Enhanced superconductivity and mixed-dimensional behaviour in infinite-layer samarium nickelate thin films

Domain: neuroscience
Published: 2026-02-14
Editorial outcome: major_revision

Abstract
Rare-earth infinite-layer nickelates are emerging unconventional superconductors, with materials synthesis largely limited to early lanthanide compounds. Here, we report phase-pure samarium-based nickelate thin films on (LaAlO3)0.3(Sr2TaAlO6)0.7 (001) substrates, including the first demonstration of Sm1-xSrxNiO2. Co-doped compounds achieve a record-small c-axis parameter (3.26 Å) and superconducting transitions up to 32.5 K, revealing a clear correlation between decreasing c-axis parameter and increasing critical temperature across different rare-earth systems. Angle-dependent magnetoresistance shows a hybrid 2D/3D superconductivity with enhanced rare-earth 5d–Ni 3d orbital coupling, confirmed by resonant inelastic X-ray scattering. In addition, increasing Eu concentration drives a shift toward 3D superconductivity, and Eu-containing samples exhibit distinctive negative magnetoresistance even in the superconducting state. These findings advocate clear materials design principles for higher transition temperatures and exotic physics in infinite-layer nickelate superconductors through structural engineering of the rare-earth site.

Introduction
Superconducting infinite-layer (IL) nickelates, since discovered 1st as a subject of continuous research interest 2,3, featured by their potential of being an analogous model system to high-Tc cuprates 4 as well as by the essential reductive materials synthesis pathways to the unconventional Ni valence state 5. Their electronic structure displays a few salient features as compared to cuprates, including the unusual role of the rare-earth orbitals 6–8 and the belated multi-band nature 9–11 with the presence of a ‘self-doping’ effect 8,12 and clear electron pockets at the Fermi surface 9,10. This raises an interesting question regarding the role of the detailed configuration of the f electrons of the rare-earth cations and their affiliated local moment 13,14, and the possible interaction with the itinerant charges of 3d character 15, a hallmark of heavy-fermion physics. However, due to the significant growth challenges 16, materials synthesis efforts have largely been limited to the La- 17–19, Pr- 20,21 and Nd-series 22–26: many of the anticipated ‘Kondo-like’ physics 12,27,28 remain to be seen. Besides, given the discrepancies reported on the (an-)isotropic nature of different rare-earth IL nickelate systems 15, designing and preparing additional IL nickelates with tuneable interplanar spacings and detailed electronic configurations, and to investigate the dimensionality of their superconducting ground state are highly demanded.

Another motivation for extending the materials paradigm to late-lanthanide IL nickelates is to drive higher Tc. Indeed, a widely employed strategy for tuning Tc is to exert chemical pressure by utilising elements of smaller cationic radius 29,30. Such evolution of the structural tolerance parameter, enabled by the rare-earth sublattices, directly modulates the long-range chemical bonding configurations embedded in the lattice distortion, resulting in direct control of the electronic bandwidth and correlation strength 31–34. This has produced various competing and often intertwined emerging orders of both commensurate and incommensurate nature, which drastically correlate to local charge and/or spin instabilities, as well as superconductivity 4,35. In this regard, example systems with properties largely underpinned by such rare-earth dependence span across from famous cuprates 4 and pnictides 36, to intermetallic compounds 37, to the Ruddlesden-Popper (RP) nickelate of various nickel valence 38–40, the latter of which has been the focus of recent investigations 41,42.

For superconducting IL nickelates, hydrostatic high-pressure experiments indicate that a shrinking lattice parameter may contribute to a higher Tc 21. Furthermore, early work on Nd- and Pr-based IL nickelates on substrates of smaller lattice constants, such as (LaAlO3)0.3(Sr2TaAlO6)0.7 (LSAT) and NdGaO3 (NGO) corroboratively suggest an enhancement of Tc (for instance, for Nd0.8Sr0.2NiO2, the onset Tc is ~15 K on the SrTiO3 (001) substrate 22,23, ~19.3 K on the LSAT (001) substrate 24, and ~25.7 K on the NdGaO3 (110) substrate 25), in which the epitaxial strain may be instrumental 43, similar to that in the doped cuprate thin films 44. All these aspects highlight the intricate yet useful role of the smaller lattice spacing in IL nickelates for higher Tc, which warrants further investigations, particularly through introducing smaller rare-earth ions. In addition, discrepancies in magneto-transport behaviours, dimensionality, and the pertained magnetic footprints across La-, Pr-, and Nd-series IL nickelates, which stem from the variations in the spin configuration of the A-site ions 19–26,45, call for the quest for new members of the IL nickelate family.

With this notion and motivated by the recent observation of a Tc above 35 K in infinite-layer Sm1-x-y-zCaxSryEuzNiO2 nickelates on NdGaO3 (110) substrates 46, we have synthesised phase-pure Sm-based IL nickelate thin films on LSAT (001) substrates and carefully studied their superconducting transport properties and electronic structure. The highest Tc of 32.5 K has been observed. Atomically-resolved scanning transmission electron microscopy (STEM) images reveal the high quality of our films of up to ~ 9 nm with minimal stacking faults. In addition, driven by the fact that a compositional A-site and the distribution in cationic radius may also significantly affect superconductivity 47,48, with the emergence of ordered phases (spin and/or charge orderings) 4,49,50, we furthered our materials growth efforts to the synthesis of a combinational series of Sm-based superconducting IL nickelate thin films with A-site (in ABO2) composition of Eu, Sr, and Ca. In particular, superconducting Sm1-xSrxNiO2 have been demonstrated for the first time. We observed a generic mixed nature of both two- and three-dimensional superconductivity revealed by high-magnetic-field measurements across all samples. As the concentration of Eu increases, the system exhibits a tendency towards 3D superconductivity. This behaviour is in concert with an enhanced coupling of the rare-earth 5d and Ni 3d orbitals, corroborated by the resonant X-ray scattering measurements. Our results add new superconducting IL nickelates with high Tc into this intriguing materials family and underscore a fundamental trend of an increasing Tc value as the c-axis constant shrinks. These findings contribute to the understanding of the superconductivity mechanism, offering clear guidelines to uncovering additional IL nickelate superconductors with even higher Tc.

Results
Multiple sets of Sm-based IL nickelate films of thicknesses of ~10 nm with various compositions and a SrTiO3 capping layer of ~2 nm were prepared using pulsed laser deposition (PLD). We note a narrower growth parameter window for high-quality, hole-doped Sm nickelate as compared to that of Nd version. We further note that the introduction of Ca2+ doping renders a more complete reduction to the IL phase, similar to previous reports 11,24. Details on the samples synthesis can be found in Methods.

The precursor perovskite phases (Sm0.8Sr0.2NiO3, Sm0.74Ca0.01Sr0.19Eu0.06NiO3, Sm0.79Ca0.04Sr0.05Eu0.12NiO3 and Sm0.75Ca0.05Eu0.2NiO3, as well as others with different Ca concentrations) were grown on LSAT (001) substrates. The detailed characterizations are shown in the Supplementary Information (Fig. S1). The presence of prominent (001) reflections 16 and finite-size fringes around the main film peaks in the X-ray diffraction (XRD) scans (Fig. S1a) suggest a good film quality. The c-axis lattice parameters calculated from the data are 3.75 Å, 3.74 Å, 3.74 Å and 3.729 Å, respectively. These values are smaller than that in Nd1-xSrxNiO3 51, in line with a smaller tolerance factor. The corresponding resistivity curves ρ(T) of all samples are shown in Fig. S1b. Unlike previously reported 46, three samples show metallic behaviour down to low temperature (2 K), consistent with charge-induced suppression of the metal-insulator transition 51,52. The intrinsic metallic behaviours inform the high crystallinity of the precursor phase. We note a few anomalies of the slope change in the ρ(T) curve for Sm0.79Ca0.04Sr0.05Eu0.12NiO3 that may be attributed to the magnetism in the system: in particular, the local ‘plateau’ in resistivity at ~60 K and the local resistivity minimum at ~8 K. These transitions are more revealing on a derivative resistivity curve 53 (see Fig. S2 in the Supplementary Information).

The reduction to the IL phase was done using an in-situ setup (see Methods for details and Fig. S3 for the reduction process). Figure 1(a-d) illustrates the XRD scans of the films in the IL phase upon reduction: Sm0.8Sr0.2NiO2 (SSNO), Sm0.74Ca0.01Sr0.19Eu0.06NiO2 (SCSE0.06), Sm0.79Ca0.04Sr0.05Eu0.12NiO2 (SCSE0.12), and Sm0.75Ca0.05Eu0.2NiO2 (SCE0.2) (for simplicity and consistency, we name them as SSNO, SCSE0.06, SCSE0.12 and SCE0.2, respectively), all of which show significant (00l) film peaks, indicative of high quality, corresponding to the c-axis lattice constant of 3.307 Å, 3.296 Å, 3.26 Å and 3.273 Å, respectively. The SCSE0.12 represents the smallest c-axis parameter so far reported for the IL nickelate thin films, with 12% Eu and 4% Ca introduced to partially replace Sm and Sr, which have larger ionic radius 54. These samples all show superconductivity at low temperatures with a Tc onset of ~15–32.5 K (Fig. 1, e-h). In particular, superconductivity in Sm1-xSrxNiO2 was observed for the first time. All four samples do not show clear T-linear dependent behaviour, implying the doping level may not be at the optimal level 24. For SCE0.2, it is worth noting that we initially aimed at achieving single-phase superconducting Sm0.8Eu0.2NiO2; however, we noticed that the introduction of Ca is of crucial importance for obtaining high-quality IL nickelates under the current optimised reduction conditions, as illustrated in Fig. S4. Therefore, we have selected SCE0.2 for our study here.

The high quality of the samples is confirmed by STEM. Figure 1i and j displays cross-sectional high-angle annular dark field (HAADF) STEM images of an SSNO sample and an SCSE0.06 sample. From the images, despite occasional RP-type extended defects, single-phase IL nickelate layers of ~ 9 nm with homogeneous lattice coherency and sharp interfaces with the LSAT substrates can be clearly seen. The lattice spacings measured from the atomically resolved HAADF images are ~ 3.34 Å, ~ 3.28 Å for the SSNO and SCSE0.06 samples, generally consistent with the XRD results. To access the elemental information, the energy dispersive x-ray spectroscopy measurements were performed on a SCE0.2 sample. As clearly demonstrated in Fig. S5 and Table S1, the Sm, Eu, and Ni elements exhibit highly uniform distribution across the entire film region.

Magnetotransport measurements were performed in-house under magnetic fields up to 14 T perpendicular and parallel to the NiO2 planes for the samples (Fig. 2). The Meissner diamagnetic responses were recorded below a characteristic temperature TM of 5.4 K, 7.2 K, 4.6 K and 15.8 K for SSNO, SCSE0.06, SCSE0.12, and SCE0.2, respectively, in the mutual inductance measurements, with the driving and pickup coils vertically aligned above and below the sample (see Methods). The data is displayed in the insets of Fig. 2e–h. These TM values are slightly lower than zero-resistance Tc (defined as Tc,0), consistent with theoretical predictions for layered superconductors, where the flux penetration dynamics (governed by weak interlayer coupling) result in delayed emergence of complete diamagnetic shielding compared to resistive transitions 55. The resistivity datasets show a clear anisotropic superconducting characteristic (across Fig. 2a–h and more visual in Fig. 2i–l) independent of Tc value (Tc,50%, defined as the midpoint of the resistive transition, ρ(T)=ρ50%, where ρ50% is the 50% of the normal-state resistivity; see Fig. S6 in the Supplementary Information for definition), and can be largely captured by the Tinkham’s framework for 2D superconductors despite the requirement of the thickness being smaller than the Ginzburg-Landau (GL) coherence length (ξGL) at T=0 K. Extrapolation of a linear-T dependence of the upper critical field (μ0Hc2) close to Tc in the out-of-plane field (H//c) configuration (Fig. 2i–l) gives ξGL at T=0 K to be 3.3 nm, 2.8 nm, 2.1 nm, 1.7 nm for SSNO, SCSE0.06, SCSE0.12 and SCE0.2, respectively. The μ0Hc2(t) ~ (1 – t)1/2 (where t=T/Tc is the reduced temperature) behaviour close to Tc under in-plane field (H⊥c) for SSNO and SCSE0.06, as shown in Fig. 2i and 2j, is attributed to the dominant spin paramagnetic pairing breaking 56,57. For SCSE0.12 and SCE0.2, a different behaviour is observed and will be discussed later.

The generic anisotropy of the system across all samples can also be corroborated by an anisotropic field response of vortex motion: as illustrated in Fig. 2m-p, the field-dependent vortex activation energy, U0 ~ H-α, extracted from the T-dependent Arrhenius relationship based on the thermally-activated flux flow (TAFF) model 58 (see Fig. S7 in the Supplementary Information for definition). The data show a large difference of the power-law exponent α for the two field directions, indicating a strong anisotropy in vortex pinning strength in the Sm-based system. Figure 2n–p reveals a monotonic decrease in α values for H⊥c with increasing Eu concentration, indicative of a progressive strengthening of the interlayer coupling strength.

