Wide field imaging of van der Waals ferromagnet Fe3GeTe2 by spin defects in hexagonal boron nitride

Emergent color centers with accessible spins hosted by van der Waals materials have attracted substantial interest in recent years due to their significant potential for implementing transformative quantum sensing technologies. Hexagonal boron nitride (hBN) is naturally relevant in this context due to its remarkable ease of integration into devices consisting of low-dimensional materials. Taking advantage of boron vacancy spin defects in hBN, we report nanoscale quantum imaging of low-dimensional ferromagnetism sustained in Fe3GeTe2/hBN van der Waals heterostructures. Exploiting spin relaxometry methods, we have further observed spatially varying magnetic fluctuations in the exfoliated Fe3GeTe2 flake, whose magnitude reaches a peak value around the Curie temperature. Our results demonstrate the capability of spin defects in hBN of investigating local magnetic properties of layered materials in an accessible and precise way, which can be extended readily to a broad range of miniaturized van der Waals heterostructure systems.

defects in a real van der Waals heterostructure remains a formidable challenge. In this work, we report nanoscale quantum sensing and imaging of exfoliated 2D ferromagnet Fe 3 GeTe 2 (FGT) flakes 33-41 by boron vacancy V À B spin defects in an adjacent hBN capping layer. Exploiting a wide-field magnetometry method [42][43][44][45][46] , we directly image the local magnetic texture of the FGT flake and its characteristic temperature and field dependent magnetization evolution behavior. Taking advantage of spin relaxometry techniques [47][48][49][50][51] , we have observed spatially varying spin fluctuations in the FGT flake, whose magnitude reaches a peak value around the Curie temperature, consistent with the expected ferromagnetic phase transition. We highlight that the presented quantum sensing platform built on spin defects in van der Waals crystals can be extended naturally to a large family of miniaturized 2D heterostructure systems 10,52,53 , bringing new opportunities for investigating the local spin, charge, and thermal properties of emergent quantum materials and devices.

