P roximity effects have been known for decades to induce superconducting properties into adjacent normal metals on length scales approaching 100 μm. 1,2 In contrast, magnetic proximity effects, for example, from an adjacent ferromagnetic layer, decay over extremely short distances of a few nanometers and can typically be neglected in bulk materials. The field of van der Waals materials offers tremendous new opportunities to harness magnetic proximity effects due to their atomically thin nature. In general, the strong interaction can be generated by two effects: 3 On one hand, the wave function from the 2D material evanescently penetrates into an adjacent insulating ferromagnet, where it acquires exchange splitting from the native ferromagnet. On the other hand, the wave function of a metallic ferromagnet can directly polarize the electronic structure in the nonmagnetic 2D material. As a result, new ways are created to induce spin polarization, degeneracy-lifting, and symmetry-breaking effects. In this way, proximity-induced ferromagnetism was reported for metallic graphene and for topological insulators. 4,5 Of much recent interest are semiconducting monolayers of transition-metal dichalcogenides (TMDCs) featuring strong spin-orbit coupling and intrinsic inversion symmetry breaking. 6,7 The valley degeneracy at K and K′ points in the conduction band can be lifted by an external magnetic field, 8,9 resulting in the moderate magnetic control of valley pseudospin splitting (∼0.1 meV/T) as well as optical addressing of K or K′ valleys using circularly polarized light, 10 giving rise to the upcoming field of valleytronics. The ability to further enhance the valley splitting energy of excitons in TMDCs is crucial to enable applications in on-chip quantum information processing, potentially even without an externally applied magnetic field. Ferromagnetic proximity coupling was recently demonstrated via polarized emission from the 2D neutral exciton in the conduction band, including WSe 2 attached to EuS, 11 WSe 2 attached to CrI 3 , 12,13 and MoTe 2 on top of EuO. 14 Whereas large valley splitting energies up to ∼4 meV were achieved at modest external magnetic fields of 6 T 11 compared with the typical ∼1 meV at 6 T without proximity coupling, the effects nevertheless remain limited with respect to the rather broad spectral line width of several tens of millielectronvolts for the 2D exciton emission. Likewise, in WSe 2 /MoSe 2 heterostructures, interlayer excitons form that feature giant effective g factors up to g = 15 and an energy splitting of 6 meV at 6 T, whereas spectra for both spin configurations still energetically overlap. 15 To be relevant for encoding quantum information in the underlying spin states, the spin-polarized transitions need to be spectrally fully separated to avoid crosstalk in absorption/ emission, which was not yet achieved. Moreover, the emission from 2D excitons (neutral, charged, or interlayer) is limited to classical light emission and has no direct relevance to realizing spin-photon interfaces for quantum light states in the form of single or entangled photons. In contrast, 0D-like excitons in the TMDC monolayer emit single photons on demand and feature ultranarrow spectral line widths (<0.1 meV) with spectrally fully separated spin states. [16][17][18][19] These quantum emitters can also be externally induced via local stressors, randomly via nanobubbles, 20 along holes, 21 or spatially deterministic via dielectric or metallic pillars patterned onto a substrate, 22,23 and further deterministically coupled to plasmonic nanocavities. 24 Despite these appealing properties, the control and manipulation of quantum emitters via ferromagnetic proximity coupling has not yet been demonstrated.

Here we utilize the recently discovered van der Waals ferromagnetic crystals of Cr 2 Ge 2 Te 6 (CGT) that behaves in the thin layer form as an ideal Heisenberg ferromagnet below a Curie temperature of 60 K 25 and demonstrate pronounced proximity coupling to site-controlled quantum emitters in WSe 2 . Magneto-optical measurements reveal a very large 0D exciton g factor up to g = 20 ± 1 for heterostructures of monolayer WSe 2 and few-layer CGT, corresponding to a threefold enhancement of the g factor compared with bare quantum emitters. By comparing the same quantum emitter before and after ferromagnetic proximity coupling, we also demonstrate a technique to directly measure the magnetic exchange field (MEF) strength, which approaches with experimental values up to 1.2 meV the theoretical limit determined from density functional theory (DFT) calculations, revealing maximum values of 2.1 meV for the ideal van der Waals heterostructure.