The samples with Eu as an effective component show interesting response to magnetic field: SCSE0.06, SCSE0.12 and SCE0.2 all display a sizable negative magnetoresistance in their normal state (insets of Fig. 2b–d for the perpendicular-field case, and Fig. S8b for the parallel-field case). The negative magnetoresistance is absent in the SSNO system but observed in Eu-containing samples, indicating an intimate connection between Eu doping and the negative magnetoresistance. This phenomenon may suggest a coupling between the local moment of the Eu f orbitals and the itinerant Ni 3d electrons.

To access the intrinsic μ0Hc2 and compare with other IL nickelates, high-magnetic-field measurements (see Methods) were performed on SSNO. The data (Fig. S9) shows a clear anisotropic behaviour in μ0Hc2(T), which is more reminiscent of that for La- and Pr-based IL nickelates 45,56,59, distinct from the Nd series 26,57. Indeed, when normalized against Tc at 0 T (defined as Tc(0T)) and plotted in comparison with data sets of all other rare-earth series (Fig. 3a, b), the μ0Hc2 - T dependence of the SSNO sample shows a clear violation of the Pauli limit (dash lines) and a strong deviation from the Nd-based IL nickelates, despite that the ground state of Sm3+ is a Kramer’s doublet with a 4f5 electron configuration and a possible enhanced magnetic permeability 15, which is similar to Nd3+. This observation further raises questions on the role that the rare-earth ions (in particular, the 4f electron configuration) may play in the unconventional nature of superconductivity in IL nickelates: a delicate balance between the detailed magnetic structure and the lattice exerted by chemical pressure.

The SSNO sample was further put on a rotator under the magnetic field for angle-dependent magnetoresistance (μ0Hc2 versus θ) measurements at T=5 K. For H//c (θ=0°), the magnetic field was large enough to suppress superconductivity: the normal-state can be attained, from which a μ0Hc2 can be extracted using 50% of the linear fit to the normal-state magnetoresistance (see Methods for details). The μ0Hc2 - θ data is shown in Fig. 3c and can be described by a combination of the Tinkham’s model for 2D superconductors and the anisotropic GL model for 3D superconductors using the following formula:

[H c2(θ) / (Hc2(θ) sin(θ)2 + β * Hc2(θ) cos(θ)2 + (1-β) * Hc2(θ) cos(θ)2)] = 1

where β is a dimension-less coefficient that informs how ‘3D’ the superconductor behaves, and θ is the angle of the magnetic field with respect to the normal of the sample surface, as illustrated in the inset of Fig. 3c. The best fit (red line) to the data yields a β of 0.366, indicating a mixed ‘2D’ and ‘3D’ character.

This behaviour is further validated by the Tc,50% - θ experiments, which can be performed by measuring Tc,50% from ρ(T) at variant θ values under a constant in-house magnetic field (at 9 T), as shown in Fig. 3d for SSNO. Here, the fitting was done in a similar manner, proportioning both the ‘2D’ and ‘3D’ contributions:

Tc(θ) = Tc(0T) + β' * [H0 = ∂Hc2c/∂T * cos2(θ) + γ sin2(θ)] 1/2 + (1-β') * [Hc2c - Tc(0T) * cos(θ) + Hc2? - Tc(0T) * sin2(θ)]

where β' is similarly defined as β above and γ represents the anisotropic mass ratio of the in-plane and out-of-plane electron motion. Note that the second and the last terms on the right-hand side of the formula correspond to the angular dependence of Tc given by the anisotropic GL 3D model and the Tinkham’s 2D model, respectively. Again, SSNO shows a clear mixed feature.

Following the same method, SCSE0.06, SCSE0.12 and SCE0.2 were all measured, and their Tc,50% - θ data, which are shown in Fig. 3e–g, respectively, suggest a mixed ‘2D+3D’ behaviour for nearly all samples. The overall increase in β' with higher Eu doping indicates a tendency toward a 3D superconducting ground state of the system. A further comprehensive polar rotation study on a full set of samples is needed to unveil the nature of such behaviours.

To further interrogate the possible implications of this ‘3D’ feature, at the electronic structure level, we performed Ni L3-edge resonant inelastic X-ray scattering (RIXS) measurements on an SCE0.2 sample (Fig. 3h–j). Consistent with earlier studies on other IL nickelate systems, the d-d excitations are observed in the energy-loss range of ~1 to 3 eV 6,43,60,61. The excitation at ~0.6 eV points to a sizable hybridization between the Ni 3d z2 and the rare-earth 5d z2, 5d xy states 6,8. The significantly enhanced intensity under the X-ray beam of π polarization at grazing-incidence geometry is consistent with a predominantly out-of-plane orbital symmetry.

This hybridization feature appears to be more intense 6,60,61, indicating that the reduced ionic radius of Sm and Eu effectively modifies the electronic structure, which could be crucial to the enhanced Tc (see Figs. S10 and S11 in Supplementary Information for more analysis).

The negative normal-state Hall coefficient (RH) of the SCSE0.12 and SCE0.2 samples display no sign change (Fig. 4a) down to low temperature, despite a higher total dopant concentration (x+y+z=0.21 for SCSE0.12 and x+y=0.25 for SCE0.2) as compared to that of SSNO (x+y+z=0.2), suggesting a lower effective hole-doping level. Such effect can also be seen for the SCSE0.06 sample (x+y+z=0.26), where the crossover temperature (Tcross) for the sign change in RH, is not far from that of SSNO. These are in line with the co-existence of Eu2+ and Eu3+ states 62 and a shift of the superconducting ‘dome’ toward higher doping in Eu-doped infinite-layer compounds 26. We further note that the all-negative RH measured in our SCE0.2 sample contrasts with the sign change at low temperatures observed in a similar thin film on NGO 46. This difference corroborates the multi-band nature of the IL nickelates, despite that a linear field-dependent Hall resistivity, ρyx(H), has been observed in our samples 62, from which RH was extracted. In Fig. 4b, we further plot Tc, Tcross as a function of an estimated effective hole doping level. The data points are largely located within the yellow-shaded region, for which a clear correlation between Tc and c-axis constant reveals the lattice motif (i.e. distance between Ni-O planes) to superconductivity and suggests the key role of the interplane coupling in mediating Tc. As indicated in previous studies 21,63, there is a general enhancement of superconductivity as the c-axis lattice constant shrinks: we can see from the figure that as the average c-axis parameter decreases from ~3.43 Å for La1-xSrxNiO2 to ~3.28 Å for Sm-based compounds, Tc increases from ~10–12 K to above 32 K, making them the ‘high-Tc’ systems surveyed from ambient pressure 21,46,64. We note that the data points are gathered from different IL systems. The highest Tc was observed in SCE0.2 with a c-axis of 3.273 Å. The red rhombus-shaped points in the figure are data from this work while other data are extracted from Refs. 17–26, 46. Data from this work are presented in both the main text and Supplementary Information.

Methods
Thin-film growth
The polycrystalline Sm1-x-y-zCaxSryEuzNiOδ ceramic targets were prepared by pelletising a mixture of Sm2O3, Eu2O3, SrCO3, CaCO3, and NiO powders, followed by decarbonisation step at 1250°C for 12 hours. After that, the targets were ground, re-pelletised and then sintered twice at 1300°C and 1270°C for 12 hours each. A slightly lower temperature for the final sintering was used to avoid a large volume change of the target due to thermal cycles. Using the targets, thin films with a thickness of ~10 nm were deposited on LSAT (001) substrates using a KrF excimer laser (λ=248 nm) in a pulsed laser deposition system. The growth temperature is 600°C measured by a thermocouple. The oxygen pressure was maintained at 100 mTorr during the growth. The laser fluence was 2.6 J/cm2 and the repetition frequency is 0.2–0.3 Hz on growth Sr-doped Sm-based nickelate films and 3 Hz repetition frequency for other films. It is noted that this frequency was adopted after a careful study on the frequency dependence and is more suitable for the phase formation of the precursor nickelates. High repetition frequency will lead to a diminution in the peak intensity of the (001) peak and induce a shift of the (002) peak position towards a lower angular value. A low laser fluence of 0.6 J/cm2 was used to grow the epitaxial SrTiO3 capping layer of ~2 nm.

Additional information on the growth of the perovskite precursor films
As a comparison, epitaxial Pr0.8Sr0.2NiO3 films were reproducibly obtained at 600°C, 100 mTorr oxygen, 2.0 J/cm2, and 3 Hz, with XRD confirming phase-pure perovskite. Under the same conditions, Sm0.8Sr0.2NiO3 films remained amorphous. By reducing the laser repetition rate to 0.3 Hz and increasing laser fluence, perovskite crystallinity emerged at 2.6 J/cm2. Higher fluence or frequency degraded film quality. Therefore, the optimal condition for Sm0.8Sr0.2NiO3 growth was identified as 2.6 J/cm2 at 0.3 Hz. Following similar procedures, it was found that the SCE0.2 sample crystallised best under 2.6 J/cm2 at 3 Hz.

Topotactic reduction
The reduction to the IL phase using CaH2 powders was conducted in a vacuum reduction chamber. The resistance of the sample was monitored in a two-probe configuration in real-time. When the resistance reaches the minimum, the reduction is regarded as complete. The reduction temperature measured by a thermocouple is ~ 270°C – 310°C and the total annealing time is ~ 0.5−1.5 hours. Detailed information is provided in the Supplementary Information.

X-ray diffraction and RIXS characterizations
The X-ray diffraction θ–2θ symmetric scans of the films were obtained by a Rigaku SmartLab (9 kW) high-resolution X-ray diffractometer with the wavelength of the X-ray being 0.154 nm. The Ni L-edge RIXS measurements were conducted at the 41A beamline of the Taiwan Photon Source (TPS) 69. All RIXS spectra were collected at T=30 K, with a grazing-incidence angle of 10° and a scattering angle of 150°. The energy resolution, determined from the elastic scattering of amorphous carbon tape, was ~68 meV.

STEM sample preparation and characterization
Cross-sectional STEM specimens were prepared using a focused ion beam (FIB) technique with the Helios G4 system. To protect the sample surface during ion beam etching, a 2 μm-thick carbon layer was deposited beforehand. The preparation process involved a series of milling and lift-out steps, after which the lamellae were carefully extracted and mounted onto Cu grids for further characterization. To minimize surface damage, a final milling step was performed at 2 keV. HAADF images were acquired using an aberration-corrected FEI Titan Themis G2 operating at 300 kV. For STEM imaging, the convergence semi-angle was set to 30 mrad, while the collection semi-angle for HAADF imaging ranged from 50 to 200 mrad. Energy-dispersive X-ray spectroscopy (EDX) analysis was performed using a JEOL JEM-ARM200F NEOARM transmission electron microscope, equipped with a cold field-emission gun and a spherical aberration (Cs) corrector. The microscope was operated at an accelerating voltage of 200 kV to optimize X-ray excitation efficiency and spatial resolution. The spectra were acquired with a typical collection time of 10-15 minutes per map ensures sufficient counting statistics.

In-house Transport Measurements
Wire connections for electrical transport measurements using the standard four-probe method were made by aluminum ultrasonic wire-bonded contacts. For measuring perovskite precursor phase, gold wires were bonded to the sample with silver paste to avoid work function mismatch. Resistivity and Hall-effect measurements were performed at temperatures down to 2 K and under magnetic fields up to 14 T using a Physical Properties Measurement System from Quantum Design Inc. Two-coil mutual inductance experiments were conducted with the driving and pickup coils aligned vertically above and below the thin film samples. Polar angle dependent measurement is done on a rotation rod with Keithley 6220&2182A system.

High-magnetic-field measurements
High-field magnetoresistance measurements were performed at the High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei, China, using the Steady High Magnetic Field Facilities (WM5) 70 with a maximum field of 35 T and a base temperature of 1.5 K. Resistance was measured using SR830 lock-in amplifiers with a built-in a.c. current source. μ0Hc2,50% is defined as the point at which the magnetoresistance ρ(H) curves intersect with an adjusted linear fit. Similar to the definition for ρ(T) in Fig. S6, this adjusted fit is attained by incorporating 50% of both the slope and the intercept of the linear fit to the normal-state data at θ=0°.

