Single crystal synthesis, structure, and magnetism of Pb_10−xCu_x(PO₄)₆O

Room-temperature superconductivity holds the potential to disrupt various technologies—from enhancing energy storage and grid efficiency to advancing maglev trains, medical imaging, and electronic devices. In this context, recent claims about the presence of superconductivity in powders of Cu-substituted lead phosphate Pb_10−xCu_x(PO₄)₆O with 0.9 < x < 1 (referred to as LK-99)^1,2 have stirred significant anticipation within the condensed matter research community and beyond. In particular, the pronounced resistivity drop and the onset of a large diamagnetic response at temperatures T ∼ 400 K have been interpreted as evidence of superconductivity in the initial studies. Yet, efforts to replicate these key observations in polycrystalline specimens have yielded disparate results,^3–12 likely due to different levels of impurity phases generated by the complex synthesis via sulfur based compounds. In particular, the initial studies^1,2 reported a significant residue of Cu₂S in their powder samples. Moreover, grain boundaries in polycrystalline samples, whose prevalence and properties may depend on the preparation conditions, often exhibit physical properties different from those of the bulk. Conclusive tests of the original claims, therefore, require a well-defined pure phase, based on single-crystalline samples.

Motivated by these considerations, we have synthesized phase-pure single crystals of Pb₉Cu(PO₄)₆O using the traveling solvent floating zone (TSFZ) growth method, relying solely on phosphate-based compounds as precursors. None of the purported signatures of superconductivity are confirmed in these specimens. In particular, the crystals are highly insulating and optically transparent. Although the magnetic susceptibility includes a small ferromagnetic component (likely due to the local magnetic order in the inhomogeneous network of Cu substituents), it does not exhibit any anomalies indicative of phase transitions (including superconductivity) in a wide range of temperatures up to 800 K. We discuss the possible origins of the anomalies reported in phase-impure powder samples. In particular, the impurity phase Cu₂S exhibits two structural phase transitions, with the one at 398 K coinciding with an insulator-to-metal transition¹³ that may be mistakenly attributed to superconductivity.

A precursor powder was prepared by mixing the corresponding stoichiometries of 9 PbO:1 CuO and 9 NH₄H₂PO₄. Subsequently, the powder was ball-milled for 20 min and the mixture was transferred in alumina crucibles to a box furnace, followed by heating to 750 °C for 10 h followed by grinding and another heating of 10 h. Cylindrically shaped feed and seed rods were prepared by ball-milling the sintered materials, which were filled into rubber forms of 6 mm diameter. The rubber was evacuated and pressed in a stainless steel form filled with water using a Riken type S1-120 70 kN press. All rods were heat-treated at 800 °C. For the first growth, pellets were prepared in a 4 mm diameter press form with the Riken press. The single-crystal growth was carried out in a Crystal System Corporation optical image furnace CSC FZ-T-10000. Four halogen lamps operating at 150 W were used as a heating source.

The as-grown crystals were characterized using an optical microscope to select the phases obtained from the growth. The structural properties of each crystal were characterized using powder x-ray diffraction (PXRD) performed at room temperature using a Rigaku MiniFlex diffractometer with Bragg–Brentano geometry, Cu K_α radiation, and a Ni filter. Rietveld refinements were conducted with the FullProf software suite. Single crystal diffraction was performed at room temperature using a Rigaku XtaLAB mini II with Mo K_α radiation. The data were analyzed with CrysAlis(Pro), and the final refinement was performed using Olex2 with ShelX. The energy-dispersive x-ray (EDX) spectra were recorded using a NORAN System 7 (NSS212E) detector in a Tescan Vega (TS-5130MM) SEM. Differential Thermal Analysis (DTA) studies and thermogravimetry (TG) were performed using a NETZSCH DTA/TG. For EDX mapping, we used a Thermo Fisher tabletop Phenom Pharos REM utilizing the high pressure option to prevent charging phenomena. Magnetic susceptibility measurements were performed using a vibrating sample magnetometer (MPMS 3, Quantum Design). For high temperature measurements, we used the oven option of the MPMS superconducting quantum interference device (SQUID). Electrical transport measurements were performed using a Physical Property Measurement System (PPMS, Quantum Design).

