Re-entrant unconventional superconductivity induced by rare-earth substitution in Nd_1-xEu_xNiO_2 thin films

Domain: chemistry
Published: 2026-03-05
Editorial outcome: accept

Abstract
High temperature superconductivity is typically associated with strong coupling and a large superconducting gap, yet these characteristics have not been demonstrated in the nickelates. Here, we provide experimental evidence that Eu substitution in the spacer layer of Nd Eu NiO (NENO) thin films enhances the superconducting gap, driving the system toward a strong-coupling regime. This is accompanied by a magnetic-exchange-driven magnetic-field-enhanced superconductivity. We investigate the upper critical magnetic field, H , and superconducting gap of superconducting NENO thin films with x=0.2 to 0.35. Magnetoresistance measurements reveal magnetic-field-enhanced superconductivity in NENO films. We interpret this phenomenon as a result of interaction between magnetic Eu ions and superconducting states in the Ni d orbital. The upper critical magnetic field strongly violates the weak-coupling Pauli limit. Infrared spectroscopy confirms a large gap-to-T ratio 2∆⁄𝑘 𝑇 ≃5−6, indicating a stronger coupling pairing mechanism in NENO relative to the Sr-doped NdNiO . The substitution of Eu in the rare-earth layer causes pronounced modifications of the superconducting gap and magnetic interactions in Nd-based nickelates, opening new pathways to engineer high-T superconductivity in infinite-layer nickelates.

Introduction
The discovery of superconductivity in layered nickelates (A, B)NiO (A=La, Pr, Nd, Sm; B=Sr, Ca, Eu) has brought about new perspectives in the study of high-temperature superconductors (1-6). While they share some common features with the copper-based high T superconductors (the cuprates), such as stacked two-dimensional metal oxide layers and the main contribution to low-energy bands from the d orbital, there are significant differences between these systems (7-11). Superconductivity in the cuprates is believed to be strongly coupled and driven by strong electron-electron interactions arising from the Cu 3d band and spin fluctuations(12). In contrast, there has not been direct evidence for strong coupling in known nickelate superconductors (13, 14). Additionally, while the spacer layer in the cuprates plays little role in the electronic structure near the Fermi level (7, 15), there is a considerable variation in superconducting properties within the RENiO family (RE=rare earth), depending on the RE-site ion (Figure 1a).

It is theoretically suggested that the spin structures, exchange interactions, and Fermi surfaces in nickelates strongly depend on the types of RE elements (16-19). Such changes are manifested in several experimental studies. The upper critical field H of La-based nickelate La Sr NiO (LSNO) thin films shows anisotropy between out-of-plane (H||c) and in-plane (H||ab) magnetic fields and a violation of the Pauli limit (16, 20-22), which is a bound on the upper critical magnetic field of a weakly-coupled singlet superconductor. In contrast, the isotropic, Pauli-limited H c2 in Nd 0.7S75 Sr 0.225 NiO 2 (NSNO) (23) makes NSNO more similar to the iron-based high-T superconductors that have multigap pairing (24, 25). London penetration depth studies in nickelates indicate that while the superconducting gap in LSNO is nodal and anisotropic, the superconducting gap in NSNO is fully gapped with differing interpretations regarding the symmetry of the gap (25, 26). Superconducting gap measurements on NSNO reveal variations in gap values and symmetries, with evidence for multiple gaps (27). MoPst data on NSNO suggest a superconducting gap consistent with BCS-like weak coupling, with gap-t o-T ratios of 2Δ/k T ≈ 3−3.4 (13, 14). These experimental observations highlight the importance of RE chemistry in modifying the superconducting gap in nickelates.

Motivated by these findings and our initial observation of anomalously high H in Nd Eu NiO (NENO) thin films with measurements up to 14 T (5), we present here comprehensive H (T) measurements in magnetic field up to 60 T, which are essential to reveal the re-entrant superconductivity behavior in NENO. We identify the microscopIic origin of this effect through density functional theory and modelling of the temperature dependence of H (T). Our key findings demonstrate that Eu substitutions in the RE layer not only provide charge doping but also introduce exchange coupling between Eu 4f magnetic moments and Ni 3d electrons, forming a rare occurrence of the Jaccarino–Peter effect in a thin film. Optical spectroscopy reveals a large superconducting gap (2Δ ≈ 75 cm-1), providing direct evidence for strong-coupling superconductivity and explaining the observed Pauli limit violation of H . Together, these results establish NENO as a strongly coupled unconventional superconductor with pronounced RE magnetism effect, in sharp contrast to the weak-coupling behavior of Sr-doped NdNiO . We demonstrate that Eu substitution offers a viable method to tune pairing strength and magnetic interactions in infinite layer nickelates.

