Abstract
By directly altering microscopic interactions, pressure provides a powerful tuning knob for the exploration of condensed phases and geophysical phenomena1. The megabar regime represents an interesting frontier, in which recent discoveries include high-temperature superconductors, as well as structural and valence phase transitions2,3,4,5,6. However, at such high pressures, many conventional measurement techniques fail. Here we demonstrate the ability to perform local magnetometry inside a diamond anvil cell with sub-micron spatial resolution at megabar pressures. Our approach uses a shallow layer of nitrogen-vacancy colour centres implanted directly within the anvil7,8,9; crucially, we choose a crystal cut compatible with the intrinsic symmetries of the nitrogen-vacancy centre to enable functionality at megabar pressures. We apply our technique to characterize a recently discovered hydride superconductor, CeH9 (ref. 10). By performing simultaneous magnetometry and electrical transport measurements, we observe the dual signatures of superconductivity: diamagnetism characteristic of the Meissner effect and a sharp drop of the resistance to near zero. By locally mapping both the diamagnetic response and flux trapping, we directly image the geometry of superconducting regions, showing marked inhomogeneities at the micron scale. Our work brings quantum sensing to the megabar frontier and enables the closed-loop optimization of superhydride materials synthesis.
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Data availability
The published data of this study are available on the Zenodo public database (https://doi.org/10.5281/zenodo.8219843).
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Acknowledgements
This work was supported as part of the Center for Novel Pathways to Quantum Coherence in Materials, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences under award no. DE-AC02-05CH11231. X.H. acknowledges support from the National Key R&D Program of China (grant no. 2022YFA1405500). C.R.L. acknowledges support from the National Science Foundation (grant no. PHY-1752727). M.B. acknowledges support from the Department of Defense through the National Defense Science and Engineering Graduate Fellowship Program. S.H. and S.M. acknowledge support from the National Science Foundation Graduate Research Fellowship under grant no. DGE-1752814. N.Y.Y. acknowledges support from the David and Lucile Packard Foundation.
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P.B. performed the experiments, simulations and data analysis. W.C. synthesized the sample, performed the experiments and analysed the data. B.H., B.K., M.B., W.W., H.M. and G.G. worked on the theoretical models and simulations of NV contrast under pressure. Z.M.G., V.S., R.J. and X.H. guided the experimental methodologies and sample preparation. S.C., B.I.H., J.E.M., C.R.L. and N.Y.Y. proposed and interpreted the investigations of the sample. Y.L., T.J.S., E.W., Z.W., S.H., S.M., B.C., E.D., Z.M.G. and C.Z. assisted in data collection. C.R.L., T.C., X.H., G.G. and N.Y.Y. supervised the project. P.B., C.R.L. and N.Y.Y. wrote the paper with input from all authors.
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University of California (co-inventors P.B., B.K., S.H., C.Z., J.E.M., R.J. and N.Y.Y.) filed US Patent Application 63/449,508 titled ‘Multimodal imaging apparatus at ultrahigh pressure’.
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Extended data figures and tables
Extended Data Fig. 1 Studies of diamagnetism in sample S1.
(a) Confocal fluorescence image of sample S1 showing the identified CeH9 region (enclosed in dotted yellow line). A comparison of the ODMR spectra measured after zero field cooling to a temperature T = 25 K (below Tc) at two spatial locations: one (b) away from the CeH9 region [purple point in (a)], and the other (c) on top of the CeH9 region [green point in (a)]. For clarity, all spectra are centered by subtracting the ODMR shift. As a function of the external field, Hz, the local field, Bz, extracted from these spectra show the diamagnetic response of CeH9 [maintext Fig. 3(f)]. We measure the temperature dependence of this response [at the green point in (a)]. (d) Applying Hz = 47 G after zero field cooling, we perform ODMR spectroscopy while heating the sample across Tc (field heating). (e) Similar to sample S2 (shown in maintext), we observe a clear transition in the diamagnetic response. Four point resistance is measured separately on warming up the sample with Hz = 0 (after zero field cooling). For sample S1, we are not able to perform simultaneous magnetometry and electrical resistance measurements due to coupling between the Pt wire for microwave delivery and the transport leads. Although, we expect a suppression in Tc measured via electrical resistance on the application of an external field, the separation between the magnetic and resistive transitions is larger than expected from this effect alone. A reduction of the temperature gradient in the sample on disconnecting the microwave lines may be responsible for this difference.
Extended Data Fig. 2 Spatial studies of diamagnetism in S1.
