Strain-tuning for superconductivity in La₃Ni₂O₇ thin films

Abstract

The recent discovery of high-transition temperature (T_c) superconductivity in pressurized La₃Ni₂O₇ bulk crystals has attracted keen attention for its characteristic energy diagram of e_g orbitals containing nearly half-filled ${d}_{{3}{z}^{2}-{r}^{2}}$ and quarter-filled ${d}_{{x}^{2}-{y}^{2}}$ orbitals. This finding provides valuable insights into the orbital contributions and interlayer interactions in double NiO₆ octahedrons that further provides a chance to control the electronic structure via varying ligand field. Here, we demonstrate that strain-tuning of the T_c over a range of 50 K with La₃Ni₂O₇ films on different oxide substrates under 20 GPa. As the c/a ratio increases, the onset T_c systematically increases from 10 K in the tensile-strained film on SrTiO₃ to the highest value about 60 K in the compressively strained film on LaAlO₃. These systematic variations suggest that strain-engineering is a promising approach for expanding the superconductivity in bilayer nickelates with tuning the energy diagram for achieving high-T_c superconductivity.

Introduction

The recent discovery of high-T_c superconductivity near 80 K in pressurized La₃Ni₂O₇ crystals¹ has sparked renewed interest in the broader family of nickelate compounds^{2,3,4,5,6,7,8,9,10,11,12}. This nickelate belongs to the Ruddlesden-Popper (RP) series (RE_n+1Ni_nO_3n+1, RE = rare-earth element), consisting of bilayer NiO₆ octahedra separated by a RE rock-salt layer, with one example being La₃Ni₂O₇ shown in Fig. 1a. Surprisingly, signatures of superconductivity at ambient pressure have been also reported in strained thin films^13,14. In a simplified picture of the electronic band structure, Ni 3d orbital adopts a d^7.5 electron configuration. Density functional theory (DFT) calculations suggest that the ${d}_{{3}{z}^{2}-{r}^{2}}$ orbital facilitates significant out-of-plane hopping t_⊥ via apical oxygens of the NiO₆ octahedra^15,16,17. This interlayer interaction causes the ${d}_{{3}{z}^{2}-{r}^{2}}$ bands to split into anti-bonding and bonding states, with the centroid of the ${d}_{{x}^{2}-{y}^{2}}$ band placed in between (Fig. 1a). In this bilayer Hubbard model, the ${d}_{{3}{z}^{2}-{r}^{2}}$ and ${d}_{{x}^{2}-{y}^{2}}$ orbitals are nearly half-filled and quarter-filled, respectively, and the strong coupling between the layers through the ${d}_{{3}{z}^{2}-{r}^{2}}$ orbital is believed to play a critical role for the emergence of high-T_c superconductivity. This bilayer and multi-orbital nature provide a distinct perspective from the high-T_c cuprates, where the single-layer and single-orbital model with nearly half-filled ${d}_{{x}^{2}-{y}^{2}}$ orbital becomes a good description¹⁸.

Fig. 1: Strain-tuning for ligand field control of La₃Ni₂O₇ thin films.

a Crystal structure of bilayer nickelates La₃Ni₂O₇ and the energy diagram of Ni e_g orbitals. b Lattice constants of SrTiO₃, NdGaO₃, and LaAlO₃ substrates. c HAADF-STEM cross-sectional image of a La₃Ni₂O₇ thin film grown on NdGaO₃ taken along the La₃Ni₂O₇ [110] axis (scale bar 5 nm). Arrow represents the interface. d Reciprocal space maps of La₃Ni₂O₇ (1117)/ LaAlO₃ (103) (left) and La₃Ni₂O₇ (1117)/NdGaO₃ (103)_pc (right). e Experimentally obtained lattice constants of La₃Ni₂O₇ films grown on SrTiO₃, NdGaO₃, and LaAlO₃ substrates. Bulk values are shown in open diamonds¹. f Calculations of a-axis length of La₃Ni₂O₇ films on NdGaO₃ and LaAlO₃ by assumption of bulk compression ratio. Bulk values are plotted with open diamonds¹.

