Magnetic detection under high pressures using designed silicon vacancy centres in silicon carbide

Pressure-induced magnetic phase transitions are attracting interest as a means to detect superconducting behaviour at high pressures in diamond anvil cells, but determining the local magnetic properties of samples is a challenge due to the small volumes of sample chambers. Optically detected magnetic resonance of nitrogen vacancy centres in diamond has recently been used for the in situ detection of pressure-induced phase transitions. However, owing to their four orientation axes and temperature-dependent zero-field splitting, interpreting these optically detected magnetic resonance spectra remains challenging. Here we study the optical and spin properties of implanted silicon vacancy defects in 4H-silicon carbide that exhibit single-axis and temperature-independent zero-field splitting. Using this technique, we observe the magnetic phase transition of Nd2Fe14B at about 7 GPa and map the critical temperature–pressure phase diagram of the superconductor YBa2Cu3O6.6. These results highlight the potential of silicon vacancy-based quantum sensors for in situ magnetic detection at high pressures. Optically detected magnetic resonance of nitrogen vacancy centres in diamond enables the detection of pressure-induced phase transitions, but interpreting their magnetic resonance spectra remains challenging. Here the authors propose implanted silicon vacancy defects in 4H-SiC for in situ magnetic phase detection at high pressures.

Pressure-induced magnetic phase transitions are attracting interest as a means to detect superconducting behaviour at high pressures in diamond anvil cells, but determining the local magnetic properties of samples is a challenge due to the small volumes of sample chambers. Optically detected magnetic resonance of nitrogen vacancy centres in diamond has recently been used for the in situ detection of pressure-induced phase transitions. However, owing to their four orientation axes and temperature-dependent zero-field splitting, interpreting these optically detected magnetic resonance spectra remains challenging. Here we study the optical and spin properties of implanted silicon vacancy defects in 4H-silicon carbide that exhibit single-axis and temperature-independent zero-field splitting. Using this technique, we observe the magnetic phase transition of Nd 2 Fe 14 B at about 7 GPa and map the critical temperature-pressure phase diagram of the superconductor YBa 2 Cu 3 O 6.6 . These results highlight the potential of silicon vacancy-based quantum sensors for in situ magnetic detection at high pressures.
The ability of pressure to alter the electronic, magnetic and structural properties of matter is a vital feature widely used in fundamental and applied sciences studies [1][2][3][4][5][6][7][8] . High-pressure techniques have been applied in many fields, including physics, material sciences, geophysics and chemistry, revealing many unusual and important phenomena observed under pressure [1][2][3][4][5][6][7][8] . In particular, claims of pressure-induced high-critical-temperature (T c ) superconductivity have attracted serious attention and excitement in recent years [6][7][8] . For example, lanthanum hydride has been inferred to be a superconductor with a T c of ~250 K at around 170 GPa (refs. 7,8 ). One of the great challenges in high-pressure research is the measurement of magnetic properties and their evolution. Conventional methods such as using superconducting quantum Article https://doi.org/10.1038/s41563-023-01477-5 qubits and bright single-photon emitters in SiC have also attracted considerable attention in the quantum community [20][21][22][23][24][25][26][27][28][29][30][31][32] . In particular, the silicon vacancy (V Si ) defect in 4H-SiC with a negative charge has been extensively used in spin-photon interfaces 23 , quantum photonics 26 , quantum information processing 22 and quantum sensing of properties such as magnetic fields 30 and temperatures 31,32 owing to its outstanding properties (an S = 3/2 spin quartet and groundstate D of ~70 MHz) (refs. 22,23 ). It has only one axis (along the c axis of 4H-SiC), and the corresponding ODMR spectrum has two resonant peaks under an external magnetic field, which is convenient for determining the resonant frequencies and enhancing the scalability of SiC devices 22 . Moreover, its D value is also almost temperature independent from 20 K to 500 K at ambient pressure, which is beneficial for temperature-pressure research 31,32 . However, most of the previous investigations on the V Si defect were performed under ambient pressure [22][23][24][25][26][27][28][29][30][31][32] . The study of the optical and spin properties at high pressure is important for V Si defect-based quantum sensing at extreme conditions. In comparison with traditional high-pressure magnetometry techniques, the spatial resolution of V Si defect detection is only around a few micrometres.
Here we investigate and characterize the optical and spin properties of the implanted silicon vacancy defects at the culets of a 4H-SiC anvil, which exhibit single-axis and temperature-independent interference devices or a.c. susceptibility cannot directly detect weak magnetic signals of micrometre-sized samples in diamond anvil cells (DACs) [9][10][11][12][13][14] . It is therefore important to explore new methods for magnetic detection.
The high sensitivity and high resolution of in situ magnetic detections in DAC chambers were achieved using nitrogen vacancy (NV) centres in diamond [10][11][12] . Diamond NV centres are versatile solid-state spin quantum sensors that have been used to detect a wide variety of physical parameters, such as magnetic and electric fields, tempera ture, strain, spins, pressure and electrical currents [9][10][11][12][13][14][15][16][17][18][19] . The zero-field-splitting parameter D of the NV centre ground spin state was shown to increase linearly with pressure with a slope of 14.6 MHz GPa −1 up to 60 GPa (ref. 9 ). On this basis, an in situ magnetic detection method based on NV centres using optically detected magnetic resonance (ODMR) technologies has recently been developed at high pressure [10][11][12][13] . Micrometre-sized diamond particles with ensemble NV centres have been placed inside DAC chambers to measure the T c -pressure phase diagram of a superconductor 10 and detect the pressure-induced magnetic phase transition of a magnet 13 . The shallow implanted NV centres on the surface of the diamond were also used to probe the magnetization of Fe particles and the Meissner effect of a superconductor, and to construct the full stress tensor on the culet surface 11,12 . Defects in silicon carbide (SiC) could also be used to measure magnetic properties under extreme conditions. SiC is a widely used semiconductor owing to its unique properties, such as mature inch-scale growth and micro/nanofabrication [20][21][22] . Several spin c d e f

