc) (inset in figure 1(e)), values C semiconductors [8], topological insulators [28], semi- of the transition temperatures of ~65 K (γ = 1) and metals [29] and graphene [27] have also been inves- ~204 K (γ ≈ 1.6) were obtained. The former shows tigated. Theoretical predictions indicate that hetero- a more distinct magnetization enhancement with structures of 2D magn­etic insulators with graphene deceasing temperature. The magnetic moment m of are expected to produce a large exchange splitting in the high temperature (Tc ∼ 204 K ) phase is, however, the graphene layer, enabling the emergence of a topo- two orders of magnitude smaller than that of the logical quant­um phase [30–32]. main magnetic phase (Tc ~ 65 K). The presence of a Here, we use van der Waals heterostructures of magnetic transition at higher temperature (figure graphene with the ferromagnetic insulator Cr2Ge2Te6 1(e) and supplement figure S2) could be due to (CGT) having a perpendicular magnetic anisotropy to imperfections in the lattice structure or an extra demonstrate a proximity-induced magnetic exchange magnetic phase leading to a magnetic transition at interaction, which is revealed by the temperature- higher temperature in the regions of the material with dependent splitting of Hanle spin precession signals. broken stoichiometry and lattice defects. The observed anisotropic spin relaxation indicates a possible nontrivial spin texture imprinted in graphene Magnetic proximity effect in graphene-Cr2Ge2Te6 by proximity to CGT. The demonstration of out-of- heterostructures plane proximity-induced magnetism induced in gra- The device schematic and an optical microscope phene is a crucial step towards realizing more exotic image of a nanofabricated device consisting of a electronic states in 2D material heterostructures. graphene–CGT heterostructure channel are shown in figures 2(a) and (b) (see methods for details about Results the device fabrication process). The ferromagnetic tunnel contacts of Co/TiO2 on graphene are used for The van der Waals heterostructures are prepared by injection and detection of the spin-polarized current dry-transferring CGT flakes (∼ 30 nm in thickness) in the heterostructure channel, with three-terminal onto chemical vapor deposited (CVD) graphene on contact resistances of 3–6 kΩ at room temperature a SiO2/n-Si substrate in a cleanroom environment (supplement figure S3). In such graphene-CGT within one minute after exfoliation. The atomic heterostructure devices, we probe the proximity- structure of the CGT flakes consists of van der induced exchange interaction by employing spin Waals layers of Cr atoms sandwiched by Te and Ge transport and Hanle precession measurements. The atoms with an interlayer distance of ∼ 6.9 Å (figure insulating behavior of CGT (two-terminal resistance 1(a)) [33, 34]. The choice of CGT is motivated by its ∼ 60 MΩ) allows charge carriers to flow mostly in layered structure, insulating behavior [30, 35], and the graphene layer with a field-effect mobility of perpendicular magnetic anisotropy [17]. CGT is ~2400 cm2 V−1 s−1 in the heterostructure channel expected to induce a magnetic exchange interaction (supplement figure S4). in graphene, splitting the spin-degenerate graphene First, spin-valve and Hanle precession measure- bands by a characteristic exchange ∆Eex (figure 1(b)). ments were carried out at room temperature (300 K), The Raman spectrum of the CGT flake in a well above the Tc of CGT, to check the functional- heterostructure with graphene is shown in figure 1(c). ity of the heterostructure devices in a nonlocal (NL) It contains the phonon mode at 108 cm−1, which is configuration (see figure 2(a)). A NL spin resistance characteristic of a CGT flake with more than one layer change ΔRNL  =  ΔVNL/I  ≈  5.5 mΩ was measured at [36]. We do not observe any broad peak at 121 cm−1, 300 K while sweeping the in-plane magnetic field (Bǁ) characteristic of an oxidized CGT surface (supplement along the easy axis of the Co contacts in a device with figure S1 (stacks.iop.org/TDM/7/015026/mmedia)) channel length L  =  6.9 µm (figure 2(c)). Next, Hanle after long exposure to the ambient atmosphere, measurements were conducted in the NL configura- indicating absence of substantial oxidation in freshly tion but with an out-of-plane applied magnetic field cleaved CGT flakes. The Raman spectrum of the CVD (B⊥), which causes in-plane Larmor precession of deposited graphene channel (figure 1(c)) contains a spins as they propagate through the heterostructure 2D peak (2642 cm−1) of stronger intensity than the channel. Such measurements at room temperature G peak (1600 cm−1), indicating monolayer thickness (figure 2(d)) for both up and down magnetic field of graphene [37]. Magnetic characterization of the sweeps showed conventional Hanle signals without bulk CGT crystal by SQUID magnetometry shows any special features [38]. By fitting the data with the 2 2D Mater. 