In the studies based on bulk crystals, it has been discussed that structural phase transition triggers the superconducting transition at roughly 10–14 GPa (refs. ^4,5); an orthorhombic Amam phase at ambient pressure transforms to a tetragonal Fmmm or I4/mmm phase^1,5,19, which enhances interlayer coupling essential for the electronic structure preferred for high-T_c superconductivity. Another structural factor is the possible involvement of monolayer and trilayer structural units in contributing to superconductivity^20,21,22. Such structural stability or uniformity is largely tied to oxygen deficiencies and the coexistence of competing RP phases (n = 1 and 3), which can hinder the optimization of superconducting properties. Specifically, oxygen vacancies, especially at inner apical oxygen sites, disrupt ${d}_{{3}{z}^{2}-{r}^{2}}$ orbital hybridization that is crucial for facilitating superconductivity, often inducing insulating behavior instead^23,24. To address these issues, concerted efforts in advancement in material synthesis are essential for achieving robust high-T_c superconductivity in this emerging class of nickelates. In this study, we applied a combination of thin-film fabrication technique based on coherent epitaxy and measurement under hydrostatic pressure for strain-tuning of the lattice and electronic structure. Strain tuning of oxide thin films offers large possibility to control the symmetry of octahedron in perovskite structures, resulting in the emergence of fascinating phenomena, for example variation of superconducting properties of cuprates^25,26, emergence of ferroelectricity in SrTiO₃ (ref. ²⁷) and metal-insulator transition in manganites²⁸. In the structural point of view, the ligand field of octahedra is directly linked to the lattice distortion, which likely provides an opportunity to control the energy diagram of the bilayer nickelates. The intuitive scenario under a compressive situation, with a large c/a ratio elongating the NiO₆ octahedra along c-axis, is as follows: the energy separation (ΔE) between ${d}_{{x}^{2}-{y}^{2}}$ and ${d}_{{3}{z}^{2}-{r}^{2}}$ orbitals in the energy diagram shown in Fig. 1a is expected to increase, due to ascending the energy level of the ${d}_{{x}^{2}-{y}^{2}}$ orbital and lowering the ${d}_{{3}{z}^{2}-{r}^{2}}$ orbital. Such modifications in the ligand field could effectively tune the electronic band structure and orbital filling, offering a promising route to maximize the superconducting properties in bilayer nickelates.

Results

Epitaxial thin film

We fabricated La₃Ni₂O₇ thin films on three substrates using pulsed-laser deposition (see Methods for details). To tune the strain, we selected SrTiO₃ (001) with (a_STO = 3.905 Å), NdGaO₃ (001)_pc (a_NGO = 3.855 Å) and LaAlO₃ (001) (a_LAO = 3.787 Å) as substrates. While NdGaO₃ adopts an orthorhombic Pbnm structure, here we employ a pseudocubic perovskite unit cell for the following discussion. Under ambient pressure, bulk La₃Ni₂O₇ adopts an orthorhombic Amam structure with lattice parameters a = 5.412 Å, b = 5.456 Å, and c = 20.45 Å. This structure can be approximated as a pseudo-tetragonal unit cell with a_pt = b_pt ~ 3.833 Å and c = 20.45 Å. Accordingly, the applicable strain in films is summarized in Fig. 1b. The film on SrTiO₃ imposes a tensile strain of +1.9%, NdGaO₃ close to the bulk lattice but still introduces a slight tensile strain of +0.6%, and that on LaAlO₃ is a compressive strain of –1.2%. Figure 1c shows the high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) cross-sectional image of La₃Ni₂O₇ film on NdGaO₃ substrate, which exhibits high-quality film with abrupt interface. While additional NiO₆ layers were sparsely detected as 3-NiO₆ layers, corresponding to approximately 6% off-stoichiometry, the bilayer structural units were predominantly observed, separated by LaO rock-salt layers, corresponding to the 2222-structure (see also Supplementary Information Fig. S1 for an overview and interface).