Optical properties of silicon vacancies under high pressure
The experimental configuration used in our experiments is shown in Fig. 1a (see the Methods and Supplementary Text 1 for details). First, we describe the optical and spin properties of the V Si defects at high pressures. The energy levels of the defects at high pressures are shown in Fig. 1b. The 720 nm laser pumped the electrons from the ground state to the phonon sideband, and the zero-phonon line (ZPL) at ambient pressure was 916 nm. Both the ZPL and the ground spin state D changed under high pressure. The room temperature photoluminescence spectra of the defects at three different compressions are shown in Fig. 1c. The photoluminescence spectra of the V Si defects are blueshifted with pressure. We then investigate the mean counts of the V Si defects as a function of compression. The counts increased as the pressure increased from ambient pressure to 8 GPa due to the higher detection efficiency at shorter wavelengths of the single-photon counting module (Fig. 1d). The counts then decreased as the pressure increased to approximately 25 GPa (see Supplementary Text 1 for more details). At the same time, we observed a decrease in the ODMR contrast with increasing pressure (Fig. 2a). We speculate that the decrease in the photon counts and ODMR contrast are both related to, and driven by, the lattice distortion of the 4H-SiC, caused by the inhomogeneity and deviation of compression at high pressures. The altered probability density and the electronic structure of the silicon vacancy due to compression may also contribute to the decrease in the photon counts and ODMR contrast 9,33-35 .

Spin properties of silicon vacancies under high pressure
We then study the spin properties of V Si defects at high pressures. The ODMR spectra at zero external magnetic field are shown in Fig. 2a. The zero-pressure ODMR peak of 72.4 ± 0.3 MHz may be due to the strain during the preparation of the SiC anvil, and the effect has been observed before [36][37][38] . The resonant frequency shifts to higher frequencies as the pressure increased, in line with the ODMR signal of NV centres in diamond [9][10][11][12][13][14][33][34][35] . The local structural distortions and the decreasing distance between V Si spin in the macroscopic compression in the SiC crystal drive the resonant frequency shifts to higher values as the pressure increases 9,33-35 . As shown in Fig. 2b, the mean D increased linearly with the pressure with a coefficient of 0.31 ± 0.01 MHz GPa −1 , which is considerably smaller than the coefficient of 14.6 MHz GPa −1 for NV centres in diamond 9,13,14 . The smaller slope is beneficial for directly observing the shift of the ODMR signal over a large pressure range. The reason for the small slope is the degeneracy of half-integer V Si defects (S = 3/2), which make it relatively insensitive to strain fluctuations 39 .
Through coherent control of V Si defects, one can detect the noise spectroscopy of magnetic materials 12 . Figure 2c shows the measurement of Rabi oscillations at ambient pressure using a standard pulse sequence 20,32 . The Rabi frequency inferred from the fit is 9 MHz. Figure 2d,e present the spin echo measurements of V Si defects at ambient pressure and at 15.1 GPa, yielding coherence times T 2 of 7.8 ± 0.9 µs and 7.3 ± 0.7 µs, respectively. Both values are consistent with previous results 32 . T 2 as a function of pressure up to 25 GPa is summarized in Fig. 2f: T 2 remains invariable up to 25 GPa, which is similar to values for NV centres in diamond 13 .

