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## Creator

[Yuta Ueki](https://orcid.org/0009-0006-5893-1096), [Hiroya Sakurai](https://orcid.org/0000-0003-1964-6023), [Hibiki Nagata](https://orcid.org/0009-0003-2656-4920), [Kazuki Yamane](https://orcid.org/0000-0002-0162-5411), [Ryo Matsumoto](https://orcid.org/0000-0001-6294-5403), [Kensei Terashima](https://orcid.org/0000-0003-0375-3043), Keisuke Hirose, Hiroto Ohta, Masaki Kato, [Yoshihiko Takano](https://orcid.org/0000-0002-1541-6928)

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©2025 The Physical Society of Japan[Copyright not evaluated](http://rightsstatements.org/vocab/CNE/1.0/)

## Other metadata

[Phase Diagram of Pressure-Induced High Temperature Superconductor La<sub>3</sub>Ni<sub>2</sub>O<sub>7+</sub><i>  <sub>δ</sub></i>](https://mdr.nims.go.jp/datasets/4ad2475b-2f6a-430d-9f4c-30ddd197d95e)

## Fulltext

Title of Paper Goes Here:Phase diagram of pressure-induced high temperature superconductor La3Ni2O7+δ  Yuta Ueki1,2*, Hiroya Sakurai1, Hibiki Nagata1,2, Kazuki Yamane1,2, Ryo Matsumoto1,  Kensei Terashima1, Keisuke Hirose3, Hiroto Ohta3, Masaki Kato3, Yoshihiko Takano1,2  1National Institute for Materials Science (NIMS) 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan 2University of Tsukuba 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan 3Doshisha University 1-3 Tataramiyakotani,  Kyo-Tanabe, Kyoto 610-0321, Japan   (Received September 10, 2021)  We successfully synthesized samples of La3Ni2O7+δ (δ = −0.50, −0.16, 0.00, +0.01, and +0.12) and measured the resistance under extremely high pressures using a diamond anvil cell to establish the electronic phase diagram. A Mott insulating state appears at δ = −0.50, where all Ni ions are divalent. With increasing oxygen content, superconductivity appears at δ = 0.00 and higher, above approximately 25 GPa, passing through Anderson localization at δ = −0.16. The superconducting transition temperature (Tc) decreases with increasing pressures for both δ = 0.00 and +0.12, with the pressure dependence of Tc being much stronger in the latter than in the former.    1.  Introduction  Electronic phase diagrams are highly informative for studying superconductors.1—7) They highlight the thermodynamic conditions suitable for superconductivity and indicate potential fluctuations that induce or compete with superconductivity. These diagrams serve as benchmarks for theoretical models of superconducting mechanisms. Their importance is especially pronounced under extremely high pressures, where experimental data is limited due to technical challenges. Recently, La3Ni2O7 was found to exhibit superconducting transitions at pressures above 14 GPa.8) This discovery is significant due to its high transition temperature of 80 K and its structural similarity to high Tc cuprates. The crystal structure of La3Ni2O7 consists of double NiO2 layers and La—O rock salt blocks,9) as shown in Fig. 1. The Ni sites form a square lattice similar to the Cu square lattice in CuO2 planes. Superconductivity on NiO2 planes has also been observed in thin films of infinite-layer nickelates,10) where it occurs at temperatures of 15 K or  lower when the Ni valence is between +1.15 and +1.25.11, 12) In these films, the Ni ion, coordinated by four oxygen ions, has 8.75—8.85 3d electrons, making a single-band model of the Ni 3dx2-y2 orbitals appropriate.13) However, in La3Ni2O7, the number of 3d electrons in Ni ions is different, and a single-band model does not apply because the Fermi surface involves two types of electronic bands, characteristic of the 3dx2-y2 and 3dz2 orbitals.14) This difference, along with the higher Tc, suggests a different superconducting mechanism for La3Ni2O7 compared to thin films. In La3Ni2O7, the Ni ion has 7.5 3d electrons, which is commensurate with its bilayered crystal structure. For