(a) We measure the local suppression in Bz along a line cut shown in the confocal fluorescence scan of sample S1. The slope s = ΔBz/ΔHz for this study is presented in maintext Fig. 3(g). (b) We show plots of the extracted Bz against the applied external field Hz at fifteen spatial points (indexed) along the line cut. Linear fits to the extracted values of Bz show a clear suppression in two regions of the sample (enclosed in dotted yellow line in (a)). (c) Schematic geometry we assumed for estimating the CeH9 sample’s diamagnetic properties. We assume a spherical chunk of CeH9 of radius R with NV centers located at a distance r from the center (directly below the sample). Under the application of an external field Hz along the NV axis, our ODMR measurements yield a suppression factor corresponding to the slope s = dBz/dHz.
Extended Data Fig. 3 Spatial studies of diamagnetism in S2.
We perform spatial studies of the local suppression in Bz in sample S2 along two orthogonal line cuts. Insets in (b) and (d) show fluorescence scans of S2 with the respective line cuts on top of the identified CeH9 region (enclosed in dotted yellow line). (a) The Bz values extracted from ODMR spectra are plotting against the applied external field, Hz, for six spatial points (indexed) along the line cut shown in inset of (b). (b) Similar to sample S1 [maintext Fig. 3(g)], we measure a spatially varying suppression in the local field suggesting the formation of ≈ 10 μm regions of CeH9 via laser heating. (c-d) A repeat of the study for six spatial points along an orthogonal line cut (inset of (d)).
Extended Data Fig. 4 Comparison of ODMR splitting and Bz on field cooling S2 at Hz = 79 G.
Measurements of four point electrical resistance and the ODMR splitting, Δ, at four spatial locations [shown in maintext Fig. 4(b)]: (a,b) two points on top the synthesized CeH9 (blue and orange), (c) one point at the edge of this region (green), and (d) one point away from region (yellow). (a,b) On top of the CeH9 region, we measure a decrease in Δ ≈ (2π) × 15 MHz as we cool below the transition point. (c) In contrast, at the edge of this region, we measure an increase in Δ ≈ (2π) × 15 MHz. (d) Away from the CeH9 region we do not measure an appreciable change in Δ across the transition point (determined via simultaneous electrical resistance measurements). (e,f,g,h) For the Δ values measured at each spatial point, we extract the magnetic field, Bz, based on the 2Π⊥ stress splitting (measured at the same spatial point at Hz = 0 G after zero field cooling to T = 86 K). Systematic disagreement between Bz and Hz for T > Tc may stem from inaccurate determination of 2Π⊥ or change in the value of 2Π⊥ with temperature.
Extended Data Fig. 5 Study of flux trapping in sample S2 (full dataset).
We field cool sample S2 at Hz = 103 G to several temperatures (indicated on the left) and ramp the magnitude and direction of Hz [experimental sequence in maintext Fig. 5(f)]. (a,d,g,j,m) Dark blue data show the ODMR spectra measured on ramping Hz to zero after field cooling at Hz = 103 G to the respective temperatures. Light blue data show the ODMR spectrum measured at Hz = 0 on zero field cooling to T = 81 K. We observe a markedly higher ODMR splitting in the field cooled data set suggesting the presence of a remnant flux trapped field. The strength of the flux trapped field (i.e., Bz values at Hz = 0) decreases with increasing temperature. (b,e,h,k,n) We show the measured ∣Bz∣ on ramping Hz after field cooling to different temperatures; first, we ramp the external field down from Hz = 106 G to Hz = − 154 G (yellow data points and arrows) and subsequently, we ramp the external field back up Hz = 154 G (green data points and arrows). In order to extract the local ∣Bz∣ field from the splitting (Δ), we use the 2Π⊥ splitting measured at Hz = 0 on zero field cooling to T = 81 K [shown as light blue data in (a,d,g,j,m)]. On switching the direction of the external field (Hz < 0), we measure a minimum in ∣Bz∣. Since the local field measured at the NV location is the sum of the flux trapped field and Hz, we see an increase in the splitting on further increasing the magnitude of the external field in the negative direction. Based on the continuity of the ∣Bz∣ data points across the minimum, we assign a direction (sign) to the local field to extract the local field Bz. (c,f,i,l,o) We plot measured local field, Bz, against the applied external field, Hz, at the respective temperatures. We find that a clear increase in hysteresis with increase in temperature. All measurements are performed at the spatial location shown by the inverted white triangle in maintext Fig. 5(c) [also shown in inset in Extended Data Fig. 7(a)].
Extended Data Fig. 6 Comparison of the slope s = dBz/dHz on field cooling and zero field cooling.