Results
Magnetic-field-enhanced superconductivity and Pauli limit violation

In conventional superconductors, magnetic fields typically suppress superconductivity through vortex formation or Pauli paramagnetic de-pairing (28). The former leads to the loss of superconducting coherence; the latter raises the energy difference between spin-up and spin-down electrons, making the formation of Cooper pairs energetically unfavorable. In a singlet superconductor, the paramagnetic effect sets an upper bound on the upper critical magnetic field, 𝐻𝑃 = √2∆/𝑔𝜇 , where 𝜇 is the Bohr magneton and g is the Lande factor. For weakly-coupled superconductors, using 2∆=3.528k T (28), and g ≈ 2, this simplifies to the nominal Pauli limit, 𝐻𝑃 = 1.86 𝑇 (K), at T=0 K. Superconductors that not only withstand high magnetic fields but also have superconductivity stabilized by magnetism are highly unconventional. Here, we show that superconducting NENO thin films exhibit magnetic-field-enhanced superconductivity and attribute this phenomenon to magnetism of the Eu dopant.

We start by examining the magnetoresistance (MR) of three Nd Eu NiO thin films which were measured with magnetic fields up to 41 T for both H||c and H||ab at the National High Magnetic Field Laboratory (NHMFL). The films are grown using the same procedure described in Ref (5) and consist of 6 nm thick NENO films with x=0.20, 0.22 and 0.35 on (LaAlO ) (Sr TaAlO ) (LSAT) substrates with a 1 nm Al O capping layer (Figure 1b). Figure 2a-f shows color plots representing temperature and applied magnetic field dependences of the resistance R(T, H), interpolated from the raw R(H) curves taken at fixed temperatures. The black curves tracking the evolution of superconducting transition temperature taken by 50% Rn (i.e. T ), where Rn is the resistance in the normal state, are overlaid in Figure 2a-f, giving us the temperature dependence of H , H (T).

The applied magnetic fields suppress superconductivity in NENO in a highly non-monotonic and distinctive manner when compared to data reported in NSNO (23). First, R(T, H) for H||c and H||ab are anisotropic, and the superconducting state persists to a high field. The H (T) curves under H||c show broadening of the superconducting phase transition, suggesting the presence of a vortex liquid phase (29, 30). In contrast, under H||ab, there is no apparent broadening, suggesting the dominance of paramagnetic depairing and a negligible role of vortex dynamics and the thermal fluctuation. At the same temperature where the paramagnetic effect is dominant, H is much larger than H . H (T) shows that superconductivity in all samples reported here persists to the highest applied magnetic fields and strongly violates the Pauli limit for both H||c and H||ab. This distinguishes NENO from NSNO (23) and brings it closer to LSNO (16, 20-22). Dissipation in the superconducting phase is observed at low field as an increase in R(H), shown in Figure 2g-h. This dissipation is then suppressed over a wide range of magnetic fields centered around 20 T. R(H) shows a maximum at low field and a minimum at ~ 20 T that reaches zero resistance at low temperatures. This anomalous behavior is often described as re-entrant superconductivity (31-36) and has not been reported in the nickelates.

Due to the anomaly in R(H), H (T) shows anomalous inflection points and an enhancement of superconductivity, manifested as an increased dH /dT in H||c and an increased T in H||ab. Similar field and temperature dependence of MR, especially a magnetic-field-enhanced superconductivity (37-39) have been explained by proximal magnetism, which is the Jaccarino-Peter (J-P) effect (40). As depicted in Figure 3a, the J-P effect involves an exchange field H that acts on the conducting electrons, and comes from the interaction 𝐻̂ = ∑ 𝐽 𝑺 ∙𝒔 between local magnetic moments 𝑺 and the conduction electron spin density 𝒔 , where i and k label nearest neighbor RE and Ni orbitals. The J-P effect requires an antiferromagnetic coupling with a positive sign of the exchange coupling. As the applied magnetic field H polarizes the localized moments S, the antiferromagnetic exchange field H acting on 𝒔 is 𝐻 = ∑ 𝐽 𝑺 , which opposes the external field H and reduces the total magnetic field on the carriers in the nickel layers, H =H+H , enabling superconductivity at higher applied fields. As shown in Figure 3b, |H | exhibits a local maximum and a compensation point at H~H , where H is the saturated exchange field when the local moments are polarized. Depending on the magnitude of the Pauli limited 𝐻𝑃 compared to H , one can expect re-entrant superconductivity (H >H ) or magnetic-field-enhanced superconductivity (H <H ). Previous work revealed mixed Eu2+ and Eu3+ valences on the RE-site cation with a large Eu2+ (J=7/2) local moment in NENO (5). Qualitatively, the H (T) data strongly resembles the case in which the Pauli limited H >H . The temperature dependence of the maxima and minima of R(H) curves under H||ab follows that of |H | calculated using a Brillouin function B(T, H) describing polarization of paramagnetic Eu2+ moment in an applied magnetic field (see Supplemental Information). We posit that the nonmonotonic behavior in NENO is a result of a large critical field H and a J-P-type mechanism due to the exchange field from the Eu ions, as explained below.

