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

Pressure-induced magnetic phase transition is attracting interest due to its ability to detect superconducting behaviour at high pressures in diamond anvil cells. However, detection of the local sample magnetic properties is a great challenge due to the small sample chamber volume. Recently, optically detected magnetic resonance (ODMR) of nitrogen vacancy (NV) centers in diamond have been used for in-situ pressure-induced phase transition detection. However, owing to their four orientation axes and temperature-dependent zero-field-splitting, interpreting the observed ODMR spectra of NV centers remain challenging. Here, we study the optical and spin properties of implanted silicon vacancy defects in 4H-SiC, which is 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.

High-pressure techniques have been applied in many fields, including physics, material sciences, geophysics and chemistry, leading to many unusual and important phenomena that have been observed under pressure [1][2][3][4][5][6][7][8] .In particular, the claims of pressure-induced high critical temperature (Tc) superconductivity have drawn serious attention and excitement in recent years [6][7][8] .For example, lanthanum hydride has been inferred to be a superconductor with a critical temperature of ~250 K at around 170 GPa 7,8 .One of the great challenges of high-pressure research is the measurement of magnetic properties and their evolution.However, conventional methods such as using superconducting quantum interference devices (SQUIDs) or AC susceptibility cannot directly detect weak magnetic signals of micrometre-sized samples in diamond anvil cell (DAC) [9][10][11][12][13][14] .Therefore, it is important to explore new methods for magnetic detection.
The high sensitivity and high resolution of in-situ magnetic detections in DAC chamber were achieved by utilizing nitrogen-vacancy (NV) centres [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, temperature, strain, spins, pressure and electrical currents [9][10][11][12][13][14][15][16][17][18][19] .The zero-field-splitting (ZFS) parameter D of the NV centre ground spin state was shown to increase linearly with pressure with a slope of 14.6 MHz/GPa up to 60 GPa 9 .On this basis, an in-situ magnetic detection method based on NV centres through optically detected magnetic resonance (ODMR) technologies has recently been developed at high pressure [10][11][12][13] .
Micron-sized diamond particles with ensemble NV centres have been placed inside the DAC chamber to measure the Tc-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 construct the full stress tensor on the culet surface 11,12 .
Defects in silicon carbide (SiC) could also be utilized to measure magnetic properties under extreme conditions.SiC is a widely used semiconductor due to its unique properties, such as mature inch-scale growth and micro/nanofabrication [20][21][22] .Also, several spin qubits and bright single-photon emitters in SiC have attracted great attention in the quantum community [20][21][22][23][24][25][26][27][28][29][30][31][32] .In particular, the silicon vacancy defect at the hexagonal lattice site with a negative charge (VSi) has been extensively used in spin-photon interfaces 23 , quantum photonics 26 , quantum information processing 22 , and quantum sensing, such as magnetic fields 30 and temperatures 31,32 due to its outstanding properties.Its spin state is an S = 3/2 spin quartet, and the ground state ZFS parameter D is ~70 MHz 22,23 .It only has one axis (along the c-axis of the 4H-SiC), and the corresponding ODMR spectrum has two resonant peaks under an external magnetic field, which is convenient to readout the resonant frequencies and enhancing the scalability in SiC devices 22 .Moreover, the ZFS parameter D is also almost temperature independent from 20 K to 500 K at ambient pressure, which is beneficial to temperature-pressure research 31,32 .However, most of the previous investigations on the VSi 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 under high pressure is important for VSi defect-based quantum sensing at extreme conditions.In comparison with traditional high-pressure magnetometry techniques, the spatial resolution of VSi defect detection is only around a few microns.
Here, we investigate and characterize the optical and spin properties of the implanted silicon vacancy defects at the culets of the 4H-SiC anvil, which exhibit single-axis and temperature-independent zero-field splitting.The experimental results show that the photoluminescence (PL) spectrum blueshifts and the ZFS parameter D increases with pressure at a rate of 0.31 MHz/GPa.We probed the pressure-induced magnetic phase transition of a Nd2Fe14B magnet at around 7 GPa at room temperature.
Finally, the Meissner effect of a YBa2Cu3O6.6superconductor at different pressures was observed, yielding its Tc-P phase diagram.These experiments demonstrate the feasibility of using VSi defects in SiC as novel quantum sensors and open up applications to study superconducting phenomena under extreme conditions.