Data availability
The data that support the findings of this study are available within the article and the Supplementary Information. All data generated in this study are provided in the Source Data file. Source data are provided with this paper (https://doi.org/10.6084/m9.figshare.31005019).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript presents a significant advancement in the field of infinite-layer (IL) nickelates by reporting the successful synthesis and characterization of superconducting Sm-based compounds, including the first demonstration of Sm₁₋ₓSrₓNiO₂ and co-doped variants with Eu and Ca. The authors observe a high Tc of 32.5 K, correlated with a reduced c-axis parameter, and provide compelling evidence of mixed 2D/3D superconductivity through magnetotransport and resonant inelastic X-ray scattering (RIXS). This work expands the family of IL nickelates and offers valuable insights into the structural and electronic factors governing superconductivity.\nWhile the study is well-executed and merits publication, the following points should be addressed to strengthen the manuscript and provide greater clarity for the research community:\n1. The authors note that the growth of high-quality, hole-doped Sm nickelates has a narrow parameter window (e.g., laser fluence, frequency, oxygen partial pressure). Given the critical importance of synthesis in stabilizing IL nickelates, it would be highly beneficial to include a discussion of how these parameters differ from those used for La-, Pr-, or Nd-based IL nickelates, which could guide other researchers in reproducing these results.\n2. The authors attribute the resistivity plateau at ~60 K in Sm₀.₇₉Ca₀.₀₄Sr₀.₀₅Eu₀.₁₂NiO₃ to possible antiferromagnetic ordering of Sm³⁺. However, this feature is absent in Sm₀.₇₄Ca₀.₀₁Sr₀.₁₉Eu₀.₀₆NiO₃, suggesting composition-dependent effects. Is there any magnetic susceptibility data to corroborate the proposed AFM ordering?\n3. The study relies on A-site doping (Sm, Sr, Eu, Ca), but no direct elemental analysis (e.g., EDX, ICP-MS, or XPS) is provided to confirm the actual doping levels. Including STEM-EDX mapping or XPS depth profiling would strengthen the claim of homogeneous doping.\n4. The authors state that Ca doping is crucial for obtaining high-quality IL films but do not explain why. Does Ca²⁺ (smaller ionic radius) improve structural stability by reducing lattice strain? Could Ca act as a charge compensator, mitigating defect formation during reduction?\n5. The authors propose that Eu²⁺ local moments may contribute to field-enhanced superconductivity and negative magnetoresistance, while Sm³⁺ is suggested to exhibit AFM ordering. Is there X-ray magnetic circular dichroism (XMCD) or muon spin rotation (μSR) data to confirm the magnetic states of Eu/Sm? How do these moments interact with superconductivity?\n6. The authors observe a general trend: smaller c-axis → higher Tc. Would a larger tensile strain further enhance Tc, or does it destabilize the IL phase? A comparison with prior studies on NdGaO₃ (110) (ref. 46, Tc ~35 K) and other studies of strain films could help reconcile differences in Tc.\n7. Many discussions hinge on the valence states of dopants (e.g., Eu²⁺/Eu³⁺, Sm³⁺), but no experimental verification is provided. XPS or EELS measurements could confirm the Eu and Sm oxidation states.", "reviewer_2": "The authors present important results by further in-depth researches about the SmNiO2 superconducting systems. They claim that the decreasing c-axis parameter is related to the increasing critical temperature and the 3D superconductivity from the enhanced coupling between the rare-earth 5d and Ni 3d orbitals is key for the enhancement of Tc. About the challenging growth of Nickelate films, they found that the introduction of Ca is important for obtaining high quality 112 phase. These findings present important understanding about the key physical factors for high critical temperature in infinite-layer nickelate systems, significantly advancing the extensively discussions of nickelate superconductors. Given these considerations, I believe their findings are suited for publication in Nature Communications. However, there are still several data analysis and discussions that require further improvement, before the manuscript can be considered for publication.\n(1) For the Sm0.75Ca0.05Eu0.2NiO2 superconducting systems, the reported highest Tc,0 is up to 31 K on NGO(110) substrate (Nature 2025, 642 (8066), 58–63.), where the c of 3.27 Å is very close to your best system with c of 2.273 Å. However, the substrate was changed to LAST(001) and the related Tc,0 of 20.2 K is lower in this work. Is the LAST substate important here for your conclusions? On the other hand, the superconductivity is missing in the buck Sm0.8Sr0.2NiO2 (J.Phys.:Condens.Matter 33 265701). Are there any key interfacial effects for deciding the superconductivity?\n(2) For the sample SCSE0.12, there is no signature about the positive normal-state Hall coefficient. Is it a typical electron-doped superconductor? Is the RH of normal carriers still negative during the superconducting transition? If it is still negative, the Sm0.75Ca0.05Eu0.2NiO2/LSAT in this work shows an electron dominated transport. However, the Sm0.75Ca0.05Eu0.2NiO2/NGO (Nature 2025, 642 (8066), 58–63.) shows a hole dominated transport. What is the different between two systems? Is there possibility that both holes and electrons contribute to the superconductors in this system?\n(3) The 2D superconducting feature of infinite-layer nickelate superconductor has been suggested by the investigation of the superlattice (Nat. Commun. 2024, 15 (1), 10215.). For their SmNiO2 systems, they claimed that there is an observed 3D superconducting behavior affected by the coupling between Eu 5d and Ni 3d orbits and it affect the electronic structure for the enhancement of Tc. Did authors try more Eu for higher Tc? What is the role of Sm for 3D behavior? Is it possible to compare the polar rotation angle dependent upper critical field for different systems to support the conclusion?\n(4) As the authors mentioned in Line 181, the Tc is extracted from the midpoint ρ(Tc) = ρ50%. Why is the Tc of SESC0.2 in this work in Fig 4c close to the Tc,onset of 32.5 K in Figure 1? And, the Tc of the SESC in ref.46 in Figure 4c is close to reported Tc,0 of 31K. What is the definition of Tc in Figure 4c?\n(5) Why is there no the temperature dependent resistivity of SCSE0.2 (113 phase) in Figure S1b? Considering the spin disorder effects of Sm and Eu mentioned in Figure S2, is there a lager upturn for negative dρ/dT at low temperature due to the more Sm and Eu?\n(6) There are some typos:\nFor example: (1) the figure 2n mentioned in main text is missing; (2) Why is the Sr missing in the legend of figure 3a and b? (3) in fig. S2, the unit is missing for the y-axis and the Fig 1B should be Fig. S1b in figure caption;", "reviewer_3": "In this manuscript, Yang et al. report the synthesis of high-quality Sm-based infinite-layer nickelate thin films, achieving a superconducting transition temperature (Tc) up to 32.5 K. Compared to the recently reported Tc above 35 K in Sm1-x-y-zCaxSryEuzNiO2 films grown on NdGaO₃ (110) substrates (Ref. 46), this study explores films grown on LSAT (001) substrates and reveals the coexistence of two-dimensional and three-dimensional superconductivity using high-magnetic-field transport measurements. The work represents a significant advancement in the growth of superconducting infinite-layer nickelates and proposes a potentially promising route to achieving higher Tc in these systems.\nWhile the study is of high technical quality, several important aspects of the data interpretation, presentation, and scientific framing require clarification and improvement before the manuscript can be considered suitable for publication in Nature Communications.\n1. The claimed correlation between increasing Tc and decreasing c-axis lattice constant across different rare-earth substituted systems is not convincingly supported by the data. As shown in Figure 4, several data points deviate significantly from the suggested linear trend, such as those for LSNO from Ref. 18. Even within the current study, the SCSE samples appear to form a dome-shaped trend rather than a monotonic one. Specifically, SCSE0.12 has the smallest c-axis lattice constant (3.26 Å), but its Tc is not the highest. This outlier is not discussed anywhere in the text.\nMoreover, while the SCSE film on NGO in ref. 46 shows the highest Tc, its c-axis lattice constant is not the smallest. These inconsistencies undermine the claim of a direct correlation.\n2. The manuscript attempts to establish a unified trend between the superconducting transition temperature and the c-axis lattice constant by combining data from multiple compounds SSNO, SCSE0.06, SCSE0.12, and SCE0.2, that contain different combinations of rare-earth and alkaline-earth dopants. These systems differ not only in chemical composition but also in doping levels, making a direct comparison problematic. For example, in Nd1-xSrxNiO2 (Nature 619, 288–292 (2023)), increasing Sr doping leads to an increase in the c-axis lattice parameter, whereas Tc exhibits a dome-shaped dependence, rather than a monotonic trend. Within the current dataset, the variation in Tc does not follow a consistent correlation with c-axis values. Given the differences in chemical composition and doping levels, it is questionable whether multiple compounds can be meaningfully combined into a single trend. The authors should clarify the rationale for aggregating these distinct materials and consider reanalyzing the data to better reflect the individual effects of specific dopants.\n3. The RIXS spectra presented for the SCE0.2 sample reveal a feature at ~0.6 eV, attributed to hybridization between rare-earth and Ni orbitals, consistent with previous observations (e.g., Nat. Mater. 19, 381–385 (2020)). However, in prior studies, this feature resonates at the shoulder A′ peak of the Ni L3 XAS spectrum, rather than at the main peak. The authors need to provide XAS data for their sample to enable direct comparison and support the resonance assignment.\nThe claim of enhanced hybridization between rare-earth 5d and Ni 3d orbitals also needs clarification. It is unclear which system this enhancement is being compared to. Is the comparison made against Nd-based nickelates or some other reference? Since RIXS absolute intensity is not reliable, it would be more appropriate to compare the relative intensity of the hybridization feature with respect to the dd excitations.\nThe conclusion regarding an \"enhancement in the electronic bandwidth\" (line 259) based solely on the increased hybridization peak intensity is ambiguous and speculative. The authors should provide quantitative or theoretical analysis to support this claim, or soften the interpretation accordingly.\n4. The authors state that Sm-based nickelates have a narrower growth window than Nd-based ones, but the discussion of synthesis parameters is too general. Given the complexity of the synthesis process (involving multiple steps and fine-tuned parameters), the authors should explicitly identify which parameters are most critical. Clearer exposition in the Methods section would enhance reproducibility and contribute to the broader effort in optimizing nickelate growth.\n5. Since both this study and Ref. 46 use films of similar composition (Sm1-x-y-zCaxSryEuzNiO2), it would be helpful for the authors to discuss why the Tc is lower on LSAT (001) substrates compared to NGO (110), as reported in Ref. 46. Differences in strain, lattice mismatch, or interfacial effects could be contributing, and a brief discussion of these factors would add valuable context.\nHere are some Minor Comments:\na. Line 240: “where β′ is similarly defined as above”. Please clarify what “above” refers to, or restate the relevant definition.\nb. Line 607: The insets of panels (i–l) are currently labeled incorrectly; they should correspond to panels (e–h).\nc. Figure 4c: The figure shows four samples, but five data points are plotted. Please clarify.\nd. Figure 4c: The acronym “SESC” should be corrected to “SCSE.”\ne. Figure S3: With increasing Ca doping in Sm0.8-xCaxEu0.2NiO2 (x = 0, 0.02, 0.05, 0.10), the c-axis lattice constant is expected to decrease due to the smaller ionic size of Ca. However, an unexpected increase is observed for x = 0.10. This deviation should be discussed.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_5": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_6": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Point-to-Point Response to Reviewers’ Comments\nReviewer #1 (Remarks to the Author):\nComments:\nThe manuscript presents a significant advancement in the field of infinite-layer (IL)\nnickelates by reporting the successful synthesis and characterization of\nsuperconducting Sm-based compounds, including the first demonstration of Sm\n1-\nSr NiO and co-doped variants with Eu and Ca. The authors observe a high Tc of\nx x 2\n32.5 K, correlated with a reduced c-axis parameter, and provide compelling\nevidence of mixed 2D/3D superconductivity through magnetotransport and\nresonant inelastic X-ray scattering (RIXS). This work expands the family of IL\nnickelates and oTers valuable insights into the structural and electronic factors\ngoverning superconductivity.\nWhile the study is well-executed and merits publication, the following points\nshould be addressed to strengthen the manuscript and provide greater clarity for\nthe research community:\nResponse:\nWe sincerely thank the reviewer for their thorough evaluation of our manuscript\nand their positive appraisal of our findings, especially for our providing compelling\nevidence of mixed 2D/3D superconductivity through magnetotransport and RIXS.\nIn response to the reviewers' suggestions, we have revised the manuscript\naccordingly as detailed below.