Uncovering origins of heterogeneous superconductivity in La$_3$Ni$_2$O$_7$ using quantum sensors

Abstract

The family of nickelate superconductors have long been explored as analogs of the high temperature cuprates. Nonetheless, the recent discovery that certain stoichiometric nickelates superconduct up to high $T_c$ under pressure came as a surprise. The mechanisms underlying the superconducting state remain experimentally unclear. In addition to the practical challenges posed by working in a high pressure environment, typical samples exhibit anomalously weak diamagnetic responses, which have been conjectured to reflect inhomogeneous `filamentary' superconducting states. We perform wide-field, high-pressure, optically detected magnetic resonance spectroscopy to image the local diamagnetic responses of as grown La$_3$Ni$_2$O$_7$ samples \emph{in situ}, using nitrogen vacancy quantum sensors embedded in the diamond anvil cell. These maps confirm significant inhomogeneity of the functional superconducting responses at the few micron scale. By spatially correlating the diamagnetic Meissner response with both the local tensorial stress environment, also imaged \emph{in situ}, and stoichiometric composition, we unravel the dominant mechanisms suppressing and enhancing superconductivity. Our wide-field technique simultaneously provides a broad view of sample behavior and excellent local sensitivity, enabling the rapid construction of multi-parameter phase diagrams from the local structure-function correlations observed at the sub-micron pixel scale.

Figures (5)