We reproduce the data for ∣Bz∣ vs. Hz measured at (a) T = 61 K and (d) T = 66 K that are also shown in Extended Data Fig. 5 (b,e). (b,c) Similarly, we show the data for Bz vs. Hz extracted for the respective temperatures. We compare these measurements performed after field cooling and ramping Hz [experimental sequence in maintext Fig. 5(f)] to one measurement performed after zero field cooling and increasing Hz [light blue data shown in all sub-panels]. We find that, deep in the superconducting phase, Bz exhibits the same slope with respect to Hz on both field cooling and zero field cooling. In the case of field cooling, this suggests that in addition to a trapped flux, there may be a contribution similar to that which gives rise to a local diamagnetic response on zero field cooling.
Extended Data Fig. 7 Flux trapping in S2.
We compare the response of the sample on sweeping Hz after field cooling and zero field cooling at T = 81 K. (a) On field cooling at Hz = 103 G we measure a trapped flux. On ramping to large fields in the direction opposite to this trapped flux (Hz = − 154 G), we measure an inversion of the flux trapped field. (b) In contrast, the sample is robust to flux penetration on zero field cooling. Specifically, on ramping the external field to ∣Hz∣ = 154 G in both the positive and negative directions, we continue to observe a local suppression in Bz without any appreciable flux trapping. (c) After zero field cooling, the sample exhibits flux penetration only on ramping the external field to much larger magnitudes (∣Hz∣ ~ 240 G). Here, we measure a response similar to the case of field cooling. Specifically, on ramping to a field Hz = 240 G we find a flux trapped field Bz = 18 G (measured after returning to Hz = 0 G). Similarly, after ramping to a field Hz = − 240 G, the direction of the trapped flux changes (i.e., we measure Bz = − 28 G on returning back to Hz = 0 G). All measurements are performed at the spatial location shown by the inverted white triangle in the fluorescence scan [inset of (a)].
Extended Data Fig. 8 Spatial studies of flux trapping in S2.
We compare the effects of zero field cooling (ZFC) and field cooling (FC) at several spatial points in sample S2 [fluorescence scan in the inset of (d)]: two locations [blue and red points in inset of (d)] on top of the CeH9 region and one location [yellow point in inset of (d)] away from this region. (a-c) We field cool the sample at Hz = 79 G to a temperature T = 36 K and measure the ODMR spectra (dark blue) after quenching the external field to Hz = 0 G. Light blue data show the ODMR spectra measured at the respective spatial locations upon zero field cooling to temperatures (a,b) T = 36 K, and (c) T = 86 K. We see markedly higher splittings on top of the CeH9 region (a,b) upon field cooling indicating the presence of a flux trapped field. Away from the CeH9 region (c), we do not observe a significant difference between ZFC and FC data. In particular, Δ for the ZFC spectrum (measured at T = 86 K) is larger by 7 MHz; this difference is likely due to temperature dependence of the stress splitting, 2Π⊥, at this spatial point. (d-f) Following the field quench after FC, we determine the local Bz field at the three spatial locations on ramping Hz to positive values (green data points). We make the same measurements on ramping Hz to negative values (orange data points). We also measure Bz as a function of Hz after zero field cooling (blue data points). (d,e) On top of the CeH9 region, our measurements indicate the presence of a flux trapped field upon FC. This contrasts with a local suppression of Hz measured at the same locations upon ZFC. In particular, the slope s = ΔBz/ΔHz on field cooling is in quantitative agreement with the slope on zero field cooling. (f) Away from CeH9 region, we see no significant difference in response on ramping Hz after FC and ZFC. To extract Bz at each point, we use the 2Π⊥ splitting measured upon zero field cooling at the respective spatial location [light blue spectra in (a-c)].
Extended Data Fig. 9 Hysteresis on T-sweeps in S2.
To study hysteresis on sweeping T, we first zero field cool the sample and apply an external field Hz [maintext Fig. 5(d)]. Then, fixing Hz, we heat the sample across the transition (field heating shown in red). Finally, we cool the sample below Tc without changing Hz (field cooling shown in blue). We perform simultaneous electrical resistance (shown in green) and ODMR measurements. Four point resistance measured on field heating (field cooling) are indicated by markers pointing right (left). All measurements are made at the spatial location shown by the inverted white triangle in fluorescence scan [inset of (d)]. We use the 2Π⊥ stress parameter measured at Hz = 0 and T = 81 K to extract the local Bz field for all data points. (a-c) We observe concurrent transitions in magnetism and electrical resistance. In addition, we see a suppression of Tc with the increase in the magnitude of Hz. (d) Surprisingly at high fields (Hz = 206 G), we see a clear sharpening of the magnetic transition. To confirm the signal we repeat the measurement on field heating near the transition region (orange squares in (d)).
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Bhattacharyya, P., Chen, W., Huang, X. et al. Imaging the Meissner effect in hydride superconductors using quantum sensors. Nature 627, 73–79 (2024). https://doi.org/10.1038/s41586-024-07026-7
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DOI: https://doi.org/10.1038/s41586-024-07026-7
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