Results
Before discussing the details of our experimental results, we first review our measurement platform and device structure, as illustrated in Fig. 1a. We exfoliated an FGT flake and mechanically transferred it onto a patterned Au microwave transmission line. Following this, we encapsulated the sample with an hBN layer. The device preparation process was performed in a glove box with argon environment to minimize environmental effects (see Methods for details). An optical microscope image shown in Fig. 1b provides an overview of a prepared device, where the thickness of the FGT and hBN flakes were characterized by atomic force microscopy (see Supplementary Information Note 1 for details). Boron vacancy V À B spin defects in the hBN flake were created by Helium ion implantation with an energy of 5 keV and a dose of 5 × 10 13 cm −2 . Figure 1c illustrates the structure of V À B in a hexagonal crystalline structure with alternating boron (red) and nitrogen (green) atoms, where three nitrogen atoms are adjacent to each boron atom vacancy V À B . The negatively charged V À B spin defect has an S = 1 electron spin and serves as a three-level quantum system, as shown in Fig. 1d. In the present study, we used microwave currents flowing in the Au microwave transmission line to control the quantum spin state of V À B spin defects, which can be optically accessed via spindependent photoluminescence (PL). The Au underlayer also enhances the PL and optical contrast of V À B spin defects 16 , aiding the quantum microscopy measurements discussed below. The distance between the V À B defect centers and the top surface of the FGT sample is estimated to be~50 nm based on Stopping and Range of Ions in Matter (SRIM) simulations. Exfoliated FGT flakes show spontaneous perpendicular magnetization due to reduced crystal symmetry of the layered structure 33,35,36 . We have prepared separate devices to systematically and reproducibly characterize the magneto-transport properties of exfoliated FGT flakes, whose Curie temperature is measured to bẽ 200 K, in qualitative agreement with previous studies (see Supplementary Information Note 2 for details) 33,35,40 .
We now utilize wide-field microscopy to demonstrate optically detected magnetic resonance (ODMR) and spin relaxation of V À B defect centers (see Methods for details). The top panel of Fig. 1e shows the optical and microwave measurement sequence. We utilize 1-μs-long green laser pulses for spin initialization and readout, and~100-ns-long microwave π pulses 54 to induce spin transitions of V À B spin defects. We sweep the frequency f of the microwave π pulses and measure the fluorescence across the field of view projected on a CMOS camera. When f matches the electron spin resonance (ESR) frequencies, V À B spin defects are excited to the m s = ± 1 states, which are more likely to relax through a non-radiative pathway back to the m s = 0 ground state and emit reduced PL. The bottom panel of Fig. 1e shows a series of c Schematic of V À B spin defects (blue arrows) formed in a hexagonal crystalline structure with alternating boron (red) and nitrogen (green) atoms. A negatively charged boron atom vacancy V À B is surrounded by three nitrogen atoms located in the nearest neighboring sites. d Energy level diagram of a V À B spin defect and schematic illustration of optical excitation (green arrow), radiative recombination (red arrow), and nonradiative decay (black dotted arrow) processes between the ground state (GS), excited state (ES), and metastable state (MS). e Top panel: optical and microwave sequence of pulsed optically detected magnetic resonance (ODMR) measurements. Bottom panel: ODMR spectra of V À B spin defects measured at a series of perpendicularly applied external magnetic fields B ext . f Top panel: optical and microwave sequence of spin relaxometry measurements. Bottom panel: a set of spin relaxometry data of V À B spin defects showing spin dependent photoluminescence measured as a function of delay time t. The external magnetic field is 185 G applied along the out-of-plane direction, and the measurement temperature is 295 K.
ODMR spectra of V À B defect centers measured at room temperature with different external magnetic fields B ext applied along the out-ofplane direction. For B ext = 0, the energy level of the m s = ± 1 states of V À B spin defects exhibit a small separation of~100 MHz due to the offaxial zero field splitting effect 14,26,55 and the average ESR frequency equals~3.47 GHz at room temperature 14,26,28,55 . For B ext > 0, the Zeeman coupling separates the m s = À1 and m s = + 1 spin states by an energy gap of magnitude 2e γB ext (see Supplementary Information Note 3 for  details), where e γ denotes the gyromagnetic ratio of V À B defect centers. To characterize the quantum coherence of V À B spin defects, we perform spin relaxometry measurements with a measurement protocol shown in the top panel of Fig. 1f. A microsecond scale green laser pulse is first applied to initialize the V À B spin defects to the m s = 0 state. During the time delay, fluctuating magnetic fields at the ESR frequencies will accelerate spin relaxation of V À B spin defects. After a delay time t, we measure the occupation probabilities of the V À B spin defects at the m s = 0 and ± 1 states by applying a microwave π pulse on the corresponding ESR frequencies and measuring the spin-dependent PL by a green-laser readout pulse. The bottom panel of Fig. 1f shows the integrated PL intensity of the m s = 0 and ± 1 states measured as a function of the delay time t. By fitting the data with a three-level model 51,56 , the spin relaxation rate Γ 0 of V À B spin defects is obtained to be 39 KHz (38 KHz) for m s = 0 ! À1 (+1) transition at 295 K, consistent with previous studies 16,21,55 .