Magnetic detection using silicon vacancies under high pressures
SiC anvils with V Si defects could be used to study magnetic and superconducting properties of materials under compression. Using the ODMR spectrum, we studied the pressure-induced magnetic phase transitions of the common magnet Nd 2 Fe 14 B. A small sample of Nd 2 Fe 14 B was placed on the surface of the culet. The confocal scanning microscopy images of the implanted shallow V Si defects and Nd 2 Fe 14 B sample on the culet surface are presented in Fig. 3a. To efficiently detect the magnetic field of the sample, a location close to the sample (the region outlined by a black dashed line) was chosen as the detection position, denoted by a black cross. As a comparison, a remote location (denoted by a blue cross) was the reference position. In the experiment, we applied a c-axis (perpendicular to the culet) magnetic field B c with a strength of 198 G. Three schematics of local magnetic field vectors at the detected position under different pressures are shown in Fig. 3b. B NdFeB and B tot represent the magnetic field of the Nd 2 Fe 14 B sample and the total magnetic field on the V Si defects, respectively. Standard lock-in technology was used to detect the ODMR signals 20,32 . The integration time for each frequency was around 5 s, and the total measurement time was ~580 s. The representative ODMR signals at the detected positions and reference during the compression process are presented in Fig. 3c. The ODMR signals at the reference position, reflecting the strength of B c , were also measured at each pressure. The ODMR resonant frequencies at the detected position did not change up to 5.1 GPa, but then abruptly shifted to a higher frequency at 6.7 GPa. Since both B tot and B c could be deduced from the measured ODMR spectra at each pressure, we calculate the magnetic field of the Nd 2 Fe 14 B sample as |B tot − B c | and plot it in Fig. 3d. The magnetic field of the sample during the compression (blue squares) and decompression (red dots) processes are shown in Fig. 3d. The sample magnetic field, as seen with the ODMR frequencies, remained unchanged as the pressure increased to approximately 6 GPa, but then had a sharp reduction at around 7 GPa. This phenomenon demonstrates that the Nd 2 Fe 14 B sample reversibly changed from a ferromagnetic phase to a paramagnetic phase at ~7 GPa, in good agreement with the literature 13,40 . Extreme conditions have recently been applied to synthesize and study novel superconducting materials, with critical temperatures well above 200 K reported (refs. [6][7][8]. As a proof-of-concept experiment, we detected the superconducting phase transition of the well-known superconductor YBa 2 Cu 3 O x (refs. 41,42 ) at different pressures and low temperatures using our SiC anvils with V Si defects. YBa 2 Cu 3 O x is a type-II high-T c superconductor with different concentrations of oxygen (x). YBa 2 Cu 3 O 6.6 was chosen due to its high T c and dramatic T c -pressure curve 41 . The YBa 2 Cu 3 O 6.6 sample was synthesized in-house by conventional heat treatment methods (see Supplementary Text 2 for more details). The confocal scanning microscopy image of V Si defects and the YBa 2 Cu 3 O 6.6 sample on the culet is shown in Fig. 4a. To measure the superconductor magnetic moment, we first cooled the superconductor below its T c in a zero magnetic field, and then a small c-axis magnetic field (7.7 G) was applied to generate a Zeeman splitting of the V Si defects [43][44][45] . The ODMR measurements were performed as the temperature increased. The raw ODMR spectra versus temperature at one pressure point (9 GPa) are shown in Fig. 4b. At 9 GPa, the splitting underwent a sudden step-like change at 95 K (Fig. 4c). This is the manifestation of the Meissner effect and the indication that the sample entered the diamagnetic state associated with the superconductivity of the sample. The red line represents the fitting of the data points using a sigmoid function: , where a, b and δT c are fitting parameters 43,45 . The fitted T c at 9 GPa yielded 95.2 ± 0.2 K, which is in excellent agreement with the previous results 41 .
We also investigated T c at different pressures. Figure 4d shows the measured ODMR splitting as a function of temperature at different pressures. The T c increased with pressure, changing slope at around 12 GPa, but continuing to increase (see Fig. 4e). Our mapping of the T c -pressure phase diagram is in excellent agreement with the previous data obtained by a.c. susceptibility methods in the DAC 41 . The pressure dependence of T c is because high pressure leads to a change in the charge carrier concentration in the CuO 2 planes within the unit cell 42 .