\nComments:\n1. The authors note that the growth of high-quality, hole-doped Sm nickelates has\na narrow parameter window (e.g., laser fluence, frequency, oxygen partial\npressure). Given the critical importance of synthesis in stabilizing IL nickelates, it\nwould be highly beneficial to include a discussion of how these parameters diTer\nfrom those used for La-, Pr-, or Nd-based IL nickelates, which could guide other\nresearchers in reproducing these results.\nResponse:\nWe thank the reviewer for the suggestion. It is indeed of vital importance to discuss\nmore about the growth challenges, in particular in the context of the growth\nparameters for the precursor perovskite phase (as it holds the key to the high\n1\nquality of the final product infinite-layer phase) in comparison with those used for\nother rare IL nickelates, such as Pr Sr NiO . Here, we provide comparative\n0.8 0.2 2\nrelated information on the growth attempts for Pr Sr NiO and include more\n0.8 0.2 3\ndiscussions and data in the Methods section and Supplementary Information.\nGrowth Conditions for Pr Sr NiO and Sm Sr NiO Thin Films for Comparison\n0.8 0.2 3 0.8 0.2 3\nPurpose\nHigh-quality epitaxial Pr Sr NiO precursor films were grown under optimized\n0.8 0.2 3\nconditions: substrate temperature of 600 °C, oxygen partial pressure of 100 mTorr,\nlaser fluence of 2.0 J/cm², and repetition rate of 3 Hz (Figure R1a). X-ray di]raction\n(XRD) confirmed phase-pure perovskite formation, with sharp (002) reflections at\n𝜃 of ~ 48.7° and 48.5° on SrTiO and LSAT substrates, respectively.\n0.8 0.2 3\nfilms on LSAT substrates, no perovskite peaks were detected by XRD (the bottom\ncurve in Figure R1b). Instead, substrate discolouration and X-ray reflectivity (XRR)\nfringes (Figure R1c) suggested the deposition of a thick amorphous layer, likely due\nto an excessively high growth rate. To mitigate this, the deposition laser frequency\nwas reduced to 0.3 Hz, but no crystalline perovskite phase appeared. Considering\nthe larger atomic mass of Sm, the laser fluence was incrementally increased while\nthe repetition rate was kept at 0.3 Hz. Crystallisation of the SSNO perovskite phase\nfirst appeared at 2.2 J/cm2 (Figure R1b). At higher energy (2.7 J/cm2) or increased\nrepetition rate, secondary phases started to form and crystallinity deteriorated.\nOptimal SSNO precursor films with good crystallinity were therefore obtained at\n2.6 J/cm² and 0.3 Hz. All Sr-containing films reported here were grown under these\noptimised conditions. For perovskite precursor films of the SCE sample, it was\n0.2\nfound that a growth frequency of 2.6 J/cm2 and 3 Hz could obtain perovskite\nprecursor phase thin films with good crystallinity.\n(a) (b) (c)\nFigure R1. (a) XRD patterns and growth parameters of Pr Sr NiO perovskite\n0.8 0.2 3\nprecursor thin films epitaxially grown on the SrTiO and LSAT substrates. (b) XRD\n3\npatterns and growth parameters for Sm Sr NiO perovskite precursor thin films\n0.8 0.2 3\n2\non LSAT substrates. (c) X-ray reflectivity (XRR) data for the Sm Sr NiO thin films\n0.8 0.2 3\nin (b). In Figure R1(a) and (b), the peaks near 44° are from the background of the\nold instrument in our laboratory. The o]icial XRD data in the article are measured\nusing another di]ractometer.\nPer the reviewer’s request and to reflect our discussion here, we have inserted the\nfollowing separate sub-section into the Methods section:\nOn Page 11,\n“Additional Information on the Growth of the Perovskite Precursor Films\nAs a comparison, epitaxial Pr Sr NiO films were reproducibly obtained at\n0.8 0.2 3\n600 °C, 100 mTorr oxygen, 2.0 J/cm2, and 3 Hz, with XRD confirming phase-pure\nperovskite. Under the same conditions, Sm Sr NiO films remained amorphous.\n0.8 0.2 3\nBy reducing the laser repetition rate to 0.3 Hz and increasing laser fluence,\nperovskite crystallinity emerged at 2.6 J/cm2. Higher fluence or frequency\ndegraded film quality. Therefore, the optimal condition for Sm Sr NiO growth\n0.8 0.2 3\nwas identified as 2.6 J/cm2 at 0.3 Hz. Following similar procedures, it was found\nthat the SCE sample crystallised best under 2.6 J/cm2 at 3 Hz.”\n0.2\nComments:\n2. The authors attribute the resistivity plateau at ~60 K in\nSm Ca Sr Eu NiO to possible antiferromagnetic ordering of Sm³⁺.\n0.79 0.04 0.05 0.12 3\nHowever, this feature is absent in Sm Ca Sr Eu NiO , suggesting\n0.74 0.01 0.19 0.06 3\ncomposition-dependent eTects. Is there any magnetic susceptibility data to\ncorroborate the proposed AFM ordering?\nResponse:\nWe thank the reviewer for the valuable comments. In the submitted version, we\nwished to point out these interesting ‘anomalies’ in the ρ(T) curve for this particular\nsample (Sm Ca Sr Eu NiO ), to perhaps stimulate more discussions on\n0.79 0.04 0.05 0.12 3\nthe presence of the (likely) magnetic Sm and/or Eu. We wanted to emphasise an\ninteresting contrast: the metallic behaviour with these ‘anomalies’ was not\nobserved in the previous related work (Ref. 46, S. L. E. Chow et al., 2025, Nature\n642, 58). After reviewing the critical comments from the reviewers, we now would\nlike to refrain from speculations based on this single curve without providing more\nexperimental evidence. We have revised this part of the discussion:\nOn Page 5, “We note a few anomalies of the slope change in the ρ(T) curve for\nSm Ca Sr Eu NiO that can be attributed to the magnetism in the system.\n0.79 0.04 0.05 0.12 3\nordering temperature of Sm, while the local resistivity minimum at ~ 8 K correlates\nwith a spin-disorder-related metal-insulator transition induced by a partial\nsubstitution of Sm with Eu53. These transitions are more revealing on a derivative\nresistivity curve (see Figure S2 in the Supplementary Information)” into the\nfollowing:\n“We note a few anomalies of the slope change in the ρ(T) curve for\nSm Ca Sr Eu NiO that may be attributed to the magnetism in the system:\n0.79 0.04 0.05 0.12 3\nin particular, the local ‘plateau’ in resistivity at ~ 60 K and the local resistivity\nminimum at ~ 8 K. These transitions are more revealing on a derivative resistivity\ncurve53 (see Figure S2 in the Supplementary Information).”\nIn addition, we have deleted the sentence “For Sm Ca Sr Eu NiO , the\n0.79 0.04 0.05 0.12 3\nlocal ‘plateau’ in resistivity at ~ 60 K may correspond to an antiferromagnetic\nordering temperature of Sm, while the local resistivity minimum at ~ 8 K correlates\nwith a spin-disorder-related metal-insulator transition induced by a partial\nsubstitution of Sm with Eu53. These transitions are more revealing on a derivative\nresistivity curve (Figure S2)” and “The sign change at 7.5 K may be attributed to the\nspin disorder e]ects of Sm and Eu1. The change of concavity and convexity at 54 K\nmay be linked to a magnetic ordering transition of Sm” in the Supplementary\nInformation.\nComments:\n3. The study relies on A-site doping (Sm, Sr, Eu, Ca), but no direct elemental\nanalysis (e.g., EDX, ICP-MS, or XPS) is provided to confirm the actual doping levels.\nIncluding STEM-EDX mapping or XPS depth profiling would strengthen the claim\nof homogeneous doping.\nResponse:\nWe thank the reviewer for this valuable suggestion. We concur with this request\nand have conducted the STEM-EDX measurements on an SCE sample. The data\n0.2\nis now shown in Figure R2. From the figure, one can clearly see that the\ndistributions of Sm, Eu, and Ni elements are highly uniform across the entire film.\nThis result provides direct evidence of a homogeneous doping e]ect and has now\nbeen included in the Supplementary Information as Figure S5.\nSCE thin film while performing the energy-dispersion x-rays spectroscopic (EDX)\n0.2\nmeasurements. (b–d) EDX mapping of Sm, Eu and Ni, respectively, of the same\nregion in (a).\nAlthough typically with a large error bar, the EDX analysis, as shown below in Table\nR1, suggests doping concentrations in line with the nominal chemical\ncomposition.\nTable R1. Quantitative analysis from the EDX data.\nsection on structural characterisations in the revised manuscript:\nOn Page 5-6, “To access the elemental information, the energy dispersive x-ray\nspectroscopy measurements were performed on a SCE sample. As clearly\n0.2\ndemonstrated in Figure S5, the Sm, Eu, and Ni elements exhibit highly uniform\ndistribution across the entire film region” and we have also added Figure R2 as\nFigure S5 and Table R1 as Table S1 as additional information in the revised\nSupplementary Information.\nFurther information regarding STEM-EDX experiments is also added into the\nMethods section:\nOn Page 12, “Energy-dispersive X-ray spectroscopy (EDX) analysis was performed\nusing a JEOL JEM-ARM200F NEOARM transmission electron microscope,\nequipped with a cold field-emission gun and a spherical aberration (Cs) corrector.\nThe microscope was operated at an accelerating voltage of 200 kV to optimize X-\nray excitation e]iciency and spatial resolution. The spectra were acquired with a\ntypical collection time of 10-15 minutes per map ensure su]icient counting\nstatistics.”\nComments:\n4. The authors state that Ca doping is crucial for obtaining high-quality IL films but\ndo not explain why. Does Ca²⁺ (smaller ionic radius) improve structural stability by\nreducing lattice strain? Could Ca act as a charge compensator, mitigating defect\nformation during reduction?\nResponse:\nWe thank the referee for the important questions. We would like to emphasise that\nthe precursor perovskite phase of all films exhibits good crystallinity. For the 112-\nphase synthesised via topotactic reduction (Supplementary Figure S4, a-d), the\nintroduction of Ca2+ ions markedly enhanced the structural integrity of the\nresulting infinite-layer phase upon topotactic reduction. In other words, adding\nCa2+ facilitates the reduction process. This improvement likely originates from the\ndynamics by lowering the kinetic barriers for H+ and O2- transport across the film\nwhen introducing dopants, in line with previous observations (see for instance, the\nSupplementary Information of Ref. 24, K. Lee et al., 2023, Nature 619, 288; Ref. 11,\nZ. Dong et al., 2025, Nano Letters 25, 1233). Considering that both Sr2+ and Ca2+\n(with rather di]erent ionic sizes) show similar e]ects, we incline to believe that the\nchange of lattice strain is not a key factor.\nWe also wish to note that, as observed in the Sr-doped LaNiO system (Nie et al.,\n3\n2025, Newton 1, 100006), X-ray absorption spectroscopy (XAS) analysis reveals\nsignificant changes in the electronic structure of Ni after reduction, including a\ndecrease in the intensity of the Ni-L₃ absorption edge, disappearance of the O-K\nedge pre-peak, and a shift in the O-K edge peak (adapted below as Figure R3).\nThese results indicate that Sr2+ ions assist in stabilising the valence state of Ni as\nwell as the infinite-layer structure, essentially in line with that suggested by the\nreviewer. We believe that Ca2+ ions may play a similar role in the currently\ndiscussed SmNiO system.\nmain text.\nOn Page 4, “We further note that the introduction of Ca2+ doping renders a more\ncomplete reduction to the IL phase, similar to previous reports11,24.”\nFigure R3. (a), (b) The synchrotron-based XAS of the (a) Ni-L and (b) O-K edges for\nthe La Sr NiO precursor, the ex-situ CaH reduced La Sr NiO , and the in-situ\n0.8 0.2 3 2 0.8 0.2 2\nAl-reduced La Sr NiO . (Adapted from Nie et al., 2025, Newton 1, 100006)\n0.8 0.2 2\nComments:\n5. The authors propose that Eu²⁺ local moments may contribute to field-enhanced\nsuperconductivity and negative magnetoresistance, while Sm³⁺ is suggested to\n7\nexhibit AFM ordering. Is there X-ray magnetic circular dichroism (XMCD) or muon\nspin rotation (μSR) data to confirm the magnetic states of Eu/Sm? How do these\nmoments interact with superconductivity?\nResponse:\nWe thank the referee for the important questions and valuable suggestions.\nSimilar to our response to Point 2 above, these proposed scenarios regarding the\npossible presence of the local moments were speculative. To be more objective\non the data, we would like to maintain consistency with the statement in the\nabstract: “Furthermore, we observe distinctive negative magnetoresistance even\nin the superconducting state in the europium-containing samples”. As shown in\nour manuscript, negative magnetoresistance is absent in the SSNO system but\nconsistently observed in Eu-containing samples. This observation suggests an\nintimate connection between Eu doping and negative magnetoresistance. The\n“field-enhanced superconductivity” (quoted in the manuscript) was referring to\nthe slight increase of H shown in Figure 2, k and l; but indeed, this was not\nc2\nobvious in all samples containing Eu. To avoid ambiguity, we have now removed\nthe related wording and discussion, and revised the text accordingly.\nIn specific, on Page 6-7, we replace “Another thing to note is that both SCSE and\n0.12\nSCE exhibit a weak but clear ‘field-enhanced superconductivity’ when H⊥c\n0.2\n(Figure 2, g and k, and Figure 2, h and i, respectively)” with “The negative\nmagnetoresistance is absent in the SSNO system but observed in Eu-containing\nsamples, indicating an intimate connection between Eu doping and the negative\nmagnetoresistance”.\nAs we briefly discussed on Page 9, we believe that the tendency of magnetic\nmoments (Eu2+) to align under an external field may be the reason for the negative\nmagnetoresistance that we observed. We wish to note that the implementation of\nmuon spin rotation (μSR) spectroscopy, despite significant importance as noted\nby the reviewer, presents significant challenges for the current system due to the\nultrathin nature of nickelate films (~ 9 nm) and the STO capping layer (a few u.c.).