The crystalline structure was characterized using x-ray diffraction techniques. Judging from no additional peak except for La₃Ni₂O₇ and substrate materials in 2theta-omega scans for three films, a single phase of La₃Ni₂O₇ is fabricated on the substrates (see Supplementary Information Fig. S2). Crucially, we conducted phi-scans around the La₃Ni₂O₇ (2 0 6) peaks to investigate the crystal rotation symmetry. The phi-scans revealed clear four-fold symmetry of the (2 0 6) peaks with 45-degree rotation from the substrate (1 0 1) peaks (see Supplementary Information Fig. S3). This rotation symmetry and appearance of a single peak in reciprocal space mapping (RSM) discussed below strongly suggests that the La₃Ni₂O₇ thin films are stabilized in the tetragonal symmetry owing to epitaxial strain. RSMs were measured around the substrate (1 0 3) peak, as shown in Fig. 1d for LaAlO₃ (left) and NdGaO₃ (right) (A cross-point of two red broken lines indicates bulk values of La₃Ni₂O₇). In both RSMs, a peak corresponding to La₃Ni₂O₇ (1 1 17) was aligned at substrate along a-axis direction, indicating that the films are almost strained to the in-plane lattice of substrates. The in-plane lattice constant was evaluated to be 3.815 ± 0.014 Å for La₃Ni₂O₇ on LaAlO₃ and 3.855 Å for that on NdGaO₃, corresponding to –0.5% and +0.6% strains, respectively. Compared with the perfect matching of the film lattice to that of NdGaO₃, the strain of the film on LaAlO₃ is partially relaxed. The experimentally obtained lattice constants are summarized in Fig. 1e, compared with reported bulk values (open diamonds: La₃Ni₂O₇ bulk crystal under ambient pressure and after structural phase transition at 14 GPa (ref. ¹)). The out-of-plane lattice constant correspondingly exhibits elongation on LaAlO₃ (c = 20.58 Å) and contraction on NdGaO₃ (c = 20.41 Å). Please note that the a-axis value for the film on SrTiO₃ is plotted to top axis due to difficulty of experimental evaluation with weak diffraction intensity in RSM measurement. Considering the Poisson’s ratio (ν = 0.5), both films are well-strained in-plane with small variation in the out-of-plane lattices, exhibiting minimal oxygen deficiency.

Based on this lattice condition at ambient pressure, we estimate the lattice distortion under hydrostatic pressure. The compression ratio of tetragonal phase of La₃Ni₂O₇ bulk single crystal around hydrostatic pressure P = 20–40 GPa is approximately –3.22 × 10^–3 Å/GPa in pseudo-tetragonal estimation for averaged a,b-axis and –16.6 × 10^–3 Å/GPa for c-axis¹. Considering the tetragonal lattice unit, hydrostatic pressure compresses the lattice of the La₃Ni₂O₇ crystal almost isotropically. As shown in Supplementary Information Fig. S4, the compression ratio of substrate materials with perovskite structure that was calculated using DFT-based methods (see Methods and Supplementary Information for details) is close values in –(5 ~ 6.5) × 10^–3 Å/GPa. By applying –3.22 × 10⁻³ Å/GPa, we roughly estimate the compressed a-axis length of La₃Ni₂O₇ films as shown in Fig. 1f. When assuming the critical lattice constant for a structural phase transition or the appearance of superconductivity, a higher critical pressure is required to reach it in tensile-strained films with a larger a-axis length. It is also an intriguing viewpoint to compare the critical lattice constant with that for the strained film exhibiting superconductivity at ambient pressure¹³. In the future, direct measurement of the lattice constant of the films under applied pressure using X-ray diffraction with a diamond anvil cell may become feasible.