A phase formation diagram for the synthesis of Pb₁₀(PO₄)₆O has already been reported in Ref. 14 and is depicted in Fig. 1(a). Using this as a guideline for the growth of Cu-substituted Pb_10−xCu_x(PO₄)₆O single crystals, we make use of the TSFZ method, where a flux pellet is first placed on the seed rod, balancing between the seed and feed rods during growth [Fig. 1(b)]. Our initial growth utilized a pure PbO pellet (batch 1). For the subsequent growth, we prepared pellets with molar PbO:CuO ratios of 9:1 and 1:1 for batches 2 and 3, respectively. The growth chamber was then evacuated and subsequently filled with Ar at 1 bar, maintaining a flow rate of 0.3 l/min. In accordance with the phase formation diagram, we initiated the growth using the PbO self-flux. Upon connecting the rods, a slow growth rate of 1 mm/h was maintained. Due to the decrease in melting temperature when progressing through the peritectic point, it was necessary to maintain a feed rate of 1 mm/h. This resulted in a broader seed, as illustrated in Fig. 1(c).

Post-growth, the boule was fractured using a mortar, yielding transparent crystals with a purple–brown shade in all batches. A representative crystal of batch 1 is shown in Figs. 1(d) and 1(e). The change in shading upon rotation of the polarized light propagation direction (dichroism) confirms the single-crystalline nature of our specimens. A powder XRD analysis of a crushed crystal from batch 1 indicated a phase-pure Pb₉Cu(PO₄)₆O composition. We refined the crystal structure with the same cell and atom positions that we have obtained from single crystal XRD, where we have solved the single crystal structure with the hexagonal P6₃/m structure (space group No. 176). We note that we have also considered other space groups as discussed in the  Appendix but found the best refinement with this space group. The refinement result is summarized in Table I and indicates a stoichiometry of Pb_8.9(1)Cu_1.1(2)P₆O₂₅.

As a next step, we performed multiple single-crystal XRD measurements, specifically aimed at re-evaluating the details of the crystal structure of the Cu substituted variant, which were previously determined only from powder samples. The result of a single crystal of batch 3 indicates a stoichiometry of Pb_8.8(3)Cu_1.2(3)P₆O₂₅ and is summarized in Table I. The reconstructed XRD maps along with the crystal structure are shown in Fig. 2. Notably, the refinement of our XRD data allows for a determination of the Cu site occupancy with a higher confidence. Furthermore, the result of the refinement suggests that the Cu substitution coincides with a reduction in the oxygen occupation, likely attributable to the square planar coordination of Cu. Overall, the XRD analysis indicates that the average Cu doping level in our crystals falls into the regime, where the initial studies on powder samples^1,2 claimed the occurrence of superconductivity. Notably, we find a slightly higher occupancy for Pb2, which agrees with energy calculations.¹⁵ Summarizing our XRD results, we have obtained large varying lattice constants moving in the range of the two presented in Table I. As our powder data of one crushed crystal in Fig. 1 from batch 1 show a, b = 9.853 19(6) Å and c = 7.441 54(5) Å, another refinement of powder data that are not shown on a crushed crystal of batch 3 yields a, b = 9.848 47(12) Å and c = 7.438 11(11) Å, while single crystal XRD measurements are as follows: batch 1 a, b = 9.8380(9) Å and c = 7422(11) Å, batch 2 a, b = 9.8140(18) Å and c = 7.4370(15) Å, batch 3 a, b = 9.778(2) Å and c = 7.3966(15) Å, and, finally, the presented one in Fig. 2 of batch 3 a, b = 9.798(2) Å and c = 7.3984(15) Å. As discussed further below, Cu is inhomogenously distributed and Pb²⁺ with a coordination of VIII has a large ionic radius of 1.29, while Cu is not even reported for such a high coordination, hence the oxygen vacancies that we find in the refinement. Cu maximally reaches an ionic radius of 0.73 as Cu²⁺ with a coordination of VI. Thus, in accordance with expectations, we see a contraction of the lattice with enhanced Cu substitution.

Figure 3 shows the EDX data compiled from over 20 broken pieces of crystals across three batches. Notably, when examining the crystals in a scanning electron microscope, we observe a charging effect from the electron beam. This suggests that the crystals are highly insulating, which was corroborated by transport measurements (see below). A closer look at two EDX spectra, taken from different locations on a single crystal’s surface [Fig. 3(a)], reveals a varying Cu content as best seen in the EDX map shown in Fig. 3(c). This implies that the Cu doping is not distributed homogeneously in the crystals. However, we highlight that Cu is incorporated in the matrix as it can be found everywhere in the single crystalline boule and is observed in single crystal XRD refinement as shown before. To shed more light on this observation, we plot the distribution of the atomic percentage (at. %) of the Cu substitution for several EDX measurement locations in Fig. 3(b), illustrating a large variation in Cu substitution levels. Due to the strong variation among the EDX points, the error bar for the average Cu and Pb stoichiometry of a crystal is relatively large. The determined average stoichiometries are Pb₈₍₁₎Cu_0.4(0.4)P₆O₂₅ for batch 1 grown with a PbO flux, Pb₉₍₁₎Cu_0.6(0.4)P₆O₂₅ for batch 2, and Pb₉₍₁₎Cu_0.6(0.7)P₆O₂₅ for batch 3. Note that our single-crystal XRD measured in transmission provides an accurate representation of the substitutional content averaged across the entire crystal.