Outlook
Silicon-defect-based in situ magnetic detection technologies could provide several immediate research opportunities in materials science. First, by using a higher NA objective, better detectors 11 and optimized samples, both the sensitivity and spatial resolution can be improved several times. The ideal spatial resolution could reach approximately 1 µm. As the size of the vortex/domains is approximately micrometre scale, the technique could be used to detect the magnetic vortices/domains walls of ferromagnetic materials 11,46,47 , magnetic two-dimensional materials 48,49 and geochemistry at high pressure. Second, we could apply the magnetic sensor to investigate the T cpressure phase diagram, lower critical magnetic field and London penetration depth of new types of superconductor, such as kagome superconductors at high pressures 44,50 . Micrometre-sized particles of 4H-SiC with V Si defects 51 and other types of spin qubits, including divacancies 20,21,52 , NV centres [27][28][29] and even transition metal ions 53 in 4H, 6H and 3C polytypes of SiC, could also be applied to local magnetic detection at high pressure. Some types of novel spin readout technologies, such as photocurrent-detected magnetic resonance 37,54 and anti-Stokes excited ODMR technology 32 could also be used for V Si defect-based magnetic sensing under high pressure. These experiments form a framework for using SiC V Si defects for local, in situ magnetic detection under high pressure.
In conclusion, we realized in situ magnetic detection of magnetic materials using an implanted V Si defect ensemble in SiC-based anvil cells under high pressure. By studying the optical and spin properties of the implanted V Si defects, we showed that the photoluminescence spectrum has a blueshift and that the mean counts decrease under high pressure. At the same time, D increases with pressure with a small coefficient of 0.31 MHz GPa −1 , which is much less than that of the NV centres in diamond. Moreover, the spin coherence time does not vary with pressure, which is vital for probing the noise spectroscopy of magnetic materials at high pressure without a direct magnetic signal. Using these results, the pressure-induced magnetic phase transitions of the magnet Nd 2 Fe 14 B sample were detected in the range of 6-10 GPa using ODMR methods at room temperature. Finally, we mapped the T c -pressure phase diagram of superconductor YBa 2 Cu 3 O 6.6 by ODMR technology at low temperatures.

Online content
Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41563-023-01477-5.

SiC anvil preparation and silicon vacancy generation
In the experiments, two high-quality single-crystal 4H-SiC cubes were used to fabricate SiC anvils with 200-µm-diameter culets. As shown in Fig. 1a, high-density shallow V Si defects in a 100-nm-deep layer were used for magnetic detection 55 . A non-magnetic rhenium gasket was used to confine the sample between the two anvils 11 . NaCl was used as the pressure-transmitting medium in all experiments. The in situ pressure was monitored by measuring the photoluminescence spectrum of the ruby (approximately 10 µm) in the chamber. A 10 µm platinum wire was placed across the culet surface and used to transmit radiofrequency signals to control V Si defect spin states. The culet diameter was 200 µm, and the crystalline orientation was the 0001 (c axis). Helium ions (He + ) with 20 keV energies at a density of 1 × 10 13 cm −2 were perpendicularly implanted into the culets to generate high-density shallow V Si defects, and the corresponding depths were approximately 100 nm 55 . We then annealed the SiC anvil at 500 °C for 2 h to increase the V Si defect density by approximately three times 55 . The surface V Si density of the defects was estimated to be approximately 7,500 µm −2 (see Supplementary Text 1 for more details).

Experimental set-up
Our set-up consisted of a custom-built confocal scanning microscope equipped with a radiofrequency system 32,55 . Two lasers with wavelengths of 532 nm and 720 nm were used to excite the ruby and V Si defects, respectively. Two 650 nm and 850 nm longpass filters were used to collect the ruby and V Si defect fluorescence. We adopted a long-working-distance (20 mm) infrared objective (0.4 numerical aperture, Mitutoyo) to excite the samples and collect the fluorescence. A single-photon counting module (SPCM-AQRH-14-FC) was applied to detect the fluorescence of V Si defects to determine the average photon counts. A liquid nitrogen temperature range optical cryostat (Oxford Instruments) combined with a confocal system was used for the low-temperature experiments 56 . Standard lock-in technology was used to measure the ODMR and coherence control signals using a photoreceiver (Femto, OE-200-Si) 20,32 . A B c field was applied to adjust the energy levels of the spin states. To eliminate heating by the laser and radiofrequency in the measurements, we used a small laser power (8 mW) and radiofrequency power (25 dBm for RdFeB experiments and 15 dBm for YBCO experiments).

Data availability
The data that support the findings of this study are presented in the article and the Supplementary Information, and are available from the corresponding authors upon reasonable request. Source data are provided with this paper.