We performed density functional theory (DFT) calculation to estimate the exchange coefficient 𝐽 between different orbitals of the RE ions and Ni ions. The results (see Supplemental Information) show non-negligible exchange fields H on Ni orbitals induced by different Eu 4f-orbitals. We ignore the contributions from Eu 5d-orbitals because their local moments are only about 0.1𝜇 , much smaller than the 4f-orbitals (about 6.5𝜇 ). Eu ions couple antiferromagnetically to Ni 3d and Ni 4p while they couple ferromagnetically to Ni 3d . Interestingly, Eu provides a 21.3 T antiferromagnetic exchange field on Ni 3d , closely matching the compensation field seen in our experiments. The same calculation was done for Nd and Sr dopants, and we find negligible exchange fields on all Ni orbitals (<1T for Nd, and <0.1T for Sr). The calculation results highlight the key contribution from the Eu dopant to the field compensation mechanism and also reveal which Ni orbitals are involved. From the calculations, we can infer that in NENO, electrons in the Ni 3d orbital are responsible for superconductivity. Since computed exchange fields for both Ni 3d and Ni 4p are too large (115 T and 128 T, respectively) compared to the applied field strengths, we expect suppressed contribution to the J-P effect from these orbitals, and the large exchange fields would likely reduce contribution from Ni 3d and Ni 4p electrons to superconductivity.

Considering the J-P effect, we modeled H (T) using two approaches. First, we employ a Ginzburg-Landau (G-L) approach, which is valid for both weak- and strong-coupling superconductors in the vicinity of the superconducting phase transition and relatively low magnetic field (see Supplemental Information). The G-L-based model we developed fits both the H||c and H||ab data up to 41 T for all samples, capturing the non-monotonic behavior of H (T) shown in Figure 2a-f. The extracted H ~17-23 T from these fits matches the DFT-calculated H of 21.3 T. Figure 3c shows extended H (T) data for the x=0.22 sample measured in pulsed magnetic fields up to 60 T for both H||c and H||ab in the pulsed field facility of NHMFL at Los Alamos National Laboratory. The G-L-based model continues to fit the data well up to ~50 T. To describe the data using a conventional modeling technique, H (T) is fitted to the Fischer formula (41), which is used to analyze J-P effect in organic and Chevrel phase superconductors (42, 43). The formula is based on the microscopic Werthamer–Helfand–Hohenberg theory (44-47). In our case, the Fischer formula fits H (T) data up to 41 T and only noticeably deviates from the data and G-L fits at higher magnetic fields (see Supplemental Information). At lower temperatures, neither model captures an upturn of H (T) above both fits (Figure 3c). An upturn in H (T) at low temperature near 0 K, also observed in NSNO and LSNO, could be related to multiband superconductivity or an emergence of an unconventional electronic state (23, 48-50). While a detailed analysis of this feature lies beyond the focus of our work, we propose that if higher order terms in powers of magnetic field were kept in the G-L expansion, they could account for the deviation from the parabolic profile shown in Figure 3c. Overall, the H (T) models support a J-P-type mechanism in NENO and suggest a strong-coupling scenario.