Superconductivity in La₃Ni₂O₇ films under hydrostatic pressure

We measured the electrical resistivity of three films under applying hydrostatic pressure up to 20 GPa using a cubic anvil cell with a liquid pressure-transmitting medium. In Fig. 2a, the superconducting transition was clearly observed at P = 20 GPa for the films on three substrates. The onset T_c and the temperature at resistivity reaching zero (T_c^zero) for the film on LaAlO₃ are approximately 60 and 48 K, respectively. The value of T_c^zero is comparable to the reported bulk values of 40 K (ref. ⁴) and 41 K (ref. ⁶). It should be noted that the resistivity of the film on NdGaO₃ and LaAlO₃ at normal state shows a linear-in-temperature, indicating a strange metal phase. In addition, the onset T_c of the films on NdGaO₃ and SrTiO₃ decreases to 40 and 10 K, respectively, which is in accord with the increase of the residual resistance. Figure 2b–f exhibit temperature dependent resistivity ρ_xx (T) of La₃Ni₂O₇ films on SrTiO₃ (Fig. 2b), NdGaO₃ (Fig. 2c, d), and LaAlO₃ (Fig. 2e, f). At P = 0 GPa, while the film on SrTiO₃ shows metallic behavior (Fig. 2b), the other two are insulating (Fig. 2c, e). Metallic behavior has been also observed in bulk samples^1,5. At low pressure regions roughly below 12 GPa, the insulating behavior is pronounced in all films, which is possibly related to the formation of spin or charge density wave phase as suggested by previous studies on bulk samples^23,29,30,31. We also note that local variations of oxygen content in thin film might be close situation as recently reported in bulk samples exhibiting such insulating phases under pressure. We focus on the clear kink of resistivity that correspond to the characteristic temperature for the formation of the density wave phase as T_DW, at P = 1 GPa, appears at 170 K for the film on SrTiO₃, 175 K for that on NdGaO₃, and 150 K for that on LaAlO₃. The kink at T_DW decreases and becomes broader with increasing pressure, indicating suppression of the density wave phase formation. By further increasing the pressure, all films exhibited metallic ρ_xx–T curves, resulting in superconducting phase (Fig. 2b, d, f). Current–voltage characteristics were carried out within the current upper limit of 10^–4 A. Although finite voltage generation was observed with approximately 10⁻⁵A in low-T_c film on NdGaO₃ (see Supplementary Information Fig. S5), the high-T_c film on LaAlO₃ would require higher currents than our measurement setup. The large c/a with elongated c-axis and compressed a-axis, that is La₃Ni₂O₇/LaAlO₃, stabilizes superconductivity, highlighting the critical role of strain engineering in maximizing superconducting properties.

Fig. 2: Pressure-induced superconducting transition in temperature dependence of electrical resistivity of La₃Ni₂O₇ films.

a Substrate dependence of normalized resistivities as a function of temperature under P = 20 GPa. Resistivities are normalized by values at 280 K. b Resistivities as a function of temperature under various pressure for La₃Ni₂O₇ films on SrTiO₃. c Resistivities as a function of temperature under P = 0–8 GPa and d those under P = 12–20 GPa for La₃Ni₂O₇ films on NdGaO₃. e Resistivities as a function of temperature under P = 0–12 GPa and f those under P = 16–20 GPa for La₃Ni₂O₇ films on LaAlO₃.