instance, two Ni ions along the c-axis, shown in the circle in Fig. 1, share three 3d electrons between the 3dx2-y2 and 3dz2 orbitals. Likely due to this commensurability and the almost consistent Tc values reported,8, 15—20) the effect of oxygen nonstoichiometry on superconductivity has received less attention, similar to the case of Sr2RuO4. However, superconductivity is clearly dependent on band filling, which can be adjusted by varying the oxygen content. Our recent findings show that the superconductivity of La4Ni3O10 is very sensitive to its oxygen content.21) Therefore, we aim to establish a comprehensive phase diagram of La3Ni2O7 that includes temperature (T), pressure (P), and oxygen content.  2. Experimental Polycrystalline samples of La3Ni2O7+δ were prepared by solid-state reaction from La2O3 and NiO. The oxygen content was initially estimated to be δ = +0.01 for samples slowly cooled in flowing oxygen gas. Detailed procedures for synthesis and oxygen-content determination are described elsewhere.15) The oxygen content was then increased to δ = +0.12 using hot isostatic pressing under 1500 kgf/cm² with 20% O2/Ar at 600°C for 2 hours. The excess oxygen atoms are likely located in the rock salt blocks, similar to La2NiO4.17.22, 23) Conversely, the oxygen content was decreased by annealing samples in air at 500°C for 2 days, or in flowing 10% H2/Ar for 12 hours at 250°C or 300°C, resulting in δ values of 0.00, −0.16, and −0.50, respectively. The oxygen atoms are likely removed from the site between two Ni atoms, as shown previously.24) Sample characterization was performed using powder X-ray diffraction (XRD) with Cu Kα radiation on a commercial diffractometer, MiniFlex600 (Rigaku), equipped with a one-dimensional high-speed detector, D/teX Ultra. Electrical resistance, R, for each sample was measured under various pressures using a diamond anvil cell (DAC) with a commercial PPMS (Quantum Design) system, from 300 K to 2 K. The sample was placed between two diamonds with cubic BN as the pressure medium and stainless steel as the gasket. Electrical terminals  made of boron-doped diamond were printed on the surface of one diamond. Detailed DAC configuration is provided elsewhere.15, 25)   3.  Results and Discussion XRD patterns for all samples are shown in Fig. 2. All peaks for δ = +0.01, 0.00, and −0.16 were indexed assuming orthorhombic Amam symmetry.9) The lattice parameters were estimated as follows: a = 5.3903Å, b = 5.4464Å, and c = 20.507Å for δ = +0.01; a = 5.3920Å, b = 5.4510Å, and c = 20.533Å for δ = 0.00; and a = 5.4083Å, b = 5.4487Å, and c = 20.480Å for δ = −0.16. For δ = −0.50, tetragonal I4/mmm symmetry was adopted, consistent with previous reports for δ = −0.65.24) The lattice parameters were a = 3.874Å and c = 20.075Å for δ = −0.50. In contrast, for δ = +0.12, both orthorhombic and tetragonal phases were observed, as shown in Figs. 2b and 2c. The orthorhombic 020 and 200 peaks of La3Ni2O7.01 partially merged into a single peak at 2θ = 32.9°, while the orthorhombic 0,0,10 peak partially remained at the same position and partially shifted to a higher angle of 44.9°. The lattice parameters for these phases were estimated to be a = 5.384Å, b = 5.453Å, and c = 20.48Å for the orthorhombic phase, and a = 3.857Å and c = 20.14Å for the tetragonal phase. The lattice parameters of the orthorhombic phase agree well with those of La3Ni2O7.01. Similar phase separation has been observed in La2CuO4+δ.26, 27) The weight ratio of the two phases in the La3Ni2O7.12 sample was estimated using the reference intensity ratio (RIR) method to be approximately 35% orthorhombic phase and 65% tetragonal phase. Assuming the oxygen content of the orthorhombic phase is the same as La3Ni2O7.01, the oxygen content of the tetragonal phase can be calculated as δ = +0.17. This estimation is reasonable, as the δ value aligns with that estimated for a commensurate superstructure of La2NiO4.17.22) From a structural perspective, the chemical formulas of these compounds can be described as (LaO1+δ)(LaNiO3)2 for La3Ni2O7+δ and (LaO1.17)LaNiO3 for La2NiO4.17, as mentioned earlier.  