Magnetic measurements on micrometer-sized samples under high pressure using designed NV centers

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Science  13 Dec 2019:
Vol. 366, Issue 6471, pp. 1359-1362
DOI: 10.1126/science.aaw4329

Diamond-based sensors

Material properties can change dramatically under pressure. Typically, to achieve high-pressure conditions, researchers place their samples in diamond anvil cells (DACs). However, monitoring the properties of the sample inside a DAC is tricky (see the Perspective by Hamlin and Zhou). Hsieh et al., Lesik et al., and Yip et al. developed monitoring techniques based on nitrogen-vacancy (NV) centers in diamond. The NV centers can act as sensors because their energy levels and the associated spectra are sensitive to strain and magnetic fields. This enabled optical readout of a spatially resolved signal.

Science, this issue p. 1349, p. 1359, p. 1355; see also p. 1312


Pressure can be used to tune the interplay among structural, electronic, and magnetic interactions in materials. High pressures are usually applied in the diamond anvil cell, making it difficult to study the magnetic properties of a micrometer-sized sample. We report a method for spatially resolved optical magnetometry based on imaging a layer of nitrogen-vacancy (NV) centers created at the surface of a diamond anvil. We illustrate the method using two sets of measurements realized at room temperature and low temperature, respectively: the pressure evolution of the magnetization of an iron bead up to 30 gigapascals showing the iron ferromagnetic collapse and the detection of the superconducting transition of magnesium dibromide at 7 gigapascals.

Compression of a solid directly changes its electron density, inducing a variety of magnetic phenomena such as magnetic quantum criticality and high-spin to low-spin transitions (1). In addition, pressure can be used to tune superconductivity in a wide range of systems, such as cuprates, transition-metal dichalcogenides, iron pnictides, heavy fermions, and topological superconductors. Recently, a new class of high-temperature superconductors has been discovered in H-rich hydrides at high pressure, with the reported critical temperature of 203 K in H3S (2) and 250 K in LaH10 at pressures >150 GPa (3, 4). Systematic exploration of these materials requires sensitive magnetic characterization that can be routinely operated in the 100-GPa range (5).

Great efforts have already been made to adapt magnetic detection methods to diamond anvil cell (DAC) specificities (6). The macroscopic magnetic susceptibility of the compressed sample can be measured using inductively coupled coils. However, the maximum size of the sample that can be integrated in the DAC decreases with increasing pressure. Two strategies have been pursued to circumvent this poor scalability that is detrimental to detection sensitivity. One is to insert the detection coil inside the sample chamber (7) and the other is to miniaturize the whole DAC to integrate it in a superconducting quantum interference device (SQUID) to benefit from the intrinsic high sensitivity of SQUID measurements (8). Synchrotron-based methods, such as x-ray magnetic circular dichroism, x-ray emission spectroscopy (XES), and nuclear resonant forward scattering, are also widely used, having been made possible by the development of focused and high-brightness synchrotron x-ray beams. By addressing atomic or nuclear resonance lines, these methods are element specific and resolve local magnetism stemming from a given electronic order (9). However, no theoretical framework has been unanimously agreed upon for the interpretation of the signals obtained with these techniques (10, 11) and therefore their quantitative analysis remains challenging. Furthermore, synchrotron-based techniques, which mainly probe nuclear or electronic transitions, are not directly sensitive to magnetic phenomena such as the Meissner effect, which is an unambiguous signature of superconductivity.