Optical properties of silicon vacancies under high pressure
The experimental configuration used in our experiments is shown in Fig 1a (For the experimental details, see the Method section and Supplementary text 1).First, we describe the optical and spin properties of the VSi defects at high pressures.The energy levels of the defects at high pressures are shown in Fig. 1b.The 720 nm laser pumps the electrons from the ground state to the phonon sideband, and the ZPL at ambient pressure is 916 nm.Both the ZPL and the ground spin state ZFS parameter D change under high pressure.The room temperature PL spectra of the defects at three different compressions are shown in Fig. 1c.The PL spectra of the VSi defects are blue-shifted with pressure.We then investigate the mean counts of the VSi defects as a function of compression.The counts increase as the pressure increases from ambient pressure to 8 GPa caused by the higher detection efficiency at shorter wavelengths of the single-photon counting module (see Fig. 1d).Then, the counts decrease as the pressure increases to approximately 25 GPa (see Supplementary text 1 for more details).At the same time, we observe the decrease in the ODMR contrast with increasing pressure (see 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 of the photon counts and ODMR contrast 9,[33][34][35] .

Spin properties of silicon vacancies under high pressure
We then study the VSi defect spin properties at high pressures.The ODMR spectra at zero external magnetic field are shown in Fig. 2a.The initial zero-pressure ODMR peak of 72.4  0.4 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 increases, in line with the ODMR signal of NV centres in diamond [9][10][11][12][13][14][33][34][35] . The loal structural distortions and the decreasing distance between VSi spin in the macroscopic compression in the SiC crystal drive the resonant frequency shifts to higher values as the pressure increases 9,[33][34][35] .As shown in Fig. 2b, the mean ZFS parameter D increases linearly with the pressure with a coefficient of 0.31  0.01 MHz/GPa, which is considerably smaller than 14.6 MHz/GPa of the 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 due to the degeneracy of half-integer VSi defects (S=3/2), which makes it rather insensitive to strain fluctuations 39 .
Through the coherent control of VSi defects, one could detect the noise spectroscopy of the magnetic materials 12 .Fig. 2c shows the measurement of the Rabi oscillation at ambient pressure using a standard pulse sequence 20,32 .Inferred from the fitting, the Rabi frequency is 9 MHz.Figures 2d and 2e present the spin echo measurement of VSi defects at ambient pressure and at 15.1 GPa, yielding the coherence times T2 of 7.8  0.9 µs and 7.3  0.7 µs, respectively.Both values are consistent with previous results 32 .The coherence time T2 as a function of pressure up to 25 GPa is summarized in Fig. 2f.The coherence time remains invariable up to 25 GPa, which is similar to that of NV centres in diamond 13 .