Evidence for enhanced coupling strength from superconducting gap measurements

As expected from the J-P effect, H in NENO is enhanced by the exchange field H , with an enhancement as large as H . This partially explains the much higher H in NENO when compared to other infinite layer nickelates. Without experimental H (T) data near T=0 K, we resort to estimating the intrinsic Pauli limit violation using an extrapolation to T=0 K of the modified G-L fit with H||ab (which underestimates the experimental data) and then subtracting the enhancement from the J-P effect. This estimation yields a Pauli limit violation ratio of 2.3-3.4 for NENO. Previous studies on Pauli limit violation in La-nickelates have discussed that mechanisms like finite momentum pairing and strong spin-orbit coupling are unlikely explanations (20-22), while spin-triplet superconductivity remains as a speculative mechanism. Strong coupling in nickelates has been proposed but it has not yet been thoroughly investigated experimentally. Using the electron spin g-factor g=2, we approximate a gap-to-T ratio of 12.1, 8.0 and 8.4 for samples with x=0.20, 0.22 and 0.35, respectively. This doping dependence is reminiscent of similar phenomenology observed in the strongly coupled hole-doped cuprates (51-53). This underscores potentially common aspects of unconventional superconductivity in these two layered oxide superconductors. To evaluate this possibility, we investigated the optical response of NENO by Fourier transform spectroscopy over the entire far-infrared range to determine its superconducting gap.

Reflectivity spectra from a NENO film with x=0.30 grown on LSAT (T at ~ 18 K) and a bare LSAT substrate were measured for different temperatures. Small changes in reflection (54) from the 6-nm thick NENO films were detected by dividing the data measured in the superconducting state by that taken at T = 22.5 K > T (see Methods). As shown in Figure 4a, when cooling below T the normalized reflectivity develops a prominent dip around 75 cm−1and a sharp upturn at lower frequencies, which is specific to superconducting NENO and absent on the substrate alone. From the temperature-dependent ratios in Figure 4b, we find that this feature, which we associate with the opening of the superconducting gap, is no longer resolved above 15 K, flattening out completely at T = 20 K. We also observed a peak centered around 170 cm−1, which we attribute to a spurious effect caused by a change in multilayer reflectivity at the LSAT phonon frequency due to the opening of the superconducting gap in NENO.

We fitted these normalized reflectivities by considering the sample as a multilayer stack consisting of an Al O capping layer, NENO film, and LSAT substrate (see Figure 1b). Since the weakly frequency-dependent optical properties of Al O are known (59) and those of the bare LSAT substrate were directly measured alongside NENO (see Supplemental Information), the multilayer reflectivity could be computed by modeling only the response of superconducting NENO. We started from a Mattis-Bardeen model (see Supplemental Information), which describes the optical properties of a superconductor (55) by assuming an s-wave gap in the dirty limit (i.e., 2∆≪ Γ, where Γ is the normal carrier scattering rate). This model yielded the measured normalized reflectivity, using only the superconducting gap (2∆) and the normal state conductivity (𝜎 ) of NENO as free parameters. As shown in Figure 4a, the best fit for the experimental data was obtained for 2𝛥 ≃ 75 cm−1 and a normal state DC conductivity of 100 Ω−1cm−1.

Note that the fitted value of 𝜎 is more than one order of magnitude smaller than the 3000 Ω−1cm−1 obtained independently from electrical transport. To improve on the fit, we next considered that uncondensed quasiparticles are likely to persist down to zero temperature due to nodal excitations if the gap symmetry is lower than s, an effect not included in the Mattis-Bardeen fit above. We tested this hypothesis by adapting the fit to a nodal d-wave superconductor in the dirty limit and with a residual metallic Drude peak (56) (see Supplemental Information). This model assumes that a part of the spectral weight at low frequencies arises from uncondensed quasiparticles, a mechanism that has been used to explain missing superfluid density in cuprates (56). As shown in Figure 4a, this model fits the data with the same value of the superconducting gap (2Δ ≃ 75 cm−1) and an improved estimate of the normal-state conductivity (~500 Ω−1cm−1). In addition, it fits well the temperature-dependent spectra (see Figure 4b) by letting the contribution of uncondensed quasiparticles increase with 𝑇.

Although the model above broadly captures the normal state conductivity, the remaining difference could be adapted by assuming that the superconductor is spatially inhomogeneous, with superconducting and normal state coexisting in different regions of the sample. As shown in the Supplemental Information, all spectra could be fitted with the correct value of the conductivity of the normal state of σ ≃ 3000 Ω−1cm−1 by tuning the filling fraction between normal and superconducting regions (57). In spite of possible inclusion of normal regions, the observation of robust zero resistance at high magnetic fields, bolstered with a high critical current density and a large diamagnetic screening signal from mutual inductance measurement, demonstrates the bulk nature of superconductivity in our samples (see Supplemental Information). While this strongly suggests d-wave pairing through the persistence of low-frequency spectral weight inconsistent with fully-gapped s-wave superconductivity, momentum-resolved gap measurement techniques are expected to add clarity to the nature of the superconducting gap.