We report an optical magnetometry method based on nitrogen-vacancy (NV) color centers used as in situ quantum sensors (Fig. 1A). The main advantages of this method are the easy sample preparation, the tabletop instrumentation, the mapping of the stray magnetic field with micrometer spatial resolution, and the absence of any sensitivity decrease with the sample size down to the micrometer scale. Being noninvasive, the method can be easily combined with complementary structural determination by x-ray diffraction. The method is based on optically detected magnetic resonance (ODMR), which exploits the triplet fine structure of the negatively charged NV center ground state (Fig. 1B). ODMR relies on the dependence of the luminescence intensity of the NV center whether it is excited from mS = 0 (high-intensity) or mS = ±1 (low-intensity) spin states (12). This property is used to perform a spectroscopy of the mS = 0 → ±1 transition excited by a microwave (MW) signal, the frequency of which is scanned across the resonance. Under a continuous MW excitation in the absence of external perturbation, the spin-dependent luminescence recorded as a function of the MW frequency exhibits a resonance peak at 2.87 GHz (Fig. 1C). An external magnetic field applied on the NV center then splits this resonance, leading to the direct measurement of the magnetic field amplitude from the ODMR spectrum (13). The influence of strain on this electron spin transition was investigated up to a pressure of ~60 GPa in Doherty et al. (14), who envisioned magnetic detection in a DAC as the main goal. Here, we fabricated the NV centers in the diamond anvil and developed a technique that enables magnetometry based on them. We illustrate the efficiency of this technique using two examples: a quantitative measurement of the magnetization of iron up to 30 GPa under ambient temperature around the α–ε phase transition (15) and the diamagnetic response associated with superconductivity in MgB2 at 7 GPa and 30 K (16).

Fig. 1 Implementation of NV magnetometry in a DAC.

(A) Scheme of the DAC setup. A 250-μm-wide disk of NV centers was implanted in the 300-μm-wide culet of one of the two anvils shown in blue. A rhenium gasket (in gray) enclosed the sample and a ruby pressure gauge. A single-loop wire was placed on the gasket to generate the microwave excitation. A green laser with 532-nm wavelength was used to excite the red luminescence of the NV centers. The electron spin resonance was detected through its effect on the luminescence by imaging the layer of NV centers on a camera. (B) Electronic structure of the NV center ground state with the modification of the energy levels induced by the strain in the anvil and the magnetic field. Hydrostatic compression shifts the resonance by δ, whereas nonhydrostatic strain splits the resonance into two components with a frequency splitting of 2Δstr. The additional influence of the applied magnetic field leads to a total frequency splitting of 2Δ. (C) Typical resonance spectra recorded with an ensemble of NV centers. In the absence of any perturbation, the spectrum consists of a single resonance at D = 2.87 GHz. The combination of the strain with the projections of the magnetic field on the four NV orientations in the crystal leads to eight resonance peaks.

We used a focused ion beam extracted from a nitrogen plasma to create the NV centers at the culet of an ultrapure synthetic (IIas) diamond anvil (17), with a layer of ~104 defects/μm2 at a depth of 20 nm below the surface of the anvil culet (18). As shown in Fig. 1A, the optical excitation of these shallow NV centers using a laser of 532 nm wavelength and the detection of their luminescence are performed through the anvil. We then implemented the wide-field ODMR scheme of Steinert et al. (19) to record on a camera the image of the spin-state-dependent luminescence emitted by the NV layer as a function of microwave frequency [see the supplementary materials (18) for additional information]. The implanted diamond anvil was mounted on a membrane DAC and a rhenium gasket laterally confined the sample. An external single-turn coil was positioned on the gasket as a MW antenna for the ODMR (Fig. 1A). As demonstrated in Steele et al. (20), the microwave excitation coil could be embedded in the anvil by metal deposition on the culet covered with a layer of diamond grown using plasma vapor deposition. A ruby crystal was used as a pressure gauge. Microscopic samples of iron or MgB2 were positioned in the sample chamber directly in contact with the implanted anvil (Fig. 2) and embedded in a pressure-transmitting medium consisting of nitrogen or argon, respectively.

Fig. 2 Frequency splittings associated with the magnetization of an iron bead.

The center image shows the iron samples inside the gasket. The four color plots show the maps of frequency splittings at 24 GPa for the four NV orientations across the region surrounding an iron bead (red square in the center image). For each NV orientation, the N atom is shown in blue, the vacancy V is shown in white, and the carbon atoms of the lattice are shown in black. The splittings combine the effect of nonhydrostatic strain in the anvil, the applied magnetic field, and the stray magnetic field created by the bead magnetization. α, β, and γ are reference axes linked to the anvil used to identify the four NV orientations. The dotted lines indicate the orientation of the anvil surface.