\nThe XMCD measurements, on the other hand, would indeed provide valuable\ninformation on magnetic ordering (if any), the data of which we unfortunately do\nnot have at the moment. We are currently submitting proposals to actively apply\nfor XMCD beam time. Given the heavy involvement of the XMCD data analysis and\nthe consideration that it is not central to our main conclusion in this work, we\nsincerely hope that the reviewer could understand that the XMCD investigation\nwill be presented in a separate study.\nOn Page 10, “Whether these Eu2+/Eu3+ ions form an ordered phase and/or exhibit a\nnon-trivial magnetic ground state present interesting questions to studies like\nresonant inelastic X-ray scattering26,61,65-68” into\n“Whether these Eu2+/Eu3+ ions form an ordered phase and/or exhibit a non-trivial\nmagnetic ground state present interesting questions to studies like x-rays\nmagnetic dichroism and/or resonant X-ray scattering26,61,65-68”\nNotably, in a separate study by our group (arXiv:2508.14666 (2025), Figure 2c and\n2d), the magnetic hysteresis measurements demonstrated that SCE thin films\n0.22\nexhibit paramagnetic behaviour. These results suggest the absence of a long-\nrange magnetic order in films with relatively low Eu content.\nComments:\n6. The authors observe a general trend: smaller c-axis → higher Tc. Would a larger\ntensile strain further enhance Tc, or does it destabilize the IL phase? A comparison\nwith prior studies on NdGaO₃ (110) (ref. 46, Tc ~35 K) and other studies of strain\nfilms could help reconcile diTerences in Tc.\nResponse:\nWe thank the referee for the valuable suggestions. As exemplified in our main text\n(Page 3) for Nd Sr NiO superconducting films and as shown in Figure 4c of the\n0.8 0.2 2\nmanuscript (𝑐 >𝑐 >𝑐 ) (Refs. 24, 25), the infinite-layer\n!\" $%&'(! !\" )$*& !\" +,-.(!\nnickelate Nd Sr NiO films on the NdGaO substrate exhibit the smallest c-axis\n0.8 0.2 2 3\nlattice constant and the highest T —compared with those on SrTiO and LSAT\nc 3\nsubstrates with data from the same research group (Hwang Lab). Even smaller c-\naxis lattice constant could potentially further enhance T , but growing the\nc\nperovskite phases on substrates with smaller lattice parameters (such as LaAlO )\n3\ninevitably becomes much more challenging: the crystallinity of the perovskite-\nphase thin films on these substrates, as well as obtaining the well-crystallized IL\nphase through topotactic reduction from the perovskite precursor phases, are\ncrucial for us to obtain samples with high-quality superconducting transitions.\nUntil now, no reported work has solved this interesting and unique growth\n‘dilemma’ related to the topotactic phase transformation.\nAs an alternative feasible approach, hydrostatic pressure experiments (Ref. 21)\ncould serve as an e]ective method to investigate the relationship between c-axis\nlattice constant and T , and experiments are currently underway.\nc\nc\nhas now been added:\nOn Page 9, “…despite that the lattice strain imposed by the substrate may vary\nacross di]erent IL compounds and intricately contribute to determining T .\nc\nFurthermore, previous studies have yet failed to observe superconductivity in IL\nphases on substrates of smaller lattice constants…” is now revised to:\n“…despite that the lattice strain imposed by the substrate may vary across\ndi]erent IL compounds and intricately contribute to determining T . In general,\nc\nsubstrate quality, lattice mismatch, strain, as well as interfacial chemistry may\nplay an important role in the formation of a high-crystallinity IL phase with higher\nT . For instance, previous studies have yet failed to observe superconductivity in\nc\nIL phases on substrates of smaller lattice constants…”\nComments:\n7. Many discussions hinge on the valence states of dopants (e.g., Eu²⁺/Eu³⁺, Sm³⁺),\nbut no experimental verification is provided. XPS or EELS measurements could\nconfirm the Eu and Sm oxidation states.\nResponse:\nWe thank the referee for the valuable suggestions. Regarding the discussion on\nvalence states, we mainly refer to the conclusions of Ref. 26, which studied the\nEu-containing Nd-series IL phases in a similar condition and is also cited in Ref.\n46. We have provided some related XAS data in a separate preprint (Figure 1b of M.\nYang et al., arXiv: 2508.14666) to corroborate some of the discussion here.\nTo include the new information, we have added this new preprint as a reference to\nthe statement, “These are in line with the co-existence of Eu2+ and Eu3+ states62…”\non Page 8.\nAs mentioned above, we have revised the following part:\nOn Page 10, “Whether these Eu2+/Eu3+ ions form an ordered phase and/or exhibit a\nnon-trivial magnetic ground state present interesting questions to studies like\nresonant inelastic X-ray scattering26,61,65-68” into\n“Whether these Eu2+/Eu3+ ions form an ordered phase and/or exhibit a non-trivial\nmagnetic ground state present interesting questions to studies like x-rays\nmagnetic dichroism and/or resonant X-ray scattering26,61,65-68”\nComments:\nThe authors present important results by further in-depth researches about the\nSmNiO superconducting systems. They claim that the decreasing c-axis\n2\nparameter is related to the increasing critical temperature and the 3D\nsuperconductivity from the enhanced coupling between the rare-earth 5d and Ni\n3d orbitals is key for the enhancement of Tc. About the challenging growth of\nNickelate films, they found that the introduction of Ca is important for obtaining\nhigh quality 112 phase. These findings present important understanding about the\nkey physical factors for high critical temperature in infinite-layer nickelate systems,\nsignificantly advancing the extensively discussions of nickelate superconductors.\nGiven these considerations, I believe their findings are suited for publication in\nNature Communications. However, there are still several data analysis and\ndiscussions that require further improvement, before the manuscript can be\nconsidered for publication.\nResponse:\nWe sincerely appreciate the reviewer’s recognition of our work, especially for\npraising the work for presenting an important understanding of the key physical\nfactors for high critical temperature in infinite-layer nickelate systems. Their\nsuggestions are crucial for improving the overall quality of the presented research.\nBelow is our point-by-point response to the review comments.\nComments:\n(1) For the Sm0.75Ca0.05Eu0.2NiO2 superconducting systems, the reported\nhighest Tc,0 is up to 31 K on NGO (110) substrate (Nature 2025, 642 (8066), 58–\n63.), where the c of 3.27 Å is very close to your best system with c of 2.273 Å.\nHowever, the substrate was changed to LAST (001) and the related Tc,0 of 20.2 K\nis lower in this work. Is the LAST substate important here for your conclusions? On\nthe other hand, the superconductivity is missing in the buck Sm0.8Sr0.2NiO2 (J.\nPhys.: Condens.Matter 33 265701). Are there any key interfacial eTects for\ndeciding the superconductivity?\nResponse:\nWe thank the reviewer for raising these important questions. As compared to Ref.\n46, where a T up to 31 K has been observed, our similar films on LSAT show lower\nc,0\nT values and wider transitions, and may still require further optimisation to\nc\neliminate T variations induced by small composition change. We wish to note that\nc\n11\nthis discrepancy may also be rooted in the di]erence in quality between NGO\n(generally of higher quality) and LSAT substrates, which was also evident from Refs.\n24, 25. Our conclusion lies in the observation of enhanced superconductivity with\na general correlation between a higher T and the smaller c-axis lattice constant,\nc\nrendered by smaller rare-earth ions, for each choice of substrates.\nTo respond to this important inquiry, we have revised the following discussion,\n“Our study was motivated by the recent report on reaching a remarkably high T in\nc\nSm-based IL nickelate thin films46” on Page 9 into:\n“Our study was motivated by the recent report on reaching a remarkably high T in\nc\nSm-based IL nickelate thin films46, and continued growth optimisation is\nwarranted.”\nRegarding the missing superconductivity in bulk Sm Sr NiO (reported in the\n0.8 0.2 2\nreference mentioned by the reviewer), this is likely due to defects created during\nthe materials synthesis and reduction processes. As indicated in the reference (C.\nHe et al., 2021, J. Phys.: Condens. Matter 33, 265701), Ni clusters or inclusions\ncan be present in these powder samples. Furthermore, a subsequent study\npublished by the same group (K. Hu et al., 2024, Nature Communications 15, 5104)\nhas convincingly shown that the lack of superconductivity is likely due to the\npresence of intersecting structural and atomic defects, in the form of disrupting\ndomains and interstitial oxygen. Therefore, it is our belief that superconductivity\nobserved in our thin-film Sm Sr NiO is not due to the interfacial e]ect, which\n0.8 0.2 2\nhas also been demonstrated in the literature (for instance, Ref. 46, and Goodge et\nal., 2023, Nature Materials 22, 466, among others).\nAs mentioned above, to have a more inclusive discussion on possible contributing\nfactors to T , an additional note has now been added:\nc\nOn Page 9, “…despite that the lattice strain imposed by the substrate may vary\nacross di]erent IL compounds and intricately contribute to determining T .\nc\nFurthermore, previous studies have yet failed to observe superconductivity in IL\nphases on substrates of smaller lattice constants…” is now revised to:\n“…despite that the lattice strain imposed by the substrate may vary across\ndi]erent IL compounds and intricately contribute to determining T . In general,\nc\nsubstrate quality, lattice mismatch, strain, as well as interfacial chemistry may\nplay an important role in the formation of a high-crystallinity IL phase with higher\nT . For instance, previous studies have yet failed to observe superconductivity in\nc\nIL phases on substrates of smaller lattice constants…”\n(2) For the sample SCSE , there is no signature about the positive normal-state\n0.12\nHall coeTicient. Is it a typical electron-doped superconductor? Is the R of normal\nH\ncarriers still negative during the superconducting transition? If it is still negative,\nthe Sm Ca Eu NiO /LSAT in this work shows an electron dominated transport.\n0.75 0.05 0.2 2\nHowever, the Sm Ca Eu NiO /NGO (Nature 2025, 642 (8066), 58–63.) shows\n0.75 0.05 0.2 2\na hole dominated transport. What is the diTerent between two systems? Is there\npossibility that both holes and electrons contribute to the superconductors in this\nsystem?\nResponse:\nWe thank the reviewer for raising this important point regarding the Hall e]ect data.\nFor the SCSE sample, we indeed observed that the normal-state Hall\n0.12\ncoe]icient (R ) remains negative over the entire measured temperature range,\nH\nwithout showing a transition to positive values. We note that due to a strong\ninfluence of superconductivity and its fluctuation on Hall signal, no attempt was\nmade to measure R across the superconducting transitions. All measurements\nH\nwere performed above T . To this end, we would like to clarify the following:\nc,onset\nOn the negative R in a hole-doped system\nH\nAlthough our films are nominally hole-doped, the sign of R in multi-band\nH\nsuperconductors does not straightforwardly indicate the nominal carrier type. In\ngeneral,\nR = \n/0\" #1\"0$ #\nH\n23/0\"4\"0$56\nwhere p, n are hole and electron concentrations, and μ , μ their respective\np n\nmobilities. If the electron mobility is significantly higher (μ >>μ ), the overall\nn p\ntransport can be dominated by electron-like carriers even when the system is\nhole-doped, yielding a negative R . Such behaviour has also been reported in\nH\ncuprates and iron-based superconductors.\nMulti-band contributions and Fermi surface topology\nBoth our RIXS data and prior theoretical studies suggest that infinite-layer\nnickelates host a complex Fermi surface with both electron and hole pockets.\nDepending on temperature and scattering mechanisms (e.g., phonon or magnetic\nscattering), the relative contributions of these pockets can vary. In the SCSE and\n0.12\nSCE films on LSAT, the electron pockets appear to dominate across the entire\n0.2\ntemperature range, evidenced by the observed negative R .\nH\n0.75 0.05 0.2 2\nNature 642, 58)\nWe agree with the reviewer that our LSAT-based films show electron-dominated\ntransport, while the NGO-based films reported in the reference exhibit hole-\ndominated behaviour. We attribute this contrast primarily to substrate-induced\nstrain and lattice mismatch:\no LSAT (a ≈ 3.87 Å) imposes a di]erent strain state than NGO (a ≈ 3.85 Å). This\npossibly influences the interlayer hybridisation and the Ni–O bandwidth.\no In contrast, films on NGO may stabilise a di]erent Fermi surface reconstruction\nwhere hole pockets dominate the transport response.\nIn this sense, substrate-driven structural e]ects can play a decisive role in\ndetermining the balance between electron- and hole-like carriers, which strikes\nas an interesting point for continued study.\nPossibility of two-carrier contributions\nWe concur with the reviewer that electron and hole carriers likely coexist in this\nsystem. The dominance of one type over the other sensitively depends on the\nstrain environment, Eu valence state distribution (Eu2+/Eu3+), and/or possibly\nsubtle di]erences in doping e]iciency. As mentioned in our response to Reviewer\n1’s comments (Point 7) above, we now have provided related XAS data in a\nseparate preprint (Figure 1b of M. Yang et al., arXiv: 2508.14666) to show\nsignatures of the mixed-valence state of Eu. Overall, our results here highlight that\ninfinite-layer nickelates are multi-carrier superconductors, and that the dominant\ntransport type can be tuned by external parameters such as substrate, pressure,\nand chemical composition.