7 (2020) 015026 B Karpiak et al Figure 1. Characterization of Cr2Ge2Te6 and its heterostructure with graphene. (a) Schematic of atomic structure of CGT/graphene heterostructure. (b) Schematic of graphene band structure in proximity with CGT in the vicinity of the Dirac point. Graphene can acquire magnetic order with a splitting of spin-degenerate bands by an exchange gap ∆Eex. (c) Raman spectrum of CGT (top panel) and graphene (bottom panel) in the heterostructure. (d) Field dependence of magnetic moment (m) of bulk CGT crystal as a function of magnetic field at 10 K for both in-plane and out-of-plane magnetic field directions. (e) Temperature dependence of magnetic moment m of CGT under perpendicular magnetic field of 100 mT. Top inset shows the same data as in main panel but with log scale on vertical axis. Bottom inset shows inverse magnetic susceptibility as a function of temperature fitted with the Curie–Weiss law. Figure 2. Magnetic proximity effect in graphene-Cr2Ge2Te6 heterostructures. (a) and (b) Schematic and false-color optical microscope picture of graphene-CGT heterostructure with ferromagnetic tunnel contacts of TiO2 (1 nm)/Co (60 nm). The scale bar is 5 µm. (c) and (d) Spin valve and Hanle spin precession signals measured in graphene-CGT heterostructure for in-plane and out-of-plane magnetic field directions, respectively, at 300 K, above the Curie temperature of CGT. The up and down magnetic field sweep directions are represented by blue and red colors. (e) The measured Hanle signal at 50 K, below the Curie temperature of CGT. (f) Simulated Hanle signal for typical channel parameters (see supplementary note 1 for details) with partial overlap of the graphene by CGT. The inset shows the assumed hysteresis for CGT flake in the simulations. The overlap area of the graphene-CGT heterostructure in the device channel is ~60%. solution of the Bloch equation that describes spin At low temperatures (50 K), below the Curie point dynamics in the channel with an applied B⊥ [38], of CGT (figure 2(e)), one can notice two distinctive the spin lifetime τs = 244 ± 32 ps, diffusion coeffi- features of the measured Hanle signal: a shift of the two cient Ds = 0.019 ± 0.005 m2 s−1 and diffusion length Hanle peaks with respect to each other and asymmetry λ = 2.1 ± 0.4 µm were obtained. of the Hanle peak. Such observations are indicative of 3 2D Mater. 7 (2020) 015026 B Karpiak et al Figure 3. Temperature dependence of spin signal in graphene-Cr2Ge2Te6 heterostructures. (a) Nonlocal Hanle spin precession measurements in the graphene-CGT heterostructure as a function of perpendicular magnetic field for up (blue) and down (red) sweeps at different temperatures. (b) Normalized nonlocal Hanle signal amplitudes (∆RNL ) as a function of temperature for a graphene-CGT device and for a 4 µm CVD graphene channel [38] (green). (c) Magnitude of the horizontal separation between positions of nonlocal Hanle signal peaks for up (B0,up) and down (B0,down ) sweeps as a function of temperature. (d) Asymmetric part of the measured Hanle signal at different temperatures. (e) Amplitude of the asymmetric signal from d as a function of temperature. The solid lines in b and grey regions in (b), (c) and (e) are guides to the eye. an out-of-plane magnetism induced in the graphene two devices with different CGT/graphene channel by proximity to CGT. These features are also seen in overlaps by the CGT flake confirm decreased asym- simulations (figure 2(f) and supplementary note 1) metry with increased channel overlap (supplementary obtained from the solution of the Bloch equation that note 3), which is in agreement with simulation results considers a magnetic exchange interaction in graphene (supplementary note 1). due to the influence of the CGT flake [39]. The CGT To further elucidate the proximity-induced magn­ flake can induce ferromagnetism in the underlying etic interaction in graphene-CGT heterostructures, graphene via the exchange field Bex, which adds to the the Hanle spin precession measurements were per- external magnetic field, B⊥  →  B⊥  +  Bex  +  Bs, and thus formed at several different temperatures in a system- modifies the Hanle spin precession signal in the het- atic manner (figure 3(a)). The measured data reveal a erostructure channel. While the stray fields Bs do con- rapid decrease of the nonlocal spin signal amplitude tribute to the spin precession in the channel in a simi- (RNL) with increasing temperature in comparison to lar way as Bex, the