Phase diagram

Figure 3a–c presents the temperature–pressure (T–P) phase diagrams of La₃Ni₂O₇ films on three substrates, which was based on the temperature dependence of resistivity shown in Fig. 2. Yellow, purple, and blue represent the metallic, insulating, and superconducting regions, respectively. First, the insulating density wave phase is strongly suppressed in the film on SrTiO₃. However, weak insulating behavior appears at below approximately 50 K (purple), resulting in narrow region of superconductivity in the T–P diagram. Second, the superconducting phase appears in close proximity to insulating state, indicating that the suppression of density wave phase is a key to the phase transition. This behavior is reminiscent of features associated with high-T_c superconductivity in cuprates^18,32, suggesting a correlation between the insulating and superconducting phases. Third, the superconducting region with the resistance reaching zero appears in the films on NdGaO₃ and LaAlO₃. The rich phases in the T–P diagrams of three films indicate that the stain effect effectively induces variations in phase stability.

Fig. 3: Phase diagrams of La₃Ni₂O₇ films.

Temperature–Pressure phase diagrams for La₃Ni₂O₇ films on a, SrTiO₃, b NdGaO₃, and c LaAlO₃ substates. T_DW (closed triangles) is defined by temperatures that resistivity changes discontinuously. T_c^zero (close squares) and T_c^onset (open circles) are defined by temperatures of onset of resistivity drops and zero-resistance.

Strain effect

The strain effect for the electrical properties in three films are discussed with the critical pressure (P_c) for appearance of superconductivity (Fig. 4a), T_DW (Fig. 4b), and T_c (Fig. 4c) as a function of c/a. It has been discussed that hydrostatic pressure plays two roles in the appearance of superconductivity in bulk studies^1,4,5: one is inducing the structural phase transition, and the other is increasing the hybridization of electronic bands. The strain effect in thin films is significantly different from the isotropic compression under applying hydrostatic pressure, because the increase in the c/a in the film corresponds to the compression of the a-axis length and elongation of the c-axis length, or vice versa. Although the c/a ratio varies in range of approximately 6% in three films, the P_c seems almost constant about 12–16 GPa, being reasonable in comparison with that of bulk values. This result indicates that the structural phase transition is not a major trigger to induce the superconductivity in La₃Ni₂O₇. The degree of hybridization may be a dominant factor in the films. Since no structural phase transition is observed in thin films under strain, while maintaining the tetragonal symmetry, it is plausible that hydrostatic pressure enhances hybridization via compression. Although we did not directly measure the structural evolution or hybridization under hydrostatic pressure in this study, the correlation between strain- and pressure-induced changes and the superconducting phase diagram suggests that hybridization plays an important role. Spectroscopic studies with a diamond anvil cell will provide further physical insight to directly clarify the orbital evolution under pressure.

Fig. 4: Strain tuning for appearance of superconductivity.

Comparison as a function of c/a ratio. a Critical pressure P_c for appearance of superconductivity. Bulk values are plotted as open diamonds^1,4,5. b Temperatures for the formation of density wave phase T_DW. c Critical temperatures of T_c^zero (close squares) and T_c^onset (open circles).

Two characteristic temperatures T_DW at P = 1 GPa and T_c at 20 GPa are summarized in Fig. 4b, c. Comparing the values of the films on NdGaO₃ and LaAlO₃, a decrease in T_DW and an increase in T_c are observed with an increasing the c/a ratio. This suggests that the change in the ligand field and the increase of ΔE is closely related to the stabilization of superconductivity. In contrast, the T_DW for SrTiO₃ is not on the trend probably due to metallic background conduction. The electron conduction in La₃Ni₂O_7−δ bulks has been reported to undergo a spin-order phase at around 150 K and a charge-order phase at approximately 115 K (refs. ^{23,24,29,30,31,33,34,35,36}). In particular, the role of oxygen deficiencies was discussed on the formation of these density wave phases in previous bulk studies^23,29,30,31. Although it is generally difficult to quantitatively analyze oxygen deficiencies in thin films, the effectiveness of ozone annealing to induce metallic behavior and superconductivity have been reported in thin-film samples^13,14. Considering the suppression of insulating behavior in the La₃Ni₂O₇ film on LaAlO₃ (see Supplementary Information Fig. S7) after ozone annealing, the observed T_DW in the as-grown films with tetragonal structure is likely linked to the oxygen deficiencies, which may be as comparable to the reported conditions in both thin films¹³ and bulk samples¹⁹. Based on the good quality of the film, it should be pronounced that the film with large c/a on LaAlO₃ show superior superconducting properties with the highest T_c^zero around 50 K. The systematic increase of T_c demonstrates that the strain tuning enables us to effectively control the ΔE in energy diagram for the emergence of superconductivity.