\nTo reflect our discussion here, a note has been added:\nOn Page 8, “We further note that the all-negative R measured in our SCE sample\nH 0.2\ncontrasts with the sign change at low temperatures observed in a similar thin film\non NGO46. This di]erence corroborates the multi-band nature of the IL nickelates.”\nComments:\n(3) The 2D superconducting feature of infinite-layer nickelate superconductor has\nbeen suggested by the investigation of the superlattice (Nat. Commun. 2024, 15\n(1), 10215.). For their SmNiO systems, they claimed that there is an observed 3D\n2\nsuperconducting behavior aTected by the coupling between Eu 5d and Ni 3d\norbits and it aTect the electronic structure for the enhancement of Tc. Did authors\ntry more Eu for higher Tc? What is the role of Sm for 3D behavior? Is it possible to\n14\ncompare the polar rotation angle dependent upper critical field for diTerent\nsystems to support the conclusion?\nResponse:\nWe thank the reviewer for raising these important questions. Although we have\nattempted more samples with higher Eu concentrations (M. Yang et al., arXiv:\n2508.14666), we have not yet performed similar polar rotation upper critical field\nstudies on those samples, which calls for a significant amount of work. In the\ncurrent work, our conclusion of a more 3D-like behaviour is mainly based on the\nμH -T relation in the polar rotation experiments (Figure 3, c-g), and we have\nc2\ncontrasted the μH characteristics (for both out-of-plane and in-plane) with those\nc2\nin other IL nickelate systems. We note that, while these transport measurements\nmay not provide direct clues to elucidate the role of Sm for such 3D-like (or a mixed)\nbehaviour, the RIXS experiments finds a stronger coupling between the Sm 5d and\nNi 3d orbitals, which can be a direct consequence of a smaller inter-plane\ndistance and serve as an indirect access to the role the rare-earth element may\nplay, via the detailed electronic structure landscape. Comprehensive polar-\nrotation experiments in full comparison with di]erent systems, as suggested by\nthe reviewer, would be a powerful assessment of the possibly unique feature that\nSm brings. We are currently working hard on these sophisticated experiments and\nwill report the findings in a separate work.\nTo appreciate the reviewer’s valuable comments, we added the following note to\nthe revised main text:\nOn Page 8, “A further comprehensive polar rotation study on a full set of samples\nis needed to unveil the nature of such behaviours.”\nComments:\n(4) As the authors mentioned in Line 181, the Tc is extracted from the midpoint\nρ(Tc) = ρ50%. Why is the Tc of SESC0.2 in this work in Fig 4c close to the Tc,onset\nof 32.5 K in Figure 1? And, the Tc of the SESC in ref.46 in Figure 4c is close to\nreported Tc,0 of 31K. What is the definition of Tc in Figure 4c?\nResponse:\nWe are grateful to the reviewer for noticing this critical discrepancy. The definition\nof ρ(T ) = ρ on Page 6 is used for the discussion on the rotation experiment data\nc 50%\ndepicted in Figure 3. In Figure 4c, T is defined as T . For the SCSE samples on\nc c,onset\nNGO, the T value was initially adopted from the original preprint version of the\nc\nwork (determined by the typical method using linear-fit\n15\ndeviations). Notably, the samples were further optimised in the formally published\nversion shown in Ref. 46; however, the data in Figure 4c were inadvertently left\nunsynchronised. This inconsistency has now been rectified, as shown below in the\nrevised Figure 4c.\n(Revised Figure 4c in the main text.)\nComments:\n(5) Why is there no the temperature dependent resistivity of SCSE0.2 (113 phase)\nin Figure S1b? Considering the spin disorder eTects of Sm and Eu mentioned in\nFigure S2, is there a lager upturn for negative dρ/dT at low temperature due to the\nmore Sm and Eu?\nResponse:\nWe thank the reviewer for asking these important questions. We conducted\nmeasurements on the SCE (‘113’ perovskite phase) sample (referred as SCSE\n0.2 0.2\nin reviewer’s comments and in the old version of the manuscript). The insulating\nbeghaviour observed in the initial measurements led us to approach the data with\ncaution. Notably, despite this initial observation, SCE (‘113’ perovskite phase)\n0.2\nsamples subjected to a topotactic reduction exhibited high-quality\nsuperconducting transitions. Subsequent measurements on additional samples\nshowed that all SCE (‘113’ perovskite phase) samples exhibited a similar\n0.2\ninsulating behaviour. The results are now presented in Figure R5 below.\n16\n49: -K##%2 -4R/S7'-#\n!$;$\n-4R/S7'-$\n2/\n-4R/S7'-%\n1 #!!\n0! -4R/S7'-8\n/\nK-,\n*)+\n)*E\n\"!\n)E\n'\nC\n!\n! \"! #!! #\"! $!! $\"! %!!\n!-K32\nFigure R5. Resistivity as a function of T for di]erent SCE (‘113’ perovskite phase)\n0.2\nsamples.\nCorrespondingly, one representative curve has now been added to Figure S1b in\nthe revised Supplementary Information. As the sample shows a full insulating\nbehaviour, there is no similar upturn in dρ/dT as mentioned by the reviewer. Now\nFigure S1b is updated as follows, with the data of Sample 3 added into Figure S1b:\n(Revised Figure S1 in the Supplementary Information.)\nTo reflect the additional data, the text has been changed accordingly in the main\ntext as follows:\nOn Page 5, “The corresponding resistivity curves ρ(T) of all samples are shown in\nFigure S1b. Unlike previously reported46, three samples show metallic behaviour\ndown to low temperature (2 K), consistent with charge-induced suppression of the\nmetal-insulator transition51,52. The intrinsic metallic behaviours inform the high\ncrystallinity of the precursor phase.”\nMeanwhile, according to our naming rules, the SCSE (113 phase) sample should\n0.2\nbe named as SCE (113) to be consistent. This revised name has been updated\n0.2\n17\nin Figure S1. We apologise for this inconsistency in the old version.\nComments:\n(6) There are some typos:\nFor example: (1) the figure 2n mentioned in main text is missing; (2) Why is the Sr\nmissing in the legend of figure 3a and b? (3) in fig. S2, the unit is missing for the y-\naxis and the Fig 1B should be Fig. S1b in figure caption;\nResponse:\nWe are grateful for the reviewer’s careful reading of our manuscript and sincerely\napologise for these careless typos. In the revised manuscript, all these mistakes\nhave been rectified: In Figure 2, Panels o, p and q have been re-labelled as Panels\nn, o and p, accordingly, and text has been revised; In Figure 3a and 3b, “20% Sr” is\nlabelled at the top-left corners to simplify the legends; In Figure S2, a unit has been\nadded to the y-axis, and the figure caption has been updated (“Fig. 1B” to “Fig.\nS1b”)\n(Revised Figure 2 in the main text.)\n18\n(Revised Figure 3a and 3b in the main text.)\n(Revised Figure S2 in the Supplementary Information.)\nReviewer #3 (Remarks to the Author):\nComments:\nIn this manuscript, Yang et al. report the synthesis of high-quality Sm-based\ninfinite-layer nickelate thin films, achieving a superconducting transition\ntemperature (Tc) up to 32.5 K. Compared to the recently reported Tc above 35 K in\nSm1-x-y-zCaxSryEuzNiO2 films grown on NdGaO₃ (110) substrates (Ref. 46), this\nstudy explores films grown on LSAT (001) substrates and reveals the coexistence\nof two-dimensional and three-dimensional superconductivity using high-\nmagnetic-field transport measurements. The work represents a significant\nadvancement in the growth of superconducting infinite-layer nickelates and\nproposes a potentially promising route to achieving higher Tc in these systems.\ninterpretation, presentation, and scientific framing require clarification and\nimprovement before the manuscript can be considered suitable for publication in\nNature Communications.\nResponse:\nWe thank the reviewer for their critical review of our manuscript and their overall\npositive appraisal of our work, particularly praising the work as “a significant\nadvancement in the growth of superconducting infinite-layer nickelates”. The\nimportant questions of the reviewer have helped improve the presentation of our\ndata and discussions. We provide our responses to address these valuable\ncomments/critiques as follows.\nComments:\n1. The claimed correlation between increasing Tc and decreasing c-axis lattice\nconstant across diTerent rare-earth substituted systems is not convincingly\nsupported by the data. As shown in Figure 4, several data points deviate significantly\nfrom the suggested linear trend, such as those for LSNO from Ref. 18. Even within\nthe current study, the SCSE samples appear to form a dome-shaped trend rather\nthan a monotonic one. Specifically, SCSE0.12 has the smallest c-axis lattice\nconstant (3.26 Å), but its Tc is not the highest. This outlier is not discussed\nanywhere in the text.\nMoreover, while the SCSE film on NGO in ref. 46 shows the highest Tc, its c-axis\nlattice constant is not the smallest. These inconsistencies undermine the claim\nof a direct correlation.\n2. The manuscript attempts to establish a unified trend between the\nsuperconducting transition temperature and the c-axis lattice constant by\ncombining data from multiple compounds SSNO, SCSE0.06, SCSE0.12, and\nSCE0.2, that contain diTerent combinations of rare-earth and alkaline-earth\ndopants. These systems diTer not only in chemical composition but also in doping\nlevels, making a direct comparison problematic. For example, in Nd1-xSrxNiO2\n(Nature 619, 288–292 (2023)), increasing Sr doping leads to an increase in the c-\naxis lattice parameter, whereas Tc exhibits a dome-shaped dependence, rather\nthan a monotonic trend. Within the current dataset, the variation in Tc does not\nfollow a consistent correlation with c-axis values. Given the diTerences in\nchemical composition and doping levels, it is questionable whether multiple\ncompounds can be meaningfully combined into a single trend. The authors\nshould clarify the rationale for aggregating these distinct materials and consider\n20\nreanalyzing the data to better reflect the individual eTects of specific dopants.\nResponse:\nWe thank the reviewer for the important comments and would like to further clarify\nthese related points. Our goal of surveying the T values as a function of c-axis\nc\nlattice constant is to obtain a general correlation between the two quantities,\nwhich was implied by the high-pressure measurements (Ref. 21, N. N. Wang et al.,\n2022, Nature Communications 13, 4367). We wish to note that, due to the limited\nchoice of substrates, a- and b-axes, on the other hand, are not widely tuneable in\nepitaxial films. However, we fully agree with the reviewer that the T values are not\nc\nexclusively determined by the c-axis constant; they can be a]ected by doping (to\nwhich other uncovered and debatable mechanisms may be at play), and subject\nto sample-to-sample di]erences due to quality variations. In fact, as pointed out\nby the reviewer, owing to growth optimisation, the T values reported for the LSNO\nc\nsamples in Ref. 18 all have higher values, and we fully appreciate that this is due\nto a higher sample quality.\nIn order to better reveal the evolution of T against c-axis, we make the same plots\nc\nusing data from di]erent representative references and show them below (Figures\nR6, R7 and R8). From the plots, clear general trends in line with our conclusions\ncan be observed: T increases as the c-axis shrinks, for di]erent classes of\nc\nsamples.\nFigure R6. T versus c-axis lattice constant of La Sr NiO samples extracted\nc 0.8 0.2 2\nfrom Ref. 18.\nc 1-x x 2\nRef. 24.\nFigure R8. T versus c-axis lattice constant of Pr Sr NiO samples extracted from\nc 1-x x 2\nRef. 20.\nWe now believe that all these aspects should be reflected in the discussion.\nTherefore, we have added the following text to the discussion part about this figure\n(Figure 4c).\nOn Page 9, “We note that these data points are surveyed from a broad range of\nsamples with distinct A-site elements and/or dopants, as well as di]erent doping\nlevels, for which other factors impacting T may be at play. In addition, the\nc\ninfluence of synthesis methods and growth optimisations is not clearly visible here.\nThe central aim of the ‘broad, orange-coloured band’ is to showcase a generic\nguiding trend.”\n3. The RIXS spectra presented for the SCE0.2 sample reveal a feature at ~0.6 eV,\nattributed to hybridization between rare-earth and Ni orbitals, consistent with\nprevious observations (e.g., Nat. Mater. 19, 381–385 (2020)). However, in prior\nstudies, this feature resonates at the shoulder A′ peak of the Ni L3 XAS spectrum,\nrather than at the main peak. The authors need to provide XAS data for their\nsample to enable direct comparison and support the resonance assignment.\nResponse:\nWe thank the referee for the valuable suggestion. Figure R9 shows the XAS\nmeasured across the Ni L -edge on our SCE sample during the RIXS experiment.\n3 0.2\nTo identify the resonance energy of the Ni-R hybridisation feature at ~ 0.6 eV, we\nintegrated the RIXS intensity over the energy loss range of 0.2 to 1.0 eV for the π\nincident light polarisation, which enhances the ~ 0.6 eV feature. The maximum\nintegrated intensity is clearly observed below the main peak of the Ni L XAS.\n3.0 eV, coincides with the main XAS peak. This analysis confirms that the ~ 0.6 eV\nfeature for the SCE sample appears below the Ni L XAS peak, consistent with\n0.2 3\nprevious observations in other systems. We have now added Figure R9 as Figure\nS10 and provided the corresponding discussion in the Supplementary Information.\nFigure R9. The XAS and RIXS data for a SCE sample. (a) XAS of the SCE\n0.2 0.2\nsample measured across the Ni L edge in the normal incidence geometry with π-\n3\n23\npolarised X-rays. The intensity is measured with total electron yield (TEY). The peak\nat 846 eV corresponds to the La M edge. (b) RIXS incident energy map measured\n4\nwith π polarised X-rays. The integrating intensities over the energy loss ranges of\n0.2-1.0 eV and 1.0-3.0 eV are plotted in (c), displaying the resonance profiles of the\nNi-R hybridisation and dd features, respectively. The integrated intensities are\nnormalised to the respective peak intensities. Dashed lines in (a) and (c) indicate\nthe resonance energies.