observed Hanle signals are mainly the temperature dependence of pristine graphene (fig- shaped by the contributions from externally applied ure 3(b)) [38], followed by a saturation of the signal and exchange fields (see supplementary note 2). above the curie temperature of the CGT. The rapid The peak splitting between the two Hanle sweeps can spin signal amplitude decay with temperature in the then originate from hysteretic behavior [20] of the range of T  <  Tc, compared to pristine graphene [38], proximity-induced magnetic exchange fields in gra- can be attributed to fluctuating proximity-induced phene. This alters the position of the Hanle peak corre­ magnetic exchange fields due to random fluctuations sponding to zero total field, which, due to hysteresis, of the magnetization of the CGT flake, which become is obtained at different values of the applied magnetic more pronounced approaching the magnetic ordering field depending on the sweep direction. temperature of CGT [15]. Such fluctuations cause ran- Meanwhile, the asymmetry of the Hanle peak dom changes of the proximity-induced exchange field arises from the spatial inhomogeneity of the proxim- and, hence, the effective field that acts on the propagat- ity-induced exchange field; a finite graphene-CGT ing spins, leading to enhanced spin relaxation [40, 41]. interfacial region leads to an asymmetry, while CGT Furthermore, the separation between the peaks for covering the entire graphene flake would result in a opposite Hanle sweeps vanishes at elevated temper­ symmetric Hanle curve (see supplementary note 1). atures (figure 3(c)). Since hysteresis gives opposite shifts of the exchange The presence of Hanle peak shifts indicates that the field depending on the sweep direction, this is reflected proximity-induced exchange field in graphene persists in the opposite asymmetry of the measured Hanle sig- above the Curie temperature for bulk CGT [28] (∼ 65 K) nals (figures 2(e) and (f)). The measurements in the up to at least 100 K. Additionally, one can deconvolute 4 2D Mater. 7 (2020) 015026 B Karpiak et al the measured Hanle signal into symmetric and asym- for in-plane spins [43]. From this expression we find metric components, where the latter contains infor- a strong anisotropy, with τ⊥ being 3.9 times the value mation on additional rotation of spins in the channel of τ|| ∼ 150 ps (assuming homogeneous channel [42] with respect to normal precession caused by the characteristics). Such observations are in contrast applied perpendicular magnetic field. Such rotation with the isotropic spin relaxation in pristine graphene can originate e.g. from the modified spin texture of channels, which have a value of r close to 1 (0.94±0.01 graphene under the CGT flake caused by the proxim- in figure 4(e)). ity to the latter. From figures 3(d) and (e) one can see The observed anisotropic spin relaxation in gra- that the asymmetric contribution to the signal also phene-CGT heterostructures could occur, for exam- vanishes with increasing temperature in a comparable ple, if spin relaxation is dominated by the so-called val- way as in figure 3(c). This suggests the same origin for ley-Zeeman spin–orbit coupling (SOC), similar to the peak splitting and asymmetry—both can arise from case of graphene on transition metal dichalcogenides the proximity-induced exchange field in the graphene [44, 45]. Valley-Zeeman SOC (λVZ) generates an out- channel under the flake, which persists at T > Tc of of-plane spin texture that, in the presence of strong bulk CGT and decays with increasing temperature, inter-valley scattering (τiv ), quickly relaxes the in-plane while being completely absent at temperatures above spins and results in large anisotropy. To determine the 165 K. Fitting the symmetric component of the Hanle type and magnitude of SOC induced in graphene by signal with the solution of the Bloch equation for spin CGT, we perform density functional theory (DFT) diffusion in a homogeneous channel gives values of the simulations of the graphene-CGT heterostructure (see in-plane spin lifetimes τǁ in the range of 90–280 ps; the methods and supplementary note 5). By evaluating comparably large spread of values results due to a large the band splitting at both K and K′ valleys, we obtain number of free fitting parameters (see supplementary a Rashba SOC λR   =  0.253 meV and λVZ  =  0.113 meV. note 4). However, most fits resulting in reasonable spin Assuming τiv = (5 − 10) τp, where τp is the momen- transport parameters yielded an exchange field on the tum scattering time, we obtain an anisotropy of the order of a few 10s of mT. 2  order r = (λVZ /λR ) τiv /τp + 1/2 = 1.5–2.5. While SOC can induce a spin lifetime anisotropy