Conclusion

We have demonstrated the systematic strain tuning of the superconducting transition temperature in La₃Ni₂O₇ thin films based on the coherent epitaxy technique. By applying this approach, we successfully achieved the highest T_c^zero = 48 K in the compressively strained film on LaAlO₃. We found that the critical pressure for superconductivity remains unchanged within this lattice tuning regime. Our results about the lattice engineering in terms of c/a will contribute to construct a unified picture of the superconductivity in bilayer nickelates under isotropic compression by hydrostatic pressure and anisotropic variation by epitaxial strain. Further investigations into strain tuning of RP nickelates are warranted^37,38,39,40, particularly for suppressing competing phases, tuning the electronic band structure, and optimizing the superconducting gap, all of which are critical for achieving high-T_c superconductivity.

Methods

Sample preparation

La₃Ni₂O₇ films were fabricated on single-crystalline SrTiO₃ (001), NdGaO₃ (001)_pc, and LaAlO₃ (001) substrates using pulsed-laser deposition. La₃Ni₂O₇ polycrystalline targets were ablated by a KrF excimer laser (wavelength 248 nm). Substrates were pre-annealed at 750 °C in an oxygen partial pressure of 1 × 10⁻⁶Torr to obtain an atomically flat surface. During growth, the substrate temperature was fixed at 650°C and the oxygen partial pressure was 200 mTorr. The laser fluence was ~1.0 J/cm² and a repetition rate was 4 Hz. The film thickness was in a range of 10–20 nm by adjusting the laser pulse counts. The films were characterized using x-ray diffraction (XRD) techniques with Cu Kα source (λ = 1.5406 Å). The interface quality of La₃Ni₂O₇/NdGaO₃ (001)_pc was examined using scanning transmission electron microscopy (STEM). Crystal structures were visualized using the VESTA software⁴¹.

Device for high-pressure measurement

The thin-film samples were cut into dimensions of 500–1000 μm in lateral size, and the substrates were mechanically polished to reduce their thickness to 0.3 mm (see Supplementary Information Fig. S6 for details). Gold wires were bonded to the samples in a van der Pauw geometry using silver paste to ensure reliable electrical contacts. The ρ_xx-T curves at P = 0 GPa were observed in physical properties measurement system (PPMS) (Quantum Design, Inc.).

High-pressure electric resistivity measurement

The measurements of the temperature dependent resistivity ρ_xx under high-pressure was performed under various hydrostatic pressure of 1–20 GPa using a cubic anvil cell with a liquid pressure-transmitting medium (see Supplementary Information Fig. S7 for resistivity variation under applied pressure at T = 300 K). The temperature dependence of resistance was measured using Keithley 2182 A nanovoltmeters and Keithley 6221 source meters in delta mode. Measurements were conducted over a temperature range from 292 K to 4.2 K.

Theoretical calculations based on density functional theory

The first-principles DFT calculations for structural optimization are performed using Quantum Espresso⁴² with a pressure convergence threshold of ±10^–3 GPa. The calculations adopt the scalar-relativistic PAW (projector augmented wave) pseudopotentials⁴³ generated by the PSLibrary package⁴⁴, for which the exchange-correlation potential is treated within the GGA-PBEsol approximation⁴⁵. The computational parameters are detailed in Supplementary Table S1 where the lattice constants were converged within an error of ±0.002 angstrom for all target materials.