Magnetic detection using silicon vacancies under high pressures
The SiC anvils with VSi defects could be used to study magnetic and superconducting properties of materials under compression.By utilising the ODMR spectrum, we have studied the pressure-induced magnetic phase transitions of a common magnet Nd2Fe14B.A small piece of Nd2Fe14B sample is placed on the surface of the culets.The PL images of the implanted shallow VSi defects and Nd2Fe14B 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 (black dashed line region) is chosen as the detection position, which is denoted with a black cross.As a comparison, a remote location (denoted with a red cross) is the reference position.In the experiment, we apply a c-axis (perpendicular to the culet) magnetic field Bc with a strength of 198 Gauss.Three schematics of local magnetic field vectors at the detected position under different pressures are shown in Fig. 3b.Bc, BNdFeB and Btot represent the c-axis external magnetic field, magnetic field of the Nd2Fe14B sample and total magnetic field on the VSi defects, respectively.Standard lock-in technology is used to detect the ODMR signals 20,32 .The integration time for one frequency is around 5 seconds, and the total measurement time is ~580 seconds.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 the external magnetic field (Bc) are also measured at each pressure.The ODMR resonant frequencies at the detected position do not change up to 5.1 GPa, but then they abruptly shift to a higher frequency at 6.7 GPa.Since both Btot and Bc could be deduced from the measured ODMR spectra at each pressure, we calculate the magnetic field of the Nd2Fe14B sample as |Btot-Bc| 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, stays unchanged as the pressure increases to approximately 6 GPa, but then it has a sharp reduction at around 7 GPa.This phenomenon demonstrates that the Nd2Fe14B sample reversibly changes from a ferromagnetic phase to a paramagnetic phase at ~7 GPa, in good agreement with the literature 13,40 .
Recently, extreme conditions have been applied to synthesize and study novel superconducting materials claiming the critical temperatures well above 200 K [6][7][8] .As a proof-of-concept experiment, we detected the superconducting phase transition of the well-known superconductor YBa2Cu3Ox 41,42 at different pressures and low temperatures using our SiC anvils with VSi defects.YBa2Cu3Ox is a type II high-Tc superconductor with different concentrations of oxygen x.YBa2Cu3O6.6 was chosen due to its high Tc and dramatic Tc-pressure curve 41 .YBa2Cu3O6.6 sample was synthesized in-house by conventional heat treatment methods (see Supplementary text 2 for more details).The confocal scanning image of VSi defects and the YBa2Cu3O6.6sample on the culet is marked in Fig. 4a: the sample (black dashed line region) and the detected position (black cross).To measure the superconductor magnetic moment, we first cool the superconductor below its Tc in a zero magnetic field, and then a small c-axis magnetic field (7.7 Gauss) is applied to generate a Zeeman splitting of the VSi defects [43][44][45] .The ODMR measurements are performed as the temperature increases.The raw ODMR spectra versus temperature at one pressure point (9 GPa)   are shown in Fig. 4b.At 9 GPa, the splitting goes through 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:

S(T)=a+b/(1+exp[-(T-Tc)/δTc])
, where a, b, δTc are fitting parameters, and Tc is the critical temperature 43,45 .The fitted critical temperature Tc at 9 GPa yields 95.2  0.2 K, which is in excellent agreement with the previous results 41 .
We further investigate the critical Tc at different pressures.Fig. 4d shows the measured ODMR splitting as a function of temperature at different pressures.The critical temperature Tc linearly increases with pressure, changing slope at around 12 GPa but continuing to increase (see Fig. 4e).The shadowed and transparent areas represent the superconducting and normal states for YBa2Cu3O6.6,respectively.Our mapping of the Tc phase diagram is in excellent agreement with the previous data obtained by the AC susceptibility methods in the DAC 41 .The pressure dependence of Tc is because high pressure leading to a change in the charge carrier concentration in the CuO2 planes within the unit cell 42 .

Outlook
The VSi-based in-situ magnetic detection technologies could open up several immediate research possibilities in materials science.First, using the 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 extend to approximately 1 μm.Since the size of the vortex/domains is approximately micrometre scale, it can be used to detect the magnetic vortices/domains walls of ferromagnetic materials 11,46,47 , magnetic 2D-materials 48,49 and geochemistry at high pressure.Second, we could apply the magnetic sensor to investigate the Tc-P phase diagram, lower critical magnetic field and London penetration depth of new types of superconductors, such as kagome superconductors at high pressures 44,50 .The 4H-SiC micrometre particles with VSi 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, may 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 can also be used for VSi defect-based magnetic sensing under high pressure.The experiments form a framework for using SiC VSi defects in local in-situ magnetic detection under high pressure.
In conclusion, we realize in-situ magnetic detection of magnetic materials using an implanted VSi defect ensemble in SiC-based anvil cells under high pressures.By studying the optical and spin properties of the implanted VSi defects, the experiments show that the PL spectrum has a blueshift and the mean counts decrease under high pressure.At the same time, the ZFS parameter D increases with pressure with a small coefficient of 0.31 MHz/GPa, which is much less than that of the NV centres in diamond.Moreover, the spin coherence time remains invariable with pressure, which is vital to probe noise spectroscopy of magnetic materials at high pressure without a direct magnetic signal.Based on these results, the pressure-induced magnetic phase transitions of the magnet Nd2Fe14B sample are detected in the range of 6-10 GPa using the ODMR methods at room temperature.Finally, we map the superconductor YBa2Cu3O6.6Tc-pressure phase diagram by ODMR technology at low temperatures.Tc-pressure phase diagram.The Tc under ambient pressure (blue dot) is measured through a magnetic property measurement system (see Supplementary text 2 for more details).The Tc under pressure (red dots) is inferred from the ODMR splittings.The shadow area represents the superconducting state, and the transparent area is the normal state for YBa2Cu3O6.6.The error bars obtained from the fitting standard deviations are smaller than the symbol sizes.