After demonstrating the ODMR and spin relaxometry measurement capabilities, next, we use V À B spin defects in hBN to directly image magnetic textures of an exfoliated FGT flake. Wide-field magnetometry exploits the Zeeman splitting effect of the ensembles of V À B defect centers to measure the local magnetic stray fields generated from the proximate FGT flake, as illustrated in Fig. 2a. It is worth noting that the V À B spins are naturally orientated along the out-of-plane direction 14 , serving as an ideal local sensor to investigate the magnetic dynamics and phase transition of FGT with spontaneous perpendicular anisotropy. The magnitude of the local static magnetic field B tot can be extracted as follows: B tot = π4f ESR =e γ, where 4f ESR characterizes the Zeeman splitting of the V À B spin defects. Subtracting the contribution from the external magnetic field B ext , the magnetic stray field B F generated from the FGT flake can be quantitatively measured. By performing spatially dependent ODMR measurements over the V À B spin ensembles, we are able to obtain a 2D stray field map as shown in Fig. 2b, which is measured at a temperature T = 6 K and an external magnetic field B ext = 142 G. Through well-established reverse-propagation protocols 46,57,58 (see Supplementary Information Note 3 for details), we can reconstruct the corresponding magnetization 4πM map of the FGT flake, as shown in Fig. 2c. The spatially averaged magnetization of the FGT flake is 1.3 kG at 6 K, in qualitative agreement with the bulk value 33 . The variation of the local magnetization could result from inhomogeneities, magnetic domains, or localized defects 39,59 .
We now present systematic wide-field magnetometry results to directly image the magnetic phase transition of the FGT flake across the Curie temperature. Figure 3a-g show the reconstructed magnetization maps of the FGT flake measured with temperatures varying from 6 to 225 K and an external perpendicular magnetic field B ext of 142 G. In the low temperature regime (T < 100 K), the exfoliated FGT flake exhibits robust magnetization, as shown in Fig. 3a, b, indicating a  long-range ferromagnetic order sustained by the intrinsic magnetocrystalline anisotropy of FGT. The measured FGT magnetization decreases with increasing temperature due to enhanced thermal fluctuations (Fig. 3c). When approaching the Curie temperature, the energy of thermal fluctuations becomes comparable to the exchange energy of FGT, resulting in significant suppression of the FGT magnetization (Fig. 3d). Further increasing of the temperature leads to shrinking of the magnetic domain and decreasing magnetization of the FGT flake (Fig. 3e, f). Above the Curie temperature (T = 225 K), measured magnetization disappears over the entire FGT flake area (Fig. 3g). Figure 3h summarizes the temperature-dependent evolution of the spatially averaged magnetization of the FGT flake. The magnetic moment of the FGT flake exhibits a gradual decay in the low temperature regime, followed by a dramatic drop during the ferromagnetic phase transition, in agreement with the magneto-transport characterization results (see Supplementary Information Note 2 for details). To further highlight the evolution of magnetic domains in the FGT flake, we present wide-field magnetometry results under different external magnetic fields.  Figure 4h shows field dependence of the spatially averaged FGT magnetization, consistent with the variation of the anomalous Hall resistance measured in the same magnetic field regime (see Supplementary Information Note 2 for details). We note that the previously observed labyrinthine magnetic domains in FGT are not visible here due to the optical diffraction dictated spatial resolution limit 35 .
In addition to sensing static magnetic stray fields, the excellent quantum coherence of V À B spin defects in hBN also provides the opportunity for probing fluctuating magnetic fields that are challenging to access by conventional magnetometry methods 47,48,50,51,55 . Lastly, we utilize the spin relaxometry method demonstrated above to probe the temperature dependence of the magnetic fluctuations in the FGT flake, revealing the intriguing physics underlying the longitudinal magnetic susceptibility and diffusive spin transport properties 60,61 . Fig. 5a-g show a series of V À B spin relaxation rate maps measured with temperatures between 165 K and 223 K. Note that the background of the intrinsic relaxation rate of V À B has been subtracted to highlight the contribution Γ M from the fluctuating magnetic fields generated by FGT (see Supplementary Information Note 4 for details). Due to the strong perpendicular magnetic anisotropy, the minimum magnon energy of FGT is larger than the ESR frequencies of V À B spin defects in our experimentally accessible magnetic field range, hence, the measured spin relaxation is driven by the longitudinal spin fluctuations of FGT, which is further related to the static longitudinal magnetic susceptibility χ 0 and the diffusive spin transport constant D 46,60,61 . When temperature is away from the quantum critical point, magnetic fluctuations in FGT are largely suppressed due to its vanishingly small magnetic susceptibility, leading to negligible spin relaxation rate Γ M of V À B defects (Fig. 5a, b). In contrast, we observed significantly enhanced spin relaxation rate during the magnetic phase transition of FGT (Fig. 5c-e), which we attribute to the increase of the magnetic susceptibility of FGT around the Curie temperature 62 . When T is above 200 K, spin fluctuations remain active in FGT due to the finite spin-spin correlation in the paramagnetic state 63 . The observed spatially varying magnetic fluctuations over the exfoliated FGT flake could be induced by inhomogeneities in magnetic susceptibility, spin diffusion constant, and exchange coupling strength. Figure 5h summarizes the temperature dependence of the spatially averaged spin relaxation rate Γ M with a peak value of 36 kHz around the Curie temperature, consistent with the ferromagnetic phase transition of FGT 62