In the case of iron, various samples were loaded to test geometric and size effects. The detailed analysis focuses on one of the iron beads [see fig. S14 in the supplementary materials (18) for the signals associated with the other samples]. A magnetic field of B0 ≈ 11 mT, created by a permanent magnet, was applied to magnetize the iron samples and to split and resolve the resonances associated with the four orientations of the NV centers existing in a 100-oriented diamond (21).

The energy levels of a given NV center are modified by the magnetic field and by the strain field existing in the anvil. The combination of these two perturbations results in both a shift and a splitting of the MW resonance frequency (22). As illustrated in Fig. 1B, the hydrostatic component of the strain shifts the resonance frequency, whereas its nonhydrostatic component and the magnetic field both split the resonance around its center frequency. Extracting the magnetic field created by the iron bead magnetization from these resonances recorded at high pressure requires taking into account the competing effects of the magnetic field and the strain field, which add quadratically (23). A typical spectrum obtained in the experiment is shown in Fig. 1C. To first order, the effect of the magnetic field is proportional to its longitudinal component along the N-V axis; this leads to a spectrum consisting of four double resonances linked to the four NV orientations. A map of the measured raw frequency splittings in an area surrounding an iron bead (red square in the sample image in Fig. 2) is shown for each family of NV centers at the pressure of 24 GPa (color plots in Fig. 2). The splitting induced by the iron bead magnetization is on the order of a few megahertz, which can be resolved over the splitting induced by B0. Even before any data analysis, such images can be recorded live during the experiment, providing direct evidence of pressure-induced modifications of the magnetic properties. This optical mapping has a resolution of ~1 μm, allowing us to reveal inhomogeneities in the sample magnetization or anisotropies in the strain distribution.

After ascribing each pair of resonances to a given 111 axis of the diamond anvil, the stray magnetic field created by the iron bead can be quantitatively extracted from the correlated information that is embedded in the spectrum shown in Fig. 1C (24). First, the strain component was extracted from the ODMR signal using a reference area of the image selected to be far from the bead where the stray magnetic field is negligible. Right below the bead, the NV centers experience a strong transverse magnetic field, which mixes the mS = ±1 states and induces a strong decrease of the ODMR contrast (25). This quenching leads to a background signal without a direct link to the iron bead magnetization. Additionally, the microwave excitation is screened by the eddy currents induced in the iron sphere; this effect also contributes to the decrease of the ODMR contrast. As shown in Fig. 3B, the area below the center of the bead was excluded by applying a mask to the data according to a threshold set on the contrast [see the supplementary materials (18) for the data processing]. At high pressures, the bead magnetization decreases and the masked area decreases accordingly.

Fig. 3 Observation of the α–ε transition of iron.

(A) Evolution of the bead magnetization inferred at each pressure. The data obtained during the pressure increase are shown by blue dots and those obtained during the pressure release are shown by red dots. The shaded area shows the uncertainty interval on the magnetization value during the pressure increase. The dotted lines are guides for the eye. bcc, body-centered cubic α-phase; hcp, hexagonal close-packed ε-phase. (B) Evolution with pressure of the amplitude of the magnetic field created by the iron bead. The mask shown in black is associated with the criteria set on the ODMR contrast.

The magnetization M of the iron bead was then determined by fitting the relevant part of the magnetic field map with a simple magnetic dipole model (18). At low pressure, we obtained M ≈ 8 ± 1 kA•m–1. The evolution of the magnetization with pressure is shown in Fig. 3A. The magnetic field of the iron bead decreases as the pressure increases from 15 GPa up to ~30 GPa (Fig. 3B), above which no value of the magnetization can be inferred. This result demonstrates the sensitivity of the detection scheme and is consistent with previous XES (26, 27) and SQUID measurements (28) that reported magnetic signals well above the α–ε transition threshold. Whether a remnant of the α phase is responsible for this magnetic signature up to 30 GPa could be investigated by implementing NV-based magnetometry on an x-ray diffraction beamline, combining structural characterization and a direct measurement of the magnetization on the same sample at each pressure. Finally, upon the release of pressure in the DAC, we observed the reappearance of the sample magnetization (Fig. 3A) with the expected hysteresis behavior related to the hysteresis of the structural transition (15).