Results. Because of the short-range nature of magnetic exchange coupling, 26,27 a high-quality and smooth interface between the van der Waals ferromagnet and the TMDCs 27 is a key requirement. Previously, we have shown that the encapsulation of monolayer TMDCs with thin films of hexagonal boron nitride (hBN) leads to a significant reduction of interface disorder, particularly from the Si/SiO 2 substrate, giving rise to an inhomogeneous exciton line width approaching the intrinsic limit. 28 In this work, we followed that approach and have passivated the silicon wafer by first exfoliating thin layers of hBN. Subsequent layers of CGT and WSe 2 have been transferred with thermal annealing between each step to avoid interface contamination. (See the Methods.). In this way, samples that feature both hBN/WSe 2 regions (uncoupled case) as well as heterostructures of hBN/ CGT/WSe 2 (coupled case) have been created, as schematically depicted in Figure 1a, with a top view of the assembled heterostructure in Figure 1b. To deliberately create quantum emitters, we used cold stamping (room temperature) and hard pressing, an approach that we have previously shown to give rise to nanobubbles that create strain-induced 0D quantum emitters. (See the Methods.) 20 The corresponding 2D hyperspectral photoluminescence (PL) image of the hBN/ CGT/WSe 2 heterostructure region highlights bright emission from a 0D quantum emitter (Figure 1c). Figure 1d displays an exemplary PL spectrum that feature a few sharp lines that are spectrally below the 2D exciton emission. When spectrally filtered, emission lines display pronounced single-photon emission signatures characterized by a second-order photon correlation function of g (2) (0) = 0.13, as shown in Figure 1e. The energy range associated with these quantum emitters is shown in the occurrence plot in Figure 1f to vary in a rather well-defined energy range between 1.51 and 1.72 eV, depending on local strain. 22 To investigate the magneto-PL properties of each quantum emitter, we applied the magnetic field parallel to the k vector of the incident laser (Faraday configuration). Figure 2a shows the magnetic field dependence of a quantum emitter with a fine structure splitting (FSS) at zero field Δ 0 of 900 μeV that originates from the electron-hole spin-exchange interaction as well as an underlying anisotropic strain, which also causes the low-energy peak of the doublet to dominate in the spectrum. 21 With increasing applied magnetic field, B, the two components of the clearly resolved Zeeman doublet split further apart. The Zeeman splitting energy, ΔE, was analyzed to determine the g factor using the well-known relation E g B ( )

, where μ 0 is the Bohr magneton and g is the exciton g factor. For the coupled case of a quantum emitter residing on the hBN/CGT/WSe 2 heterostructure, we determined an ultrahigh exciton g factor of g = 20 ± 1, which is unprecedented in TMDC materials (Figure 2b). Interestingly, at magnetic field values above 3 T, the slope of the Zeeman splitting is drastically reduced, as indicated by the red solid line, corresponding to a much smaller g factor of 6.5 ± 0.5. This behavior is expected when the saturation magnetization of CGT has been reached (3μ B ), above which any additional Zeeman splitting of the quantum emitter is driven by the increasing external magnetic field alone.

To provide statistical evidence as well as a reference for the g factor in the absence of CGT, we carried out magneto-PL measurements of 58 quantum emitters located on five different samples.

The statistical ensemble of 21 individual emitters residing on hBN/WSe 2 in the absence of ferromagnetic proximity coupling displays a large variety of g factors ranging from g = 4.8 to 9.8, with an average value from the occurrence plot of g ave = 6.4 ± 2 (Figure 2c, bottom). Note that the average value of the g factor for uncoupled emitter matches the finding of g = 6.5 in Figure 2b at higher fields, supporting the picture that CGT has reached full saturation under optical laser illumination at applied external fields around 3 T. The measured g factors for the uncoupled case are comparable to previous reports for 0D exciton g factors for quantum emitters in WSe 2 , [16][17][18][19][20][21][22]29 which appear larger than g factors of 2D excitons and trions with typical values around g = 4. 30 It is found that about half of the quantum emitters display a nonmagnetic behavior, that is, a single peak with no zero-field splitting that does not split up even at high fields of 9 T. 29 Because no Zeeman effect is present in these cases, we naturally have excluded those from our study and only considered quantum emitters with magnetic behavior. In addition, we found that the g factor distribution for 0D quantum emitters in the uncoupled case weakly depends on the crystal growth technique when comparing samples grown by standard chemical vapor transport (CVT) with the superior flux-growth technique that produces significantly higher quantum yield in the optical emission. 24,31 The latter displays slightly lower FSS and g factor values for the uncoupled case. (See Figure S1.) Despite these large variations of the exciton g factor in the WSe 2 host crystal, Figure 2c (top) shows a clear difference for the 37 quantum emitters residing on hBN/CGT/WSe 2 that display g factor values under ferromagnetic proximity coupling varying from 7.2 to 20, with an average of g ave = 10.8 ± 2.3, which is 1.7 ± 0.3 times larger as compared with the average of the uncoupled case, whereas the best case (g = 20) is improved three-fold. The standard deviation of 0.3 corresponds to only a 17% variation, indicating that the g factors of all quantum emitters were enhanced by an underlying magnetic proximity coupling.