\nComments:\nThe claim of enhanced hybridization between rare-earth 5d and Ni 3d orbitals also\nneeds clarification. It is unclear which system this enhancement is being\ncompared to. Is the comparison made against Nd-based nickelates or some other\nreference? Since RIXS absolute intensity is not reliable, it would be more\nappropriate to compare the relative intensity of the hybridization feature with\nrespect to the dd excitations.\nResponse:\nWe thank the reviewer for their valuable suggestions. For a quantitative\ncomparison of the hybridisation peak intensity, we adapted the RIXS data on\nNd Sr NiO from Rossi et al., Phys. Rev. B, 2021, 104, L220505. To our\n0.875 0.125 2\nknowledge, among the reported RIXS studies, this dataset was obtained under\nconditions most comparable to our study — using π polarisation and a grazing\nincidence geometry. Importantly, the data were recorded at the resonance energy\nof the Ni-R hybridisation feature, which enables a direct comparison of the\nhybridisation peak intensities.\n0.2 0.875 0.125 2\nat the resonance energy of the respective Ni-R hybridisation features. The\nintensities are normalised to the weight of the dd excitations between 1.0 and 3.0\neV. Data for Nd Sr NiO is adapted from Rossi et al., PRB 104, L220505 (2021).\n0.875 0.125 2\nIn Figure R10, we plot the RIXS data measured at the resonance energy of SCE\n0.2\n(blue) and Nd Sr NiO (red). After normalizing the intensity to the weight of\n0.875 0.125 2\nthe dd excitations between 1.0 and 3.0 eV, it is clear that the Ni-R hybridization\nfeature at ~ 0.6 eV in SCE is significantly enhanced compared to that in\n0.2\nNd Sr NiO .\n0.875 0.125 2\nTo reflect the discussion and upon the reviewer’s suggestions, we now provide this\nfigure in the revised Supplementary Information as Figure S11 and relevant\ndiscussions.\nComments:\nThe conclusion regarding an \"enhancement in the electronic bandwidth\" (line 259)\nbased solely on the increased hybridization peak intensity is ambiguous and\nspeculative. The authors should provide quantitative or theoretical analysis to\nsupport this claim, or soften the interpretation accordingly.\nResponse:\nWe agree with the reviewer. In the revised manuscript, we have softened the\ninterpretation by changing this sentence to “This hybridization feature appears to\nbe more intense6,60,61, indicating that the reduced ionic radius of Sm and Eu\ne]ectively modifies the electronic structure, which could be crucial to the\nenhanced T ”, on Page 8.\nc\nComments:\n4. The authors state that Sm-based nickelates have a narrower growth window\nthan Nd-based ones, but the discussion of synthesis parameters is too general.\nGiven the complexity of the synthesis process (involving multiple steps and fine-\ntuned parameters), the authors should explicitly identify which parameters are\nmost critical. Clearer exposition in the Methods section would enhance\nreproducibility and contribute to the broader eTort in optimizing nickelate growth.\nResponse:\nWe thank the reviewer for this request, as it indeed serves to enhance the\nreproducibility by providing more detailed information. As mentioned above (in\nresponse to Reviewer 1’s comments), we provide more related information on the\n25\ngrowth attempts for Pr Sr NiO and include more discussions and data in the\n0.8 0.2 3\nMethods section and Supplementary Information.\nGrowth Conditions for Pr Sr NiO and Sm Sr NiO Thin Films for Comparison\n0.8 0.2 3 0.8 0.2 3\nPurpose\nHigh-quality epitaxial Pr Sr NiO precursor films were grown under optimized\n0.8 0.2 3\nconditions: substrate temperature of 600 °C, oxygen partial pressure of 100 mTorr,\nlaser fluence of 2.0 J/cm², and repetition rate of 3 Hz (Figure R1a). X-ray di]raction\n(XRD) confirmed phase-pure perovskite formation, with sharp (002) reflections at\n𝜃 of ~ 48.7° and 48.5° on SrTiO and LSAT substrates, respectively.\n0.8 0.2 3\nLSAT substrates, no perovskite peaks were detected by XRD (the bottom curve in\nFigure R1b). Instead, substrate discolouration and X-ray reflectivity (XRR) fringes\n(Figure R1c) suggested the deposition of a thick amorphous layer, likely due to an\nexcessively high growth rate. To mitigate this, the deposition laser frequency\nwas reduced to 0.3 Hz, but no crystalline perovskite phase appeared. Considering the\nlarger atomic mass of Sm, the laser fluence was incrementally increased while the\nrepetition rate was kept at 0.3 Hz. Crystallisation of the SSNO perovskite phase\nfirst appeared at 2.2 J/cm2 (Figure R1b). At higher energy (2.7 J/cm2) or increased\nrepetition rate, secondary phases started to form and crystallinity deteriorated.\nOptimal SSNO precursor films with good crystallinity were therefore obtained at\n2.6 J/cm² and 0.3 Hz. All Sr-containing films reported here were grown under these\noptimised conditions. For perovskite precursor films of the SCE sample, it was\n0.2\nfound that a growth frequency of 2.6 J/cm2 and 3 Hz could obtain perovskite\nprecursor phase thin films with good crystallinity.\n(a) (b) (c)\nFigure R1. (a) XRD patterns and growth parameters of Pr Sr NiO perovskite\n0.8 0.2 3\nprecursor thin films epitaxially grown on the SrTiO and LSAT substrates. (b) XRD\n3\npatterns and growth parameters for Sm Sr NiO perovskite precursor thin films\n0.8 0.2 3\non LSAT substrates. (c) X-ray reflectivity (XRR) data for the Sm Sr NiO thin films\n0.8 0.2 3\nin (b). In Figure R1(a) and (b), the peaks near 44° are from the background of the\n26\nold instrument in our laboratory. The o]icial XRD data in the article are measured\nusing another di]ractometer.\nPer the reviewer’s request and to reflect our discussion here, we have inserted the\nfollowing separate sub-section into the Methods section:\nOn Page 11,\n“Additional Information on the Growth of the Perovskite Precursor Films\nAs a comparison, epitaxial Pr Sr NiO films were reproducibly obtained at\n0.8 0.2 3\n600 °C, 100 mTorr oxygen, 2.0 J/cm2, and 3 Hz, with XRD confirming phase-pure\nperovskite. Under the same conditions, Sm Sr NiO films remained amorphous.\n0.8 0.2 3\nBy reducing the laser repetition rate to 0.3 Hz and increasing laser fluence,\nperovskite crystallinity emerged at 2.6 J/cm2. Higher fluence or frequency\ndegraded film quality. Therefore, the optimal condition for Sm Sr NiO growth\n0.8 0.2 3\nwas identified as 2.6 J/cm2 at 0.3 Hz. Following similar procedures, it was found\nthat the SCE sample crystallised best under 2.6 J/cm2 at 3 Hz.”\n0.2\nComments:\n5. Since both this study and Ref. 46 use films of similar composition (Sm1-x-y-\nzCaxSryEuzNiO2), it would be helpful for the authors to discuss why the Tc is lower\non LSAT (001) substrates compared to NGO (110), as reported in Ref. 46.\nDiTerences in strain, lattice mismatch, or interfacial eTects could be contributing,\nand a brief discussion of these factors would add valuable context.\nResponse:\nWe thank the reviewer for pointing out this critical observation. The reviewer\nmakes a good point that, as compared to Ref. 46, where a T up to 31 K has been\nc,0\nobserved, our similar films on LSAT show lower T values and wider transitions. As\nc\nmentioned above in response to Reviewer 2’s comments, we note that further\noptimization is still required to eliminate T variations. We also wish to mention\nc\nthat this discrepancy in T values may also be rooted in the quality di]erence of\nc\nNGO (generally of higher quality) and LSAT substrates, which was also evident\nfrom Refs. 24, 25. Our conclusion lies in the observation of enhanced\nsuperconductivity with a general correlation between a higher T and the smaller\nc\nlattice constant, rendered by smaller rare-earth ions, for each choice of substrate.\nTo respond to this important inquiry, we have revised the following discussion,\n“Our study was motivated by the recent report on reaching a remarkably high T in\nc\nSm-based IL nickelate thin films46” on Page 9 into:\n27\n“Our study was motivated by the recent report on reaching a remarkably high T in\nc\nSm-based IL nickelate thin films46, and continued growth optimisation is\nwarranted.”\nTo further facilitate the discussion on the potential role of strain, lattice mismatch,\nand interface, an additional note has been added:\nOn Page 9, “…despite that the lattice strain imposed by the substrate may vary\nacross di]erent IL compounds and intricately contribute to determining T .\nc\nFurthermore, previous studies have yet failed to observe superconductivity in IL\nphases on substrates of smaller lattice constants…” is now revised to:\n“…despite that the lattice strain imposed by the substrate may vary across\ndi]erent IL compounds and intricately contribute to determining T . In general,\nc\nsubstrate quality, lattice mismatch, strain, as well as interfacial chemistry may\nplay an important role in the formation of a high-crystallinity IL phase with higher\nT and a well-defined superconducting transition. For instance, previous studies\nc\nhave yet failed to observe superconductivity in IL phases on substrates of smaller\nlattice constants…”\nComments:\nHere are some Minor Comments:\na. Line 240: “where β′ is similarly defined as above”. Please clarify what “above”\nrefers to, or restate the relevant definition.\nResponse:\nWe apologize for not being specific on the definition of β′. We have now included a\nclear definition of β′ and revised the original sentence “where β′ is similarly defined\nas above” to “where β′ is similarly defined as β above”.\nComments:\nb. Line 607: The insets of panels (i–l) are currently labeled incorrectly; they should\ncorrespond to panels (e–h).\nResponse:\nWe are sorry for these typos and thank the reviewer for pointing them out. The\nlabels in the caption of Figure 2 are now corrected and checked.\nComments:\nc. Figure 4c: The figure shows four samples, but five data points are plotted. Please\n28\nclarify.\nResponse:\nWe apologize for not being specific. The five data points in Figure 4c were obtained\nfrom the four samples presented in the main text (Figure 1) and also from another\nsample Sm Ca Eu NiO (Figure S4). We have now added an additional note in\n0.78 0.02 0.2 2\nthe figure caption of Figure 4: “Data from this work are presented in both the main\ntext and supplementary information.”\nComments:\nd. Figure 4c: The acronym “SESC” should be corrected to “SCSE.”\nResponse:\nWe thank the reviewer for pointing out this mistake. This has now been updated as\nsuggested in the revised Figure 4c.\nComments:\ne. Figure S3: With increasing Ca doping in Sm Ca Eu NiO (x = 0, 0.02, 0.05,\n0.8-x x 0.2 2\n0.10), the c-axis lattice constant is expected to decrease due to the smaller ionic\nsize of Ca. However, an unexpected increase is observed for x = 0.10. This\ndeviation should be discussed.\nResponse:\nWe appraise the reviewer’s careful review of the manuscript. Indeed, from Figure\nS4, a monotonic evolution of the c-axis lattice constant upon varying Ca\nconcentration is not clearly shown. We attribute this to the fact that, for certain\ncompositions, especially those with high doping levels, further growth\noptimisation may facilitate to reveal more intrinsic properties. In fact, films of\nvarious compositions were presented here; for each composition, extra work to\nfine-tune in the growth parameter space is needed, for a cleaner illustration of the\ntendencies of all properties.\nWe have now added the following sentence into the Supplementary Information\nto clarify this:\nOn Page 5 of the Supplementary Information, “The non-monotonic change in the\nlattice constant with the Ca substitution is likely due to the fact that, for certain\ncompositions, further fine-tuning of growth parameters is needed.”\nComments:\nI co-reviewed this manuscript with one of the reviewers who provided the listed\nreports. This is part of the Nature Communications initiative to facilitate training\nin peer review and to provide appropriate recognition for Early Career Researchers\nwho co-review manuscripts.\nResponse:\nWe are thankful to the reviewer for their invaluable time in reviewing our\nmanuscript.\nReviewer #5 (Remarks to the Author):\nComments:\nI co-reviewed this manuscript with one of the reviewers who provided the listed\nreports. This is part of the Nature Communications initiative to facilitate training\nin peer review and to provide appropriate recognition for Early Career Researchers\nwho co-review manuscripts.\nResponse:\nWe are thankful to the reviewer for their invaluable time in reviewing our\nmanuscript.\nReviewer #6 (Remarks to the Author):\nComments:\nI co-reviewed this manuscript with one of the reviewers who provided the listed\nreports. This is part of the Nature Communications initiative to facilitate training\nin peer review and to provide appropriate recognition for Early Career Researchers\nwho co-review manuscripts.\nResponse:\nWe are thankful to the reviewer for their invaluable time in reviewing our\nmanuscript.\n(END)\nReviewer #2 (Remarks to the Author):\nComments:\n(1) Based on Hall measurements, the authors had a thorough discussion about\nthe possible types of carriers. However, the multi-band model they provided only\nthe approximate expression of two-band model in a low-field limit, and only can\nreflect the carrier density with high mobility as they mentioned in response.\nHowever, this is not the complete expression and cannot reflect the feature of\nmultiband. For typical two-band model, the R curve is predicted nonlinearity,\nxy\nwhich can provide direct evidence of the two types of carriers. Allowing readers to\nbetter follow the authors' statements, it is necessary to show these raw data (such\nas Hall resistance) and to add related discussions in the main text and the\nSupplementary Information.