• Figure 1: Micron-scale structure-function mapping at high pressure in an NV-DAC.a The Nitrogen-Vacancy equipped Diamond Anvil Cell (NV-DAC) enables submicron-scale imaging of functional magnetic responses of samples at high pressure. Correlating these maps with the local stress environment (from in situ NV-DAC tensor barometry) and local chemical composition (eg. from EDX) permits a wealth of structure-function information to be obtained from a single inhomogenous sample. b Schematic depiction of the sample loading between two opposing anvils. The top anvil contains a layer of NV centers approximately 500 nm below the culet surface. A platinum wire for microwave delivery and leads for electronic transport measurements are placed on the insulated gasket, facing the top diamond. We note that there is a $\sim 3^{\circ}$ misalignment between the culet normal and the [111] NV symmetry axis, which is discussed in the Methods. c White light image of sample S1 with false color overlays obtained at $21$ GPa. A crystal of La$_3$Ni$_2$O$_7$ (gray) is embedded in NaCl as a pressure medium (tan) within an insulating cBN gasket (dark). d Schematic of the spin $S=1$ sub-levels of the electronic ground state of the NV center. The common shift $D = D_{gs} + \Pi_Z(\overleftrightarrow{\sigma})$ of the upper two levels depends on the stress tensor $\overleftrightarrow{\sigma}$ but is insensitive to the magnetic field. The splitting $\Delta \nu$ is dominated by the linear Zeeman effect due to the magnetic field $B_z$ along the NV axis. The positions of peaks in the optically-detected magnetic resonance (ODMR) spectra (e) thus reflect the local magnetic and stress fields. e The ODMR spectra obtained at regularly spaced pixels along the line cut indicated after zero-field cooling (ZFC) to temperature $20$ K and turning on a magnetic field of $H = 97$ G. Away from the sample boundaries (points A and B), the measured splitting $\Delta \nu \approx 0.27$ GHz is consistent with a local $B = 97$ G, while above the sample there are regions where $\Delta \nu$ is both smaller (magnetic suppression) and larger (enhancement) than normal state expectations. Spectra are scaled to have uniform peak contrast, but are otherwise unprocessed. We observe inverted 'positive contrast' peaks, which extend our ability to measure both magnetic fields and traction to higher pressures (see Methods for details).
• Figure 2: Imaging local superconductivity and flux trapping.a Sub-micron diffraction-limited maps of sample S1, showing the magnetic field $B$ obtained after zero-field cooling (ZFC) to $20$ K, turning on $H\sim100$ G and then field warming (FW). The magnetic ratio $s \equiv B/H$ above the sample deviates from 1 below a dome in the $\overline{\sigma_{ZZ}}, T$ plane, although clear spatial inhomogeneities exist. b Corresponding $\sigma_{ZZ}$ maps for these stress points, taken at 150 K. c, d Simultaneously measured resistance at $\overline{\sigma_{ZZ}} =$ 21 and 25 GPa, with the ZFC-FW magnetic response of two spatial points marked on (a) [pink and purple stars, bottom right panel]. Kinks in the magnetic response correspond to kinks in resistance at corresponding stress points. e Spatial regions of strongest ZFC diamagnetic response (left) at $\overline{\sigma_{ZZ}} =$ 23 GPa correspond to regions with the most remnant magnetic flux (right) trapped after field cooling (FC) at $H=150$ G and quenching to $H=0$ G. For the left panel, gray regions correspond to $0.97 \le B/H < 1$ while black regions correspond to $0.85 \le B/H < 0.97$. For the right panel, green regions correspond to ODMR spectra with NV resonances that were unable to be resolved.
• Figure 3: Local superconductivity and normal stress maps.a Maps of the ZFC-FW magnetic response and b normal stress maps of sample S2 analogous to those in Fig. 2 for sample S1. c Correlation of the resistive transition (above) with the magnetic response (below) at one stress point. Sample S2 shows qualitatively similar diamagnetic and resistive responses to those of sample S1 in the $\overline{\sigma_{ZZ}}-T$ plane but in a smaller spatial volume and with a weaker local $s$ response.
• Figure 4: Multimodal correlations, superconducting phase diagram and the role of shear stresses.a The local surface stoichiometry of sample S1 obtained via energy-dispersive X-ray spectroscopy (EDX) shows regular Ni rich inclusions (purple) at the several micron scale as well as smaller regions of enhanced La (orange). This chemical texture does not alone explain the bulk features observed in the ZFC magnetic response. For example, at the lowest stress point, $\overline{\sigma_{ZZ}}=16~$GPa, where S1 exhibits diamagnetic response b, the region of the sample that goes superconducting turns out to be locally at higher normal stress $\sigma_{ZZ} \approx 17.5$ GPa than the mean shown in panel c. e The shear stress vector $\mathbf{\tau}$ with components $(\sigma_{XZ}, \sigma_{YZ})$ (white arrows) across the culet boundary at optimal mean stress, $\overline{\sigma_{ZZ}} = 21$ GPa. Color indicates the magnitude of the shear stress vector $\tau$. The region of high shear correlates strongly with the hole in the annular region of diamagnetic response in the corresponding ZFC-FW magnetic response shown in panel d. Gray region indicates overlap with ruby pellet which prevents the accurate extraction of the local shear. f depicts a three dimensional phase diagram of the superconducting response as a function of temperature, normal stress, and shear stress. Data is extrapolated down to zero on all axes using a spline fit (see Methods). Note that there is no data extrapolation for the phase diagrams shown in the subsequent panels (g) and (h). g The superconducting dome in the temperature, normal stress plane extracted from pixel-registered local responses across samples S1-S3. Dashed line corresponds to a guide to the eye delineating the superconducting region. h A low temperature projection of the phase diagram in the normal and shear stress plane. The dashed line provides a guide to the eye delineating the superconducting region.
• Figure 5: Correlating local superconductivity with chemistry.a Optical image of S3 (gray) with transport leads (blue), microwave antenna (yellow) and ruby (red). b Global four terminal resistance (above) shows no visible kinks even as the local diamagnetic response (black star in (e)) turns on below 60K (below). c The local ZFC diamagnetic response ($B/H$) at $9$ K shows a sharp peak where the ratio of La:Ni obtained by EDX is in the expected 3:2 ratio of stoichiometric La$_3$Ni$_2$O$_7$. The dashed line serves as a guide to the eye. d The spatial map of the La:Ni ratio shows two large stripes of enhanced Ni which cut across S3. These correlate strongly with regions which fail to show a magnetic response when overlaid (panel e) with the magnetic map obtained after ZFC at $9$ K as shown in panel f.