Regarding the electronic transport properties, the optical transparency of our crystals [Figs. 1(d) and 1(e)] suggests an insulating or semiconducting nature. However, there have been some reports of superconductivity coexisting with optical transparency either due to an exceptionally low plasma frequency^16–18 or due to electronic phase separation into insulating majority and superconducting minority phases.^19,20 We, therefore, attempted to perform four-point DC resistivity measurements in a PPMS setup (see Sec. II) but found resistance values above several MΩ at room temperature. This behavior is also in line with the charging effects observed in the electron microscopy investigation presented above. Together, these findings conclusively falsify the claim of room-temperature superconductivity in LK-99.^1,2

We next discuss the magnetic response of crystals between 2 and 800 K. A first observation is a remarkably low measured signal strength, and hence, we note that a small temperature-independent offset might be present in our data, originating from a minute signal from the sample holder, which was not subtracted. For measurements in a small applied field of 5 mT, we detect a positive magnetic susceptibility signal at all temperatures [Fig. 4(a) inset] but no indications for a clear phase transition besides a tiny kink at 490 K. Certainly, there is no transition into a superconducting phase. Figure 4(a) shows the magnetic susceptibility measured in a field of 7 T, revealing a diamagnetic response of the crystal at least up to 800 K. The measurement was carried out on a crystal from batch 2. To verify the thermal stability of our crystals and confirm that they do not decompose at elevated temperatures, we conducted a differential thermal analysis (DTA/TG) up to 820 K. Importantly, no mass loss was observed during this analysis (not shown here). In addition, we carried out powder XRD measurements both before and after heating, where we did not observe significant changes compared to the XRD of the Pb₉Cu(PO₄)₆O sample shown in Fig. 1(f).

We tried to evaluate the real signal strength of the diamagnetism in this compound by using the room temperature value for the largest sample mass of 63 mg that we measured in a field of 1 T. In this case, we carefully measured the background signal and subtracted it from our signal. Here, we observed a moment of −2.5· 10⁻⁴ emu and a background signal of −1.46 · 10⁻⁴ emu, resulting in −1.04 · 10⁻⁴ emu for a sample with the volume of 3 × 3 × 1 mm³. Thus, our volume susceptibility amounts to $−1.04⋅10−41000⋅4π⋅10−6m33⋅3⋅1⋅10−9m3≈−1.452⋅10−4$⁠, which is a value that is remarkably comparable to Bi (notably, for a superconductor, we expect −1).

For zero field cooling (ZFC), a Curie tail due to isolated paramagnetic impurities is observed at low temperatures, which leads to an upturn of the susceptibility [Fig. 4(a)]. Nevertheless, the overall magnetic response remains negative (diamagnetic) down to the lowest measured temperatures of 2 K. For field cooling (FC) from 800 K, we observe a continuous rise in the susceptibility as the temperature decreases. The termination of the FC measurement below 300 K is due to technical constraints of our measurement setup (see Sec. II). The difference between the ZFC and FC curves persists up to 800 K, where the curves merge due to the here employed measurement protocol heating to a maximum of 800 K. Note that this intersection simply reflects the temperature where the cooling sequence is started, e.g., 390 K for the sequence shown in Fig. 5(a). This behavior hints at spin glass dynamics, possibly arising from partially ordered magnetic clusters within the sample. (Note that we cannot rigorously rule out the presence of minute amounts of ferromagnetic Fe impurities due to contaminated starting materials, but such contamination is below the detection limits of both EDX and XRD measurements.) Indeed, a magnetic field sweep at selected temperatures [Fig. 4(b)] reveals an initial increase in the sample magnetization for increasing fields, pointing to the presence of ferromagnetic or canted-antiferromagnetic correlations. We ascribe this phenomenon to Cu clusters formed due to the inhomogeneous substitution, resulting in a cluster spin glass effect also proposed theoretically for the material.²¹ Importantly, when exposed to stronger magnetic fields, this effect saturates, and the material exhibits a purely diamagnetic response [Fig. 4(b)]. Further evidence for a cluster spin glass state is derived from the time dependence of the magnetic susceptibility signal, observed for a measurement at 2 K in a constant field of 7 T [Fig. 5(b)]. The glassy dynamics of the magnetic susceptibility, with saturation on a characteristic time scale, is typical for disordered systems. Note that for this measurement, the temperature was firmly stabilized at 2 K, hence ruling out potential temperature fluctuations as the origin of the observed time dependence.