\nResponse:\nWe sincerely thank the reviewer for their detailed follow-up on this issue and for\ntheir careful thought. We have now replaced the two-band formula for the Hall\ncoe<icient provided in our previous response with a generalised formula for the\nHall resistivity, which accounts for the non-linearity in R (B) and therefore a field-\nxy\ndependent R , as shown below.\nH\n𝐵 (𝑛 𝜇$ −𝑛 𝜇$)+(𝑛 −𝑛 )𝜇$𝜇$𝐵$\n# # % % # % # %\n𝜌 =\n!\" 𝑒 (𝑛 𝜇 +𝑛 𝜇 )$ +(𝑛 −𝑛 )$𝜇$𝜇$𝐵$\n# # % % # % # %\nHowever, despite the consideration on the two-band (or multi-band) picture\nbased upon the electronic structure of the system [Phys. Rev. X 10, 011024(2020),\nPhys. Rev. B 100, 201106(R) (2019), Phys. Rev. B 101, 081110(R) (2020), Phys. Rev.\nLett. 125, 077003 (2020), Natl Sci Rev 8, nwaa218(2021), npj Quantum Mater. 5,\n1(2020), Nat. Mater. 19, 381 (2020)], we wish to note that in our measurements, R\nxy\nshows a perfect linear behaviour up to 14 T. This is possibly due to the distinctive\nmobility possessed by the various bands and/or the limitation of the magnetic field\nstrength (which can be revealed in the formula above). We also agree with the\nreviewer that it is comparative to illustrate the raw R (B) data for more direct\nxy\n1\ninformation. These Hall data, for some of our samples of similar compositions and\nquality, have now been demonstrated in a separate work [arXiv:2508.14666] (the\nExtended Data Fig. 4 in the referenced work). Similar behaviour has also been\nseen in earlier studies using di<erent dopants, for instance, on Nd Sr NiO [Phys.\n1-x x 2\nRev. Lett. 125, 147003(2020), Phys. Rev. Lett. 125, 027001(2020)].\nTo address the reviewer’s comments, we have now revised the following sentence:\nOn Page 8, “This di<erence corroborates the multi-band nature of the IL nickelates.”\ninto\n“This di<erence corroborates the multi-band nature of the IL nickelates,\ndespite that a linear field-dependent Hall resistivity, 𝜌 (H), has been observed in our\nyx\nsamples62, from which R was extracted.”\nH\nTo provide more discussion, we have also added the following paragraph in\nSection XII of the Supplementary Information:\nOn Page 14, “We note that these infinite-layer nickelates should be multi-band\nsystems. In this regard, the field-dependent Hall resistivity, 𝜌 (H), can be generally\nyx\nframed by the following formula, despite that a general linear behaviour has been\nobserved in our samples [62], which is consistent with previous reports in other\ninfinite-layer nickelates [22].\n𝐵 (𝑛 𝜇$ −𝑛 𝜇$)+(𝑛 −𝑛 )𝜇$𝜇$𝐵$\n# # % % # % # %\n𝜌 =\n!\" 𝑒 (𝑛 𝜇 +𝑛 𝜇 )$ +(𝑛 −𝑛 )$𝜇$𝜇$𝐵$\n# # % % # % # %\n”\nComments:\n(2) For the statement of “there is a general enhancement of superconductivity as\nthe c-axis lattice constant shrinks”, authors summarized diOerent systems at\nvarious substrates. Authors also mentioned that the sample quality is also\nimportant. It is still unclear that why the c-axis is more important than other\nphysical factors, for example c/a. Other reviewers also have the same doubts. Due\nto the diOerent in-plane axis for diOerent substrates, what is the evolution of Tc as\na function of volume or other parameters? More discussions should be described\nin details.\nResponse:\nthat T may be governed by multiple factors beyond the c-axis lattice constant,\nc\nincluding dopant species, carrier concentration, sample quality, and details of the\ngrowth and optimisation procedures. Our intention is therefore not to claim that T\nc\nis determined solely by the c-axis parameter, but rather to highlight a generic\nphenomenological correlation that emerges when di<erent representative\ndatasets are considered together. We wish to firmly clarify that, through our\nadditional analysis organised around di<erent situations (a. fixed composition,\ndi<erent substrates; b. fixed substrate, improved growth optimisation; c. varying\ncompositions in doping-dependent phase diagrams), illustrated below, we trust\nthat our use of the c-axis lattice constant can be a good empirical indicator of a\nstructural/electronic environment that is favourable for superconductivity in\ninfinite-layer nickelates.\nIn the manuscript, we now explicitly state that the “broad, orange-coloured band”\nin the T – c-axis plot is intended as a guiding trend rather than a strict universal\nc\nlaw: superconductivity tends to be enhanced as the c-axis lattice constant\ndecreases, while recognising that dopant chemistry, carrier density, and synthesis\noptimisation inevitably introduce scatter and deviations from a simple monotonic\nrelation. The datasets below were shown in our previous reply.\nFigure R6. T versus c-axis lattice constant of La Sr NiO samples extracted\nc 0.8 0.2 2\nfrom Ref. 18.\nc 1-x x 2\nRef. 24.\nFigure R8. T versus c-axis lattice constant of Pr Sr NiO samples extracted from\nc 1-x x 2\nRef. 20.\nAs mentioned in our previous response, to reflect our viewpoint and to be inclusive,\nwe have added the following text into the discussion part regarding Figure 4c:\nOn Page 9, “We note that these data points are surveyed from a broad range of\nsamples with distinct A-site elements and/or dopants, as well as di<erent doping\nlevels, for which other factors impacting T may be at play. In addition, the\nc\ninfluence of synthesis methods and growth optimisations is not clearly visible here.\nThe central aim of the ‘broad, orange-coloured band’ is to showcase a generic\nguiding trend.”\n(3) About the diOerent definition of Tc, please use the clear expressions\neverywhere to avoid the misunderstanding, such as Tc,50%, Tc,onset, Tc,0 and so\non. The Tc,0 (page 6) and Tc0 (page 7) defined in the main text have the diOerent\nphysics, and were rather misleading due to the similar spelling.\nResponse:\nWe thank the reviewer for these valuable suggestions. We have now checked\ncarefully to ensure clear definitions for these T values. To lift the potential\nc\nambiguity, we have replaced T with T to give a clearer definition throughout\nc0 c(0 T)\nthe revised manuscript.\nComments:\nIn addition, some spellings should be improved or corrected.\n• For example: the “T = 0” in page 6 lost the unit of “K”.\n• “in-plane field (H⊥c)” should be corrected.\n• “the thickness (d)” in page 6 is a unnecessary abbreviation because it was\nonly used once.\n• The non-uniform spelling of μ0Hc2 in figures and Hc2 in texts were rather\nmisleading.\n• The legend of red solid rhombus is missing in figure 4b and S12.\nResponse:\nWe sincerely thank the reviewer for their careful check and apologise for the\nconfusion these spellings may cause. All suggested revisions have now been\nthoroughly incorporated into the manuscript accordingly.\nResponse to All Other Reviewers:\nWe are grateful to the reviewers for their invaluable time spent reviewing our\nmanuscript and for their support in publishing it.\n(END)\nReviewer #2 (Remarks to the Author):\nComments:\nIn response to the point on multiband characterization in IL nickelates, the issue\nwith certain descriptions has been addressed. The explanation they provided is\nacceptable.\nResponse:\nWe sincerely thank the reviewer for finding the issues having been resolved and\nour response was acceptable.\nComments:\nWhile the authors identify the c-axis as important, a more thorough exploration of\ninfluencing factors (such as the c/a ratio) is warranted. Given that this is a central\nfinding, enriching the discussion—potentially in the Supplementary Information—\nwould greatly solidify the argument and provide deeper insight for the reader.\nResponse:\nWe concur with the reviewer’s suggestion and have now provided such further\nexploration. In Figure R1, we provide the plot of T versus c/a, from which we could\nc\nobserve that the variation trend of T under diDerent substrates in the original figure\nc\nbecomes less pronounced.\nTo include this information, as suggested by the reviewer, we now list this figure as\na new figure (Figure S13) in the Supplementary Information, with additional\ndiscussion labelled as “XIII. T versus c/a”. Now this part of the Supplementary\nc\nInformation reads, “\nVI. T versus c/a\nc\nThe correlation of T and the normalized lattice parameter ratio c/a is plotted in\nc\nFigure S135,7–16. It can be observed that when c is replaced by the lattice parameter\nratio c/a, the trend of T in the original figure becomes less pronounced.”\nc\n1\n+,-EKL0NLOP4)5+ST+0N8P4G9+N:;\"EA\nGC +,-EKL0NLOP4)5+ST+0N8P4G9+N:;\"E#\n+,-EKL<-LOP4)5+ST+0N8P4G9+N:;\"E=\n+>NEKL0NLOP4)5+ST+0N8P4G9+N:;\")!\nG! +>NEKL0NLOP4)5+ST+0N8P4G9+N:;\"E\n+O?EKL0NLOP4)5+ST+0N8P4G9+N:;\")\n+O?EKL0NLOP4)5+ST+0N8P4G9+N:;\")G\n)C +O?EKL0NLOP4)5+ST+,0@89+N:;\")'\n+O?EKL0NLOP4)5+ST+O?A-4G9+N:;\"C\ni\nh\n+O?EKLBCLOP4)5+ST+,0@89+N:;\")%\nJ )!\n+0<0B5+ST+O?A-4G9+N:;\"'%\n+ +0<0B5+ST+,0@89+aEPc+dSNe\nf\n!\nEC\nE!\nC\n!\n!\"## !\"#A !\"#% !\"#C !\"#'\n\"M#\nFigure R9 (Figure S13 in the Supplementary Information). T plotted against c/a\nc\nfor all infinite-layer nickelate samples listed in Figure 4c in the main text.\nComments:\nFinally, the typos should be carefully minimized throughout the manuscript. Why\ndo both B and H appear in the revised sections? The B is totally replaced by μ0H.\nResponse:\nWe sincerely apologize for our carelessness in making the typos, especially in the\nnewly added sections. We have now carefully checked to eliminate the typos and\nunify the presentation of magnetic field to be μ H in the added section.\nOverall, this version could be considered for publication.\nResponse:\nWe are thankful to the reviewer for their invaluable time in reviewing our\nmanuscript and for their support in publishing our manuscript.\n(END)\n2"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed all of my comments, and I now recommend this paper for publication.", "reviewer_3": "In the revised manuscript, the authors have provided detailed information on the sample synthesis procedure and added further data and discussion to address the concerns raised in our previous review. These revisions significantly improve the clarity and support for the conclusions. We consider all prior comments satisfactorily resolved and recommend the manuscript for publication in Nature Communications.", "reviewer_5": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_6": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": ""}, {"round": 3, "reviewer_comments": {"reviewer_2": "In response to the point on multiband characterization in IL nickelates, the issue with certain descriptions has been addressed. The explanation they provided is acceptable. While the authors identify the c-axis as important, a more thorough exploration of influencing factors (such as the c/a ratio) is warranted. Given that this is a central finding, enriching the discussion—potentially in the Supplementary Information—would greatly solidify the argument and provide deeper insight for the reader. Finally, the typos should be carefully minimized throughout the manuscript. Why do both B and H appear in the revised sections? The B is totally replaced by μ0H.\nOverall, this version could be considered for publication."}, "author_response": "Point-to-Point Response to Reviewers’ Comments\nReviewer #2 (Remarks to the Author):\nComments:\nIn response to the point on multiband characterization in IL nickelates, the issue\nwith certain descriptions has been addressed. The explanation they provided is\nacceptable.\nResponse:\nWe sincerely thank the reviewer for finding the issues having been resolved and\nour response was acceptable.\nComments:\nWhile the authors identify the c-axis as important, a more thorough exploration of\ninfluencing factors (such as the c/a ratio) is warranted. Given that this is a central\nfinding, enriching the discussion—potentially in the Supplementary Information—\nwould greatly solidify the argument and provide deeper insight for the reader.\nResponse:\nWe concur with the reviewer’s suggestion and have now provided such further\nexploration. In Figure R1, we provide the plot of T versus c/a, from which we could\nc\nobserve that the variation trend of T under diDerent substrates in the original figure\nc\nbecomes less pronounced.\nTo include this information, as suggested by the reviewer, we now list this figure as\na new figure (Figure S13) in the Supplementary Information, with additional\ndiscussion labelled as “XIII. T versus c/a”. Now this part of the Supplementary\nc\nInformation reads, “\nVI. T versus c/a\nc\nThe correlation of T and the normalized lattice parameter ratio c/a is plotted in\nc\nFigure S135,7–16. It can be observed that when c is replaced by the lattice parameter\nratio c/a, the trend of T in the original figure becomes less pronounced.”\nc\n1\n+,-EKL0NLOP4)5+ST+0N8P4G9+N:;\"EA\nGC +,-EKL0NLOP4)5+ST+0N8P4G9+N:;\"E#\n+,-EKL<-LOP4)5+ST+0N8P4G9+N:;\"E=\n+>NEKL0NLOP4)5+ST+0N8P4G9+N:;\")!\nG! +>NEKL0NLOP4)5+ST+0N8P4G9+N:;\"E\n+O?EKL0NLOP4)5+ST+0N8P4G9+N:;\")\n+O?EKL0NLOP4)5+ST+0N8P4G9+N:;\")G\n)C +O?EKL0NLOP4)5+ST+,0@89+N:;\")'\n+O?EKL0NLOP4)5+ST+O?A-4G9+N:;\"C\ni\nh\n+O?EKLBCLOP4)5+ST+,0@89+N:;\")%\nJ )!\n+0<0B5+ST+O?A-4G9+N:;\"'%\n+ +0<0B5+ST+,0@89+aEPc+dSNe\nf\n!\nEC\nE!\nC\n!\n!\"## !\"#A !\"#% !\"#C !\"#'\n\"M#\nFigure R9 (Figure S13 in the Supplementary Information). T plotted against c/a\nc\nfor all infinite-layer nickelate samples listed in Figure 4c in the main text.\nComments:\nFinally, the typos should be carefully minimized throughout the manuscript. Why\ndo both B and H appear in the revised sections? The B is totally replaced by μ0H.\nResponse:\nWe sincerely apologize for our carelessness in making the typos, especially in the\nnewly added sections. We have now carefully checked to eliminate the typos and\nunify the presentation of magnetic field to be μ H in the added section.\nOverall, this version could be considered for publication.\nResponse:\nWe are thankful to the reviewer for their invaluable time in reviewing our\nmanuscript and for their support in publishing our manuscript.\n(END)\n2"}]

Decision letter