The R—T curves at various pressures for δ = 0.00 and δ = +0.12 are shown in Fig. 3. The resistance of each sample decreases with increasing pressure. The temperature dependence is partly negative, likely due to grain boundary scattering, especially above around 160 K, as seen in La4Ni3O10. This is because La3Ni2O7+δ (δ ≥ 0) is known to exhibit metallic temperature dependence at least above 160 K at ambient pressure.9, 28—35) Below approximately 160 K, semiconducting behavior attributed to a kind of density wave formation has been reported at ambient pressure in some studies,33—35) although the other studies have reported metallic  behavior even below 160 K. For δ = 0.00 and δ = +0.12, the resistance at pressures above 25.6 GPa and 26.1 GPa, respectively, shows a kink at around 80 K or lower, indicating the superconducting transition. The transition temperature, estimated as the crossing point of lines just above and below the kink, is summarized in Fig. 4. The pressure dependence of Tc is clearly different for each sample; the decrease in Tc for δ = 0.00 is much smaller than that for δ = +0.12. Interestingly, despite the robustness of Tc against pressure, the decrease in resistance below Tc for δ = 0.00 is smaller than that for δ = +0.12. For example, the resistance at T = 43 K at 29.2 GPa for δ = 0.00 is 95% of that at Tc, whereas at 26.1 GPa and T = 2 K, it is 83% of that at Tc for δ = +0.12. Although the reduction in resistance does not always represent the superconducting volume fraction, one might infer that the fraction is smaller for δ = 0.00. However, it is important to note that the reduction strongly depends on the sample configuration in the DAC, which is hard to control precisely, although Tc is less affected. In fact, the resistance below Tc decreased significantly for δ = +0.01, although the pressure dependence of Tc was almost the same as that for δ = 0.00 up to the maximum pressure measured of 35 GPa.  The R—T curves at various pressures for δ = −0.16 and δ = −0.50 are shown in Fig. 5. The resistance for δ = −0.16 is several orders of magnitude higher than that for δ = 0.00, indicating that the insulating nature is intrinsic. Nevertheless, the resistance does not follow Arrhenius-type behavior but agrees well with variable-range hopping (VRH) behavior, at least above approximately 100 K (T1/4 = 3.16), as it can be reproduced by the equation R ∝ exp(T0/T)1/4, where T0 is a parameter representing the degree of carrier localization. This is consistent with the fact that the Ni valence is incommensurate with the crystal structure, suggesting that Anderson localization caused by partially removed oxygen ions is likely the origin of the insulating nature. The T0 value decreases with increasing pressure, as shown in the inset of Fig. 5b, indicating that carrier localization becomes weaker at higher pressures. The resistance for δ = −0.50 is significantly higher than that for δ = −0.16, showing Arrhenius-type behavior with the energy gap of Δ ~ 1900 K above approximately 200 K. This aligns with the expectation that La3Ni2O6.5 is a Mott insulator with only divalent Ni ions, as predicted by electronic band structure calculations.36) Insulating behavior has also been reported for δ = −0.6524) and δ = −0.55.37) For the former, VRH behavior was observed, while for the latter, Arrhenius-type behavior was assumed. The VRH behavior seems reasonable because the Ni valence in the compound is far from two. For δ = −0.55, one might question the validity of Arrhenius-type behavior at high pressures, as suggested by the curvature of the R—T curves  and the small gap values