Anisotropic spin relaxation in r > 1, the temperature dependence of the spin signal graphene-CGT insulator heterostructures in figure 3(b) suggests that magnetic exchange fluc- tuations are playing a role in the spin relaxation. In The proximity-induced exchange interactions in the this scenario, an apparent spin relaxation anisotropy graphene-based heterostructures can also result in spin can also emerge. In case of the exchange fluctuation relaxation anisotropy. Here we observe spin relaxation mechanism the spins are dephased by the fluctuations, anisotropy in graphene-CGT heterostructures but if magnetic field is applied the fluctuations are sup- by employing the same NL Hanle measurement pressed. This is different for spins parallel and perpend­ configuration. However, here the field sweep range is icular to the applied magnetic field, which results in an broader, allowing the injection and detection of both increase of anisotropy with increasing out-of-plane in-plane and out-of-plane spins in different field magnetic field B⊥. Assuming that exchange fluctua- ranges. In-plane spins are injected and detected at tions are the sole source of spin relaxation in the gra- low field values when the contacts are magnetized in- phene-CGT devices, we find that the spin relaxation is plane at magnetic fields B⊥  <  0.4 T (figure 4(a)). With nearly completely isotropic (r ≈ 1.002) at B⊥  =  0 and increasing out-of-plane field the magnetization of the becomes anisotropic with increasing values of B⊥ (see contacts starts to rotate to the out-of-plane direction, supplementary note 6). This analysis indicates that if reaching saturation at B⊥  >  2 T (figure 4(b)). When the spin relaxation is dominated by exchange fluctua- spins relax with different rates in the in-plane or out-of- tions, the large anisotropy seen in figure 4(d) can be plane direction, different amplitudes of the signal are driven by the external field B⊥ and may not be intrin- observed for the corresponding magnetic field ranges sic to the graphene/CGT interface. This is because the (figure 4(c)). Therefore, the in-plane spin lifetime τ|| perpendicular proximity-induced exchange field Bex, is estimated from low B⊥-field Hanle data, while the while sufficiently large to see in Hanle measurements, out-of-plane spin lifetime τ⊥ is extracted from large is not large enough to suppress exchange fluctuations out-of-plane B⊥-field measurements. As shown in in graphene. It is still unclear whether spin relaxa- figure 4(d), in the graphene-CGT heterostructure the tion is dominated by SOC, exchange fluctuations, or spin signal magnitudes at B⊥  =  0 for in-plane spins a combination of the two. However, considering that || (∆RNL ) and at B⊥  =  2.5 T for spins perpendicular according to DFT calculations the exchange splitting to plane (∆R⊥ is expected to be an order of magnitude stronger than NL ) show strong anisotropy, with || || SOC (see discussion for supplement figure S10), one ∆R⊥ NL > ∆R ⊥ NL and with a ratio ∆RNL /∆RNL ∼ 10. can expect the origin of the experimentally observed The spin lifetime anisotropy r ≡ τ⊥ /τ|| is obtained || √ −(L/λ|| )( √1 r −1) anisotropy of spin relaxation to be mainly caused by from ∆R⊥ NL /∆RNL = re , where L is the exchange fluctuations. Figure 3(b) points to at least the channel length and λ|| is the spin diffusion length some contrib­ution of exchange fluctuations, while 5 2D Mater. 7 (2020) 015026 B Karpiak et al Figure 4. Anisotropic spin relaxation in graphene-Cr2Ge2Te6 heterostructure. (a) Measurement geometry with small perpendicular magnetic field B⊥  <  0.2 T, where the magnetization of the ferromagnetic Co contacts and injected spin polarization are in- plane, resulting in Hanle spin precession. (b) Measurement geometry with large perpendicular magnetic field B⊥  >  2 T, where the magnetization of the ferromagnets and injected spin polarization are out of plane, resulting in no Hanle precession. (c) The measurements of graphene-CGT channels indicate anisotropic relaxation with faster rates of spin relaxation for in-plane spins, as demonstrated in the schematic and (d) experimental nonlocal measurements in a channel with ~60% flake overlap at 60 K and 100 K. A parabolic magnetoresistance background is subtracted from the measured data. (e) The reference measurement in pristine CVD graphene showing very low anisotropy with almost similar signal for in-plane and perpendicular spins. the aniso­tropy measurement in figure 4(d) can be holds great potential for applications in spintronics explained by either of the mechanisms. and low-power quantum electronics. Summary and outlook Methods In summary, the observed modulation of the spin Device fabrication and measurement