This demonstrated statistical approach is nevertheless limited because it is not possible to compare the same quantum emitter with and without proximity coupling. It thus remains unclear to what extent a change in microscopic origin from one quantum emitter to another or a change in local strain due to stamping onto CGT layers could cause a change in the 0D exciton g factor. To minimize variations from the growth process, we have solely utilized CVT-grown WSe 2 for the data set presented in the following. Previous work on quantum dots showed that the biaxial compressive strain of 0.025% induced via piezo actuators can lower the exciton g factor by ∼2%. 32 To exclude differences in microscopic origin as well as uncontrolled tensile strain as a cause of the observed proximity-enhanced g factor and to directly determine the MEF strength, we devised a measurement scheme to compare the same quantum emitter before and after coupling. To this end, we utilized the strain-induced quantum emitter formation via substrate nanopillars and further monitoring of the quantum emitter directly through the partially transparent CGT layer. Figure 3a shows an atomic force microscope (AFM) scan of the CGT/WSe 2 heterostructure stamped over a nanopillar array, which was patterned as the letters TMDC. (See the Methods.) After layer transfer, the 100 nm tall/wide nanopillars remain intact. The white box indicates the region for which the corresponding hyperspectral PL image filtered over the 1.7 meV energy range was recorded. The PL hotspots of the 0D exciton emission correlate nicely with the location of each nanopillar, as is evident from the hyperspectral mapping in Figure 3b. The corresponding AFM image in Figure 3c further indicates that only the nanopillars located at the outer edges provide a full strain modulation (100 nm), whereas the nanopillars located in between are modulated to only a ∼25 nm height difference at a separation of 1.5 μm. Nevertheless, this dense arrays of nanopillars produce a good yield, with six out of eight spatial sites inducing quantum emitters.

Quantum emitters induced by the stressors can be investigated for proximity coupling to CGT in two ways: (1) with CGT transferred first and WSe 2 on top or (2) the other way around. The former approach can maintain bright 0D exciton emission, giving rise to a proximity-enhanced g factor of g = 11.2 ± 0.2 (Figure S2). Whereas this demonstrates the successful proximity coupling of spatially deterministic quantum emitters as compared with randomly located ones in Figure 2, the drawback of this approach is that, again, no information about the spectral properties of the emitter before attaching CGT can be recorded. In contrast, when first stamping WSe 2 , the magneto-PL properties of the uncoupled case can be studied (Figure 4a) and directly compared with the case after transferring CGT on top (Figure 4b). In the latter case, the PL emission is significantly weaker due to the absorption loss through the CGT layer. To mitigate this effect, we increased the laser pump power from 100 to 300 μW and the integration time from 1 to 20 s to record PL spectra. The increased laser power causes a minor spectral broadening from 148 to 178 μeV from pump-induced exciton dephasing. As a key finding, the FSS at the zero field remains with Δ 0 = 570 ± 15 μeV before and Δ 0 = 560 ± 15 μeV after coupling unchanged, clearly indicating that the degree of strain anisotropy of the WSe 2 monolayer is not affected by the added material. In addition, a minor shift in the exciton emission of 1 meV to higher energies is most likely caused by a change in local strain after stamping of CGT. Following previous work on strain-tuning of quantum emitters, 21 a 1 meV change in energy corresponds to a relative strain variation of Δε = 0.02% in the host crystal. Such a small change in local strain would cause only a minor change in the g factor of <2%, that is, an amount within the error bar of the determined g factors. Note that CGT is a soft ferromagnet 25 and thus displays only a small hysteresis effect in the electric resistivity below applied fields of 0.1 T. 33 The corresponding additional Zeeman energy for an exciton with a g factor of 10 and an applied magnetic field of 0.1 T is only 2 μeV, which is well below the exciton line width and is thus not resolvable.

