Quantum sensing is a rapidly developing field, with spin defects in solid-state materials emerging as strong candidates for various applications. Nitrogen-vacancy (NV) centers in diamond and spin defects in silicon carbide (SiC) have shown promise, but suffer limitations due to their three-dimensional nature, making it challenging to position the defects close to the sample surface for high-sensitivity nanoscale sensing. The proximity to the surface often degrades spin coherence properties. This paper investigates the potential of recently discovered defects in layered materials, specifically the negatively charged boron vacancy (VB−) in hexagonal boron nitride (hBN), to overcome these limitations. hBN is a promising 2D material with various atom-like defects, including single-photon emitters and spin-carrying defects. The VB− center, readily created by various methods, exhibits spin-optical properties that make it a promising candidate for quantum information and nanoscale quantum sensing. The VB− center displays photoluminescence (PL) emission around 850 nm and is an electronic spin-triplet (S = 1) system with a ground-state zero-field splitting (ZFS). This study focuses on the effects of external stimuli (temperature, pressure, and magnetic fields) on the VB− center's properties and demonstrates its suitability for sensing applications, highlighting its potential advantages over similar defect-based sensors in 3D materials.

The authors review existing literature on spin defects in 3D materials, such as NV centers in diamond and spin defects in SiC. They highlight the advantages and limitations of these systems in quantum sensing applications. They then discuss the recent discoveries of spin-carrying defects in 2D materials, particularly in hBN, focusing on theoretical predictions and experimental confirmations of the VB− center's properties. The review emphasizes the VB− center's potential as a promising candidate for quantum information and nanoscale sensing applications due to its unique spin-optical properties and its potential advantages over defects in 3D materials. The literature review sets the stage for the study by demonstrating the need for improved nanoscale sensors and highlighting the potential of VB− centers in hBN to meet this need.

The experiments were conducted on single-crystal hBN samples. VB− centers were generated using neutron irradiation. The absolute number of VB− defects was determined using electron paramagnetic resonance. The hBN sample consisted of a stack of several thousand monolayers with known lattice parameters. Optically detected magnetic resonance (ODMR) measurements were performed using a lab-built confocal microscope setup. A 532-nm laser excited the sample, and the photoluminescence was detected using an avalanche photodiode. Microwaves were applied using a copper strip-line. Lock-in detection was used by modulating the microwaves on and off. Temperature-dependent measurements were performed by varying the sample temperature. Magnetic field-dependent measurements used a permanent magnet. Pressure-dependent measurements involved applying pressure to the sample by stacking weights. To improve sensitivity in pressure-dependent measurements, sinusoidal modulation was applied to the static magnetic field. For high magnetic fields beyond the confocal ODMR setup limit, cw electron paramagnetic resonance (cw EPR) and electron spin-echo detected (ESE) EPR measurements were employed at X-band (9.4 GHz) and W-band (94 GHz) microwave frequencies, respectively. Data analysis involved fitting the ODMR spectra to extract the zero-field splitting (ZFS) parameter and its dependence on temperature, pressure, and magnetic field. The temperature-dependent changes in the ZFS were analyzed using a model based on temperature-induced structural deformations of the crystal lattice, which considers the anisotropic thermal expansion of hBN. For pressure measurements, a model based on the elastic moduli of hBN was used to relate pressure to the changes in lattice parameters and their effect on the ZFS. The study also considered the impact of heating effects from the laser excitation and resonant microwaves.

The study found that the zero-field splitting (ZFS) parameter, D, of the VB− center in hBN is highly sensitive to temperature, pressure, and magnetic fields. The temperature dependence of D was found to be remarkably linear over a wide temperature range (295-10 K), with a change in D of approximately 195 MHz, significantly larger than that observed in analogous spin systems in 3D materials (e.g., NV− centers in diamond). The temperature dependence was attributed to the temperature-induced changes in the lattice parameters *a* and *c*. By analyzing the temperature-dependent lattice parameters from the literature, and fitting the temperature-dependent ZFS data, they extracted the proportionality factors that connect lattice deformation and ZFS parameter D. The analysis suggested that in-plane lattice distortion influences ZFS at least three times stronger than the interplanar distance. A polynomial function was developed to accurately represent the relationship between temperature and ZFS parameter D for different temperature ranges. The researchers also demonstrated the VB− center's sensitivity to pressure, showing that the ZFS parameter D shifts linearly with applied pressure. The experimentally determined pressure sensitivity was found to be close to the theoretically expected value based on the elastic moduli of hBN. Finally, the study showed that the VB− center is highly sensitive to magnetic fields, with a linear relationship between the ODMR resonant frequencies and the applied magnetic field. The g-factor of the VB− center was determined with high accuracy. A comparison with other spin defects in diamond and SiC revealed that the VB− center in hBN offers comparable or even superior sensitivity to temperature and pressure changes, specifically exhibiting an eight-fold larger coupling coefficient to temperature change in the temperature range 50-350K. Additionally, the VB− center shows measurable temperature dependence of ZFS even at cryogenic temperatures (down to a few K), unlike NV− centers in diamond. Although Diamond NV- centers demonstrate higher resolution due to stronger PL emission, higher ODMR contrast, and optimized measurement protocols, the VB− center offers superior proximity to the surface, which is crucial for nanoscale sensing.

The findings address the research question by demonstrating the potential of VB− centers in hBN as highly sensitive nanoscale sensors for temperature, pressure, and magnetic fields. The superior sensitivity of VB− centers compared to defects in 3D materials, particularly at cryogenic temperatures, suggests significant advantages for applications requiring high spatial resolution. The linear dependence of ZFS parameter D on both temperature and pressure simplifies calibration and enhances the precision of measurements. The hBN's compatibility with other 2D materials opens new avenues for integrating VB− sensors into heterostructures, enabling advanced sensing functionalities. The study's limitations regarding optical detection efficiency could be addressed with improved optical systems to fully exploit the potential of VB− centers in future studies. Further investigations are also needed to explore the potential of utilizing VB− centers for simultaneous measurements of multiple physical quantities.

This work demonstrates the potential of negatively charged boron vacancies (VB−) in hexagonal boron nitride (hBN) as highly sensitive quantum sensors for temperature, pressure, and magnetic fields. The superior sensitivity, particularly at cryogenic temperatures, and the potential for nanoscale sensing applications, highlight the advantages of using VB− centers in hBN compared to existing sensor systems. Future research directions include optimizing the measurement protocols, improving the optical detection system, and investigating the use of VB− centers in heterostructures for multi-parametric sensing.

The study notes that the optical detection efficiency in the current setup is relatively low (η ≈ 1%), potentially limiting the sensitivity. Improved optical detection systems, such as those employing high numerical aperture objectives or nanophotonic structures, could improve the sensitivity. The pressure-dependent measurements were performed by applying pressure in the c-direction, while in-plane pressure measurements could provide further insights. Additionally, the effects of temperature and pressure were not fully decoupled in the experimental setup, meaning that temperature and pressure measurements must be performed under isobaric or isothermal conditions, respectively. However, the study demonstrates that the VB− center can be used for simultaneous magnetic field measurements with high sensitivity, due to the invariability of its g-factor with respect to temperature and pressure.