transport signal demonstrates the existence of an To fabricate the devices, CVD graphene was wet- exchange interaction in graphene proximity-coupled transferred onto a Si/SiO2 substrate (from Graphenea). to the layered magnetic insulator CGT. This is revealed After patterning the graphene into stripes of typical by the observation of nontrivial features in the lateral width of 1–4 µm by photolithography and measured nonlocal Hanle spin precession signals in the annealing in an Ar/H2 atmosphere, 2D flakes (~30 nm graphene-CGT channel. Namely, at low temperatures thick) of the hexagonal ferromagnetic insulator there is a hysteretic shift of the Hanle signal maxima Cr2Ge2Te6 (from HQ Graphene), prepared by for opposite magnetic field sweep directions, exfoliation method, were dry transferred immediately accompanied by a corresponding asymmetry in the to reduce oxidation from air exposure. Suitable Hanle signal. These features persist up to at least 100 K, graphene-CGT heterostructure areas were chosen above the Tc of bulk CGT. Supporting simulations by optical microscope for further fabrication of reveal that these features can be explained by out-of- ferromagnetic contacts by electron beam lithography plane magnetism induced in the graphene layer by and electron beam evaporation of metals (1 nm CGT. Additionally, measurements of large spin lifetime TiO2/65 nm Co). The magnetic field sweeps at anisotropy indicate that proximity coupling of the different temperatures were carried out in a Quantum graphene channel to CGT can modify its spin texture. Design Physical Property Measurement System while This anisotropy can arise from the magnetic exchange electrical biases were applied and measured by an induced in the graphene, while DFT simulations external Keithley 6221 current source and a Keithley suggest that spin–orbit coupling could also be playing 2182A nanovoltmeter, respectively. a role. Looking ahead, the proximity-induced effects can be further tuned by tailoring the van der Waals gap DFT simulations between graphene and CGT [30], and by placing it on For calculation of the electronic structure and both sides of the graphene layer. These achievements structural relaxation of graphene on CGT density are important for the realization of quantum states functional theory (DFT) [46] was used within of matter characterized by edge states which are Quantum ESPRESSO [47] using a previously topologically protected from backscattering without developed model ([31]) with a k-point sampling of the application of an external magnetic field, namely, 6  ×  6  ×  1, a Hubbard parameter of U  =  1 eV [17], the quantum anomalous Hall effect [30–32]. This an energy cutoff for charge density of 500 Ry, and a 6 2D Mater. 7 (2020) 015026 B Karpiak et al kinetic energy cutoff for wave functions of 60 Ry ORCID iDs [48, 49]. When SOC is included, we used the relativistic versions of the pseudopotentials. For the Bogdan Karpiak https://orcid.org/0000-0001-7462- relaxation of the heterostructures, we added van der 8405 Waals corrections [50, 51] and used a quasi-Newton Aron W Cummings https://orcid.org/0000-0003- algorithm based on a trust radius procedure. A 2307-497X vacuum gap of 20 Å was used to simulate quasi-2D Klaus Zollner https://orcid.org/0000-0002-6239- systems. To determine the interlayer distances, the 3271 atoms of graphene were allowed to relax only in z Marc Vila https://orcid.org/0000-0001-9118-421X direction (vertical to the layers) for determination of Dmitrii Khokhriakov https://orcid.org/0000-0002- the interlayer distances, while the atoms of CGT were 5515-9081 free to move in all directions until reaching a state Anamul Md Hoque https://orcid.org/0000-0002- when all components of all forces were reduced below 2117-7177 10−3 [Ry/a0] (a0 is the Bohr radius). For more details, Peter Svedlindh https://orcid.org/0000-0002-3049- see [31]. 6831 Stephan Roche https://orcid.org/0000-0003-0323- Acknowledgments 4665 Saroj P Dash https://orcid.org/0000-0001-7931- Authors from Chalmers, ICN2, and University 4843 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 References Chalmers acknowledge financial support from EU [1] Wang J and Zhang S-C 2017 Topological states of condensed FlagEra project (from Swedish Research Council matter Nat. Mater. 16 1062–7 VR No. 2015-06813), Swedish Research Council VR [2] He Q L et al 2017 Chiral Majorana fermion modes in a quantum anomalous Hall insulator–superconductor structure project Grants (No. 2016-03658), Graphene center Science 357 294–9 and the AoA Nano program at Chalmers University [3] Qiao Z et al 2014 Quantum anomalous Hall effect in graphene of Technology. 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