The resulting ΔE values as a function of magnetic field are s h o w n i n F i g u r e 4 d . T h e s o l i d l i n e s f o l l o w

, resulting in g = 8.0 ± 0.2 without and g = 15 ± 0.5 with proximity coupling, corresponding to a 1.7-fold enhanced g factor, which is in close agreement with the average in ensemble studies (Figure 2). Above 3 T, the slopes of the Zeeman splitting for the uncoupled and coupled quantum emitter (solid blue trend line) are identical, clearly indicating that saturation magnetization of CGT has been reached. Because the same quantum emitter was measured with and without the ferromagnetic proximity layer, the additional Zeeman splitting by the underlying MEF can be directly determined from the energy difference between the two curves in Figure 4d, as shown by the blue bars. In this way, we determined an MEF value in the saturation regime of MEF = 1.05 ± 0.01 meV for this quantum emitter. In addition, Figure S3 and Figure S4 show two additional cases with comparable magnetic field behavior resulting in MEF = 1.2 ± 0.01 meV and MEF = 0.5 ± 0.01 meV, respectively. Given that the proximity effect varies exponentially with distance, we attribute the local variations in the experimentally determined interfacial MEF values to the observed surface roughness of 0.52 nm, as determined from AFM measurements of the heterostructure.

To determine an upper limit for MEF in the best case, that is, for an ideal heterostructure between WSe 2 and CGT without interface roughness, we have carried out theoretical modeling. It is expected that the g factor enhancement originates from the interfacial MEF, which is proportion to ∼J<S z >. In this framework, J is an exchange coupling between two adjacent atoms based on the Heisenberg model. At 4 K, and moderate external fields, <S z > saturates at 3μ B , as was experimentally determined for Cr 3+ ions in CGT. 34 Previous efforts based on DFT calculation show that, depending on geometry, the nearest-neighbor intralayer J values and J interlayer exchange in the CGT lattice are in the range of -3.7 to 0.05 meV. 25 Because the proximity effects are strongly band-dependent, 35 we have carried out DFT calculations to gain insight into the mechanism for the enhancement of the effective exciton g factor in the adjacent WSe 2 monolayer based on the Perdew-Burke-Ernzerhof (PBE) functional. (See the Methods.) Top and side views of the optimized atomic model are shown in Figure 5a,b, respectively. We considered the ferromagnetic state of CGT with the magnetic moments of the Cr atoms pointing toward the WSe 2 . The MEF splitting energy can be calculated from the electronic band structure from the K and K′ points in the first Brillouin zone, which is illustrated in Figure 5c. This model predicts a value of Δ MEF = 2.1 meV for our system. Note that for isolated WSe 2 , the DFT calculated energy value is nearly three orders of magnitude smaller, which confirms that the predicted 2.1 meV splitting energy for the heterostructure is not influenced by numerical noise.

Apparently, the experimental values for MEF up to 1.2 meV approach the theoretical limit of 2.1 meV from the DFT calculations, indicating that the proximity coupling is only slightly degraded by interface roughness.

In summary, we have shown that magnetic proximity coupling of the van der Waals soft ferromagnet CGT with quantum emitters in WSe 2 gives rise to ultrahigh 0D exciton g factors up to g = 20 ± 1. The observation of a clear saturation behavior of the CGT magnetization as well as the comparison of the same site-controlled quantum emitter before and after ferromagnetic proximity coupling allows us to directly quantify the interfacial magnetic change field via the additional induced Zeeman splitting. Our work extends the on-chip control of magneto-optical properties in van der Waals heterostructures previously reported for 2D excitons here to 0D excitons that are of interest to encode quantum information in the spin states of solid-state quantum emitters. In particular, if combined with recent advances with ferromagnetic van der Waals materials such as Fe 3 GeTe 2 36 as well as gatecontrolled ferromagnetism, 37 the on-chip manipulation of magneto-optical properties of quantum emitters might become feasible, even in the absence of externally applied magnetic fields.