Figure 5 displays the magnetic susceptibility of a crystal from batch 3, corresponding to the highest realized Cu concentrations. Notably, for this sample, the amplitude of the paramagnetic upturn at low temperature exceeds the diamagnetic response [Fig. 5(a)]. Moreover, we find an enhanced ferromagnetic response for small applied fields (not shown here). Again, we highlight the small value of this ferromagnetic part. A possible scenario is that both the Curie tail and the ferromagnetic (or canted-antiferromagnetic) response are due to the Cu substituents, as expected since this is the only d-electron species in the crystal structure. According to electronic-structure calculations, Cu is divalent and, therefore, indeed, carries a nonzero spin magnetic moment.²¹ 

In Fig. 5(c), we have subtracted the linear diamagnetic contribution, thus highlighting the ferromagnetic contribution vs the applied field. The saturated magnetization amounts to only about 0.001 μ_B per Cu and is, therefore, much smaller than 1 μB, the full spin-1/2 moment of Cu²⁺. We note, however, that partial Cu substitution in Pb₉Cu(PO₄)₆O is expected to generate a complex (and likely highly disordered) network of Cu–O–Cu bonds, which may elicit strong antiferromagnetic exchange interactions [Figs. 2(c) and 2(d)]. Canting of the Cu moments due to magnetic frustration and/or local inversion symmetry breaking can then result in canted antiferromagnetism at high temperatures, as observed, for instance, in nanocrystalline CuO (see Ref. 22 and references therein). The connectivity of this network (and hence the amplitude of the net magnetic moment) may depend on the preparation conditions and might be enhanced at grain boundaries in polycrystalline samples. Regardless of its origin, the weakly ferromagnetic response, perhaps in conjunction with the diamagnetic background, may well be at the heart of the partial levitation of Pb₉Cu(PO₄)₆O above a permanent magnet at room temperature.^1,2,7,9

In summary, we have successfully grown single crystals of Pb_10−xCu_x(PO₄)₆O (LK-99) via the TSFZ method. The phase-pure crystals are highly insulating, suggesting that previously reported transport anomalies in powder samples, such as an insulator-to-metal transition that might have mistakenly been interpreted as a superconducting transition, are likely attributable to Cu₂S impurity phases.²³ The diamagnetic response of our crystals is broadly consistent with expectations for a non-magnetic insulator, although we also detect weakly ferromagnetic correlations, presumably originating from an inhomogeneous distribution of the Cu substituents. No anomalies indicative of phase transitions are detected for temperatures up to 800 K. These results suggest that the previously claimed occurrence of room-temperature superconductivity in LK-99 is highly unlikely.

The authors have no conflicts to disclose.

P. Puphal: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Project administration (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). M. Y. P. Akbar: Investigation (equal). M. Hepting: Writing – original draft (equal); Writing – review & editing (equal). E. Goering: Investigation (supporting). M. Isobe: Conceptualization (supporting); Investigation (supporting). A. A. Nugroho: Investigation (equal). B. Keimer: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

In our single crystal diffraction experiment, we found the hexagonal P6₃/m (No. 176) structure to describe our experimental data the best with R = 0.0450(409) and wR2 = 0.1015(690). Notably, the related P6(3) (No. 173) structure that was proposed in Ref. 24 can fit the data as well with all atom positions summarized in Table II but leads to a worse overall refinement with R = 0.0524(648) and wR2 = 0.1096(1176). Recently, a study on pure Pb₁₀(PO₄)₆O has found a superstructure to be realized with a doubled c-axis parameter.²⁵ Thus, we have carefully investigated a single crystal by enforcing a doubled c-axis in the cell pre-selection process and counted for an enhanced time. Nonetheless, for our Cu substituted variant, we found no superstructure reflexes. Notably, for our crystals, any formation of Pb₁₀(PO₄)₆O_x(OH)_2−x as discussed in Ref. 25 is highly unlikely if not impossible, as we perform a molten zone experiment in flowing Ar gas, and hydroxide materials evaporate under these conditions losing the (OH), which, however, might form in powder samples obtained from NH₄H₂PO₄.