relative to the rather high measurement temperatures. Despite these concerns, the potential issue does not affect our conclusion because the chemical composition for δ = −0.55 is different from La3Ni2O6.5. In general, Mott insulating state is sensitive to the band filling.38, 39)  The above-mentioned experimental findings result in the phase diagram shown in Fig. 6. Clearly, superconductivity appears adjacent to the insulating region, where Anderson localization occurs. The Tc values show a stronger dependence on δ as the pressure increases. This observation can help narrow down the possible mechanisms of superconductivity and suggests that higher Tc values may be achievable in certain areas of the phase diagram. For example, at a slightly smaller δ than 0.00, Tc may be higher than 80 K at pressures significantly greater than 60 GPa. Although the Anderson localization tends to occur below δ = 0.00, it weakens and the metallic nature is expected to appear under high pressures, as indicated by the pressure dependence of T0 shown in Fig. 5b.   3.  Conclusions By preparing samples of La3Ni2O7+δ (δ = −0.50, −0.16, 0.00, +0.01, and +0.12), we established a comprehensive electronic phase diagram showing Tc as a function of P and δ, by measuring resistance under high pressures. For δ = −0.50, a Mott insulating state appears, which is destroyed by adding oxygen, leading to Anderson localization. For δ = 0 or higher, superconductivity appears above approximately P = 25 GPa. Although Tc remains almost constant against δ at 25 GPa or slightly higher, the pressure dependence of Tc becomes stronger with increasing δ. Consequently, Tc rapidly decreases with increasing pressure for larger δ values.  Acknowledgment We would like to express our gratitude to Professors K. Kuroki (Osaka Univ.), H. Sakakibara (Tottori Univ.), and M. Ochi (Osaka Univ.), and Dr. M. Kohno (NIMS) for fruitful discussion. 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B, 83, 245128 (2011). 37) R. Guo, L. Jin, S. Huyan, D. Ni, H. Wang, X. Xu, S. L. Bud’ko, P. Canfield, W. Xie, and R. J. Cava, Appl. Mater. Interface, 3c, 17376 (2024). 38) M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998) 39) M. Kohno, Phys. Rev. Lett., 108, 076401 (2012) 40) https://atomwork-adv.nims.go.jp/ 41) K. Momma and F. Izumi, J. Appl. Crystallogr., 44, 1272 (2011).   Fig. 1  Crystal structure of La3Ni2O7. The red, blue, and green circles represent Ni, O, and La atoms, respectively. The box and circle indicate the unit cell and a pair of Ni atoms (see the text), respectively.    Fig. 2  Powder XRD patterns of the samples of La3Ni2O7+δ (δ = −0.50, −0.16, 0.00, +0.01, and +0.12), and the calculated patterns for La3Ni2O7 with the orthogonal and tetragonal symmetries of space groups Amam and I4/mmm, respectively (a). Panels b and c magnify the XRD patterns for δ = +0.12 and +0.01 between 30° and 35°, and between 43° and 46°, respectively.    Fig. 3  Temperature dependence of electrical resistance for δ = 0.00 (a and b) and δ = +0.12 (c and d) under various pressures.    Fig. 4  Pressure dependence of Tc estimated for δ = 0.00 (red diamonds) and δ = +0.12 (blue squares). The lines are guides for the eye.    Fig. 5  Electrical resistance under various pressures for δ = −0.16 as a function of T (a) and 1/T1/4 (b), and for δ = −0.50 (c). The inset in the panel b shows the pressure dependence of T0 estimated from the data between approximately 100 K and 300 K using the equation R ∝ exp(T0/T)1/4.    Fig. 6  The T—δ phase diagrams under approximately 26 GPa, 50 GPa, and 60 GPa. The three phase diagrams for the pressures are depicted overlapping each other. The Tc under the pressures are shown by the red circles, green diamonds, and blue squares, respectively. The black squares on the δ axis show the δ position for the samples used. The colored areas are guides for the eye.