Methods. Sample Preparation. The CGT and hBN were mechanically exfoliated down to few-layer thin films (3-20 nm) from commercial crystals (HQ Graphene). Monolayers of WSe 2 were exfoliated either from commercial crystals (HQ Graphene) that were grown by CVT or from bulk crystals grown by the flux-growth technique that gives rise to one to two orders of magnitude lower defect density and higher exciton emission quantum yield, as we previously reported. 24,31 To achieve clean interfaces, we employed the "hot stamping" process 20 including substrate heating to 55 °C for the transfer process, followed by thermal annealing at 350 °C for 12 h between each stamping process. In contrast, to produce nanobubbles for the data in Figures 1 and2, we utilized cold stamping: Samples were held at room temperature, stamping was carried out by hard pressing, and no additional thermal annealing was carried out in the last step to preserve the nanobubbles. To achieve spatially deterministic quantum emitter arrays, we fabricated Au nanopillar (100 nm tall and 100 nm diameter) arrays via electron-beam lithography (Elionix ELS-G100), followed by capping with 2 nm Al 2 O 3 grown via atomic layer deposition, similar to our previous work on deterministic plasmonic coupling 24,31 but here on 90 nm SiO 2 substrates instead of sapphire and assembled into the letters "TMDC". The heterostructures were transferred onto the nanopillars by subsequent hot stamping to suppress detrimental nanobubble formation, either in CGT/WSe 2 or in WSe 2 /CGT ordering configuration.

Photoluminescence Spectroscopy. Microphotoluminescence (μ-PL) measurements were taken inside a closed-cycle cryogen-free cryostat with a 3.8 K base temperature and ultralow vibration (attoDRY1100). Samples were excited with a laser diode operating at 532 nm in continuous-wave mode. A laser spot size of ∼0.85 μm was achieved using a cryogenic microscope objective lens with a numerical aperture of 0.82. The relative position between the sample and the laser spot was adjusted with a cryogenic piezoelectric xyz stepper, whereas 2D scan images were recorded with a cryogenic 2Dpiezo scanner (Attocube). The spectral emission from the sample was collected in a multimode fiber, dispersed using a 0.75 m focal length spectrometer, and imaged by a liquidnitrogen-cooled silicon charge-coupled device (CCD) camera.

Atomic Force Microscope Imaging. The AFM measurements were obtained using a Bruker Dimension FastScan AFM in noncontact mode at a scan rate of 1.3 Hz with a FastScan-B tip. The AFM high profiles were extracted from the images using Gwyddion open-source software.

Theoretical Methods. The plane-wave DFT calculations were carried out using VASP 38,39 with PAW pseudopotentials, 40 an energy cutoff of 500 eV, Gaussian smearing of 0.01 eV, the PBE exchange correlation functional, 41 gammacentered k-point samplings, a force cutoff of 0.01 eV/Å for relaxations, and a vacuum spacing of ∼15 Å when appropriate. The lattice and ions were first optimized for single-layer WSe 2 (primitive cell, 16 × 16 × 1 k-point sampling) and bulk CGT (conventional standard cell with three layers per unit from Materials Project, 42 8 × 8 × 3 k-point sampling). Even without using the PBE+U method, we found the correct ferromagnetic state for CGT, with ∼3μ B per Cr atom. For the composite system, we considered the single layer of WSe 2 on three layers of CGT with the magnetic moment pointing toward the WSe 2 . The lattice vectors of both materials are conveniently parallel, and to minimize the lattice mismatch, we used a (2 × 2) supercell of WSe 2 on a (1 × 1) cell of CGT. The in-plane lattice vectors of the CGT were compressed by 4% to exactly match those of the isolated WSe 2 supercell, which is similar to what was required when WSe 2 on ferromagnetic EuS was studied. 11 Straining the substrate instead of the adsorbate prevents a band alignment modification for the system component of interest. 43 The bulk CGT ions were first relaxed with the new lattice constant imposed, and the local magnetic moments changed by only ∼0.1μ B per Cr atom as compared with the unstrained bulk. To form the final composite system, the ions were relaxed, keeping the two bottom layers of the CGT fixed to simulate a "bulk" substrate (8 × 8 × 1 k-point sampling). Spin-orbit coupling was included throughout all calculations. Site projections were used to determine the bands belonging to WSe 2 near the Fermi energy.

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.9b02920.

The authors declare no competing financial interest.