Discussion
In summary, we have demonstrated V À B spin defects in hBN as a local probe to image magnetic phase transitions and spin fluctuations in the archetypical van der Waals ferromagnet FGT at the nanoscale. The spatially resolved wide-field magnetometry results reveal the characteristic evolution behavior of magnetic domains during the phase transition of FGT. By using V À B spin relaxometry techniques, we are also able to access the spin fluctuations in the FGT flake, whose magnitude reaches a maximum value around the Curie temperature. Our results illustrate the appreciable capability of V À B spin defects hosted by hBN  of investigating local magnetic properties of layered materials in van der Waals heterostructure formats. The presented measurement platform also shows optimal field sensitivity with nanoscale sensor-tosample distance 15,16,64 , offering new opportunities for advancing the state of the art of existing quantum sensing technologies. While the current study is conducted using wide-field magnetometry with a spatial resolution set by the optical diffraction limit, we anticipate that the spatial sensitivity of V À B spin defects could potentially reach the tens of nanometers regime by utilizing single-spin defects and developing scanning microscopy measurement schemes 2,44,50,57,65,66 , opening the possibility of uncovering detailed microscopic features in a broad range of 2D material systems.

Materials and device fabrication
The hBN and FGT crystals used in this study were commercially available from 2D Semiconductors. Thin samples were mechanically exfoliated onto Si/SiO 2 (285 nm) substrates. hBN flakes were subsequently irradiated by Helium ions with an energy of 5 keV and a dose of 5 × 10 13 cm −2 . Irradiated hBN flakes with desirable lateral shape and dimensions are selected for fabricating FGT/hBN bilayer devices. FGT/ hBN stack was prepared using the standard polydimethylsiloxane stamp process 67 . Selected flakes were picked up one-by-one by a stamp consisting of a thin layer of polycarbonate on polydimethylsiloxane, then released onto an Au transmission line pre-patterned on a separate Si/SiO 2 (285 nm) substrate. The residual polycarbonate on the device was dissolved in chloroform before measurements. All the device fabrication processes involving handling FGT flakes were performed inside a glovebox filled with argon to minimize environmental degradation. Multiple control samples have been prepared and tested to ensure the reproducibility of the presented results (see Supplementary Information Note 5 for details).

Pulsed ODMR and spin relaxometry measurements
Pulsed ODMR and spin relaxometry measurements were performed by a wide-field microscope. The prepared FGT/hBN heterostructure was positioned in a closed-cycle optical cryostat allowing for measurements from 4.5 K to 350 K. Microsecond-long green laser pulses used for spin initialization and readout were generated by an electrically driven 515-nm laser. The laser beam spot width after passing the objective was about 25 μm × 25 μm, and was subsequently focused on the hBN layer. Fluorescence of V À B spin defects was imaged using a CMOS camera. Pulses to drive the green laser and to trigger the camera exposure were generated by a programmable pulse generator. Continuous microwave currents were generated using Rohde & Schwarz SGS100a and/or Rohde & Schwarz SMB100a signal generators. 100-nanosecondlong microwave current pulses were generated by sending the continuous microwave currents to a microwave switch (Minicircuits ZASWA-2-50DR+) electrically controlled by a programmable pulse generator. The microwave pulses were sent through a microwave combiner (Mini-Circuits ZB3PD-63-S+) and amplified by + 50 dB (Mini-Circuits ZHL-25W-63+) before being delivered to the on-chip Au stripline. The external magnetic field was generated by a cylindrical NdFeB permanent magnet attached to a scanning stage. The field sensitivity and other merits of the presented ODMR measurement platform are discussed in Supplementary Information Note 6 in detail.

Data availability
All data supporting the findings of this study are available from the corresponding author on reasonable request.

Code availability
All code not included in the paper are available upon reasonable request from the corresponding authors.