This technique can be straightforwardly implemented at low temperature to observe the diamagnetic response associated with superconductivity. As a proof-of-principle experiment using a testbed compound, we chose a sample of MgB2 that was confined in the DAC at 7 GPa and first cooled in a cryostat in the absence of external magnetic field. At a temperature of ~18 K, an external magnetic field ≈1.8 mT was applied. The direction of this applied magnetic field was chosen parallel to the 100-diamond axis so that the four NV orientations in the crystal had identical responses. As shown in Fig. 4A, the comparison between the frequency shift in the ODMR spectra of the NV centers located above the sample and the homogeneous background gives a direct image of the exclusion of the magnetic field above the MgB2 sample. This shielding is induced by the superconductor diamagnetic response to the applied magnetic field. Under heating of the DAC, the exclusion of the magnetic field disappeared >30 K (Fig. 4B). This behavior agrees with the reported pressure evolution of the critical temperature of MgB2 superconductivity (16).

Fig. 4 Exclusion of the magnetic field by the superconducting state of MgB2.

(A) Maps of the ODMR frequency splitting above the MgB2 sample recorded for an increasing temperature. A control magnetic field B0 ≈ 1.8 mT is applied and induces a background ODMR splitting. The total ODMR splitting combines the influence of B0 with the strain in the anvil. Below 30 K, the exclusion of the magnetic field is observed above the MgB2 sample owing to the diamagnetic response associated with superconductivity. This effect disappears above 30 K, leading to a homogeneous distribution of the ODMR splitting. Inset: Optical image of the sample. The red square indicates where the ODMR splitting is mapped. (B) Evolution of ODMR splitting above the sample when the temperature is increased. The data points are averaged on the black squares of (A). The dotted line is a guide for the eye.

It would be worthwhile to investigate how this direct optical detection of superconductivity can be implemented at a pressure range >100 GPa. This may require adapting the excitation and readout wavelengths of the NV center to compensate for the pressure-induced energy shifts of the electronic levels (14). NV engineering based on controlled nitrogen doping during the plasma-assisted growth of a diamond layer (29) or using laser writing (30) can bury a thin sheet of NV centers at a depth where the influence of strain in the anvil could be less detrimental. We anticipate a major research direction to be the investigation of high-temperature superconductivity in the various superhydride compounds that can be directly synthesized at high pressure, such as H3S (2), LaH10 (3, 4), UH7 (31), and FeH5 (32). The technique could also enable the observation of the predicted magnetic properties of metallic hydrogen (3336), for which various challenging experimental probes have already been proposed (37, 38).

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S16

References (4042)

References and Notes

  1. See the supplementary materials for additional information.
Acknowledgments: We thank V. Jacques, K. De Hantsetters, N. Vast, and F. Bouquet for fruitful discussions. Funding: This project received funding from the European Union’s research and innovation program (H2020-FETFLAG-2018-2020) under grant agreement no. 820394 (ASTERIQS), the Agence Nationale de la Recherche (projects Envie-FIB and ASPEN), the Investissements d’Avenir program through the LabEx PALM (ANR-10-LABX-0039-PALM), the Paris-Saclay Strategic Research Initiative for Quantum Engineering (IQUPS), and the Paris Île-de-France Région in the framework of DIM SIRTEQ. Author contributions: J.F.R., T.P., and P.L. designed and supervised the project; M.L., T.P., L.T., and J.F.R. performed the ODMR experiments; T.P., F.O., and P.L. assembled the high-pressure cells; L.T., T.D., L.R., T.P., and J.F.R. developed the wide-field magnetic imaging system and the magnetization measurement; J.R., M.L., O.S., A.D, M.S., and J.F.R. customized the Orsay Physics FIB; M.L., J.R., M.S., and O.S. performed the nitrogen implantation in the diamond anvils; L.T., M.L., T.P., and J.F.R. performed the data analysis. All authors contributed to manuscript preparation. Competing interests: The authors declare no competing interests. Data and materials availability: All data described here are available at Zenodo (39).
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