Fig. 1
Fig. 1 The SiC anvil and VSi defect optical properties with pressure.a, Schematic of a SiC anvil.The samples are placed on the surface of the culet, and local shallow (100 nm) VSi defects are used for in-situ magnetic detection.A 10 µm ruby is placed close to the samples to measure the pressure.The c-axis is perpendicular to the culets of the SiC anvil.b, Energy levels of VSi defects at high pressure.The red line indicates the 720 nm excitation laser.The pressure changes the ZPL emission and shifts the ground state ZFS parameter D with Δ. c, Room temperature PL spectra of the VSi defects at three representative pressures.d, The mean counts of VSi defects with 10 mW laser excitation as a function of the pressure.Error bars are due to the standard deviations of mean counts in an 8×8 µm 2 area.

Fig. 2
Fig. 2 The spin properties of VSi defects at high pressures.a, The ODMR spectra at three different pressures with zero external magnetic field.The solid lines represent Lorentzian fittings.b, The mean ZFS parameter D linearly increases with pressure up to 27 GPa.Error bars represent the standard deviations of the mean of the measured D. c, Rabi oscillation at 31 Gauss at ambient pressure.The red line is fitted using an exponentially decaying sine function.d, and e, The spin echo results at ambient pressure and 15.1 GPa, respectively.Red lines represent the exponential decay fittings to the data.f, The coherence time T2 as a function of the pressure.Error bars are the data fitting standard deviations of the mean T2.

Fig. 3
Fig. 3 The detection of the pressure-induced magnetic phase transition of a Nd2Fe14B magnet using shallow VSi defects.a, The confocal scanning image of the VSi defects and Nd2Fe14B sample on the culet surface.The black and red crosses are the detected and reference positions, respectively.The black dashed line region indicates the Nd2Fe14B sample.The scale bar is 20 μm.b, Three typical local magnetic field vectors during the pressure-induced magnetic phase transition in the compression and decompression processes.The external magnetic field Bc is along the c-axis of the 4H-SiC.The magnetic field of the Nd2Fe14B sample and the total magnetic field are labelled BNdFeB and Btot, respectively.c, The shallow VSi defect ODMR spectra in the detected and reference positions in the culet surface during the compression process.d, The inferred magnetic fields of the Nd2Fe14B sample were measured by VSi defects during the compression (blue squares) and decompression (red circles) processes.

Fig. 4
Fig. 4 Measurement of the temperature-pressure phase diagram of the superconductor YBa2Cu3O6.6 using implanted VSi defects.a, The confocal scanning image of the YBa2Cu3O6.6sample and VSi defects in the culet surface.The black dashed line region marks the investigated YBa2Cu3O6.6sample, and the black cross marks the corresponding detected position.The size scale bar is 20 μm.b, The ODMR spectra with superconductivity diamagnetism in the detected position at different temperatures at 9.0 GPa.The dashed lines are guides to an eye only.c, The inferred ODMR splitting during the sample superconducting phase transition at 9.0 GPa.The red line is the fitting of the data.The superconducting transition temperature Tc is deduced to be 95.2 ± 0.2 K. d, The inferred ODMR splittings as a function of temperature under different pressures.The labelled coefficients are the ODMR splitting magnification times to normalize the data.The error bars in c and d are the standard deviation of the mean fitted ODMR splittings.e, The YBa2Cu3O6.6