In the aggregate, regardless of the model used, the gap amplitude 2∆ is consistently estimated as 2Δ ≃ 75 cm−1 (9.3 meV). This value is about two times greater than that reported for NSNO (13, 14), resulting in a gap-to-𝑇 ratio of 2∆⁄𝑘 𝑇 ≃5−6, in the same range as reported for the hole doped cuprates in the overdoped range (51-53). The large gap-to-𝑇 ratio may plausibly explain the unusually high upper critical field reported here in NENO and in La-based nickelates (20, 22). While the measured 2∆⁄𝑘 𝑇 does not fully align with the ratio estimated from the Pauli limit violation, the discrepancy likely arises from the distinction between zero-field FTIR measurements and high-field transport measurements, suggesting that the superconducting gap may be magnetic-field-dependent due to interactions of Eu magnetic moments with superconductivity.

The large difference in pairing strength between NSNO and NENO demonstrates that Eu substitution in the RE layer can be an effective method for modifying the superconducting gap size in the Nd-based nickelates. The presence of Eu magnetic moments and Eu-Ni exchange interactions may indirectly influence the Ni-Ni magnetic exchange interactions (58), and facilitate strong coupling, while Nd-Ni and Sr-Ni exchange interactions are negligible (smaller than 0.1meV based on our DFT calculations). Furthermore, the smaller ionic radius of Eu2+/Eu3+ relative to Sr2+ is suggested to reduce the NiO plane separation and strengthen the pairing interaction through dimensionality control (59-61), with the observation of a T above 35K in the smaller RE size infinite layer nickelate Sm Ca Sr Eu NiO (6). The reported c-axis lattice constant in NENO is smaller by 0.05Å compared to NSNO (5, 62), which may contribute to the observed increase in pairing strength in NENO.

In conclusion, we show that NENO thin films exhibit magnetic-field-enhanced superconductivity driven by a Jaccarino-Peter-type effect, in which the exchange fields from local magnetic moments of Eu ions reduce the effective field acting on the superconducting states in the Ni d orbital. This behavior is the first indication of a strong interaction between Eu dopants and the superconducting state. The anomalously high H exceeding the Pauli limit, in conjunction with a large 2∆⁄𝑘 𝑇 ≃5−6 measured by infrared spectroscopy, confirms a strong coupling superconductivity mechanism in the Eu doped NdNiO , in stark contrast to the weak coupling mechanism suggested for the Sr doped NdNiO . The reflectivity data in NENO fits well to a dirty node-line d-wave pairing model. These observations reveal a pairing energy scale that is similar to values in the strongly coupled, hole-doped cuprates. The distinct superconducting characteristics of NENO compared to NSNO highlight the potential of dopants like Eu to tune the electronic structure in infinite-layer nickelates. Specifically, Eu magnetic moments can be manipulated to control superconducting states, and Eu substitution in the rare-earth layer offers a new dimension to tune superconducting pairing strength, an essential factor in understanding high-T nickelates (6).

Methods
Thin film growth and characterization

Thin films of Nd Eu NiO are grown to a thickness of 18-21 unit cells (uc) on as-received commercial 5×5 mm LSAT (001) substrates (from CrysTec) using molecular beam epitaxy (MBE). The substrates are cleaned at 605°C by using an activated oxygen source at a chamber pressure of 8×10-6 Torr for 15 minutes prior to thin film synthesis. The thin films are grown under the same conditions as for the plasma cleaning process. After growth, the films are cooled in activated RF plasma oxygen to 150°C to eliminate oxygen vacancies. The thin film Nd Eu NiO is kept in the chamber for in-situ reduction using metallic Al in a process as described in Ref. (63).

θ-2θ scans (see Supplemental Information) of the films around the (002) pseudo-cubic peak show a lattice constant corresponding to 112 phase and finite size oscillations visible in all the curves, indicating the high crystallographic quality of the films. X-ray diffraction data shows the c-axis lattice constant of 3.31 Å in NENO with small doping dependence.

Transport measurement at high magnetic fields

For angular magnetoresistance measurements, the samples were contacted using wire-bonded aluminum wires in a Hall bar geometry. The high-field measurements were conducted at NHMFL DC Field Facility in Tallahassee, with 35 T and 41 T resistive magnets and temperature from 2 K to 21 K using the He-3 insert. The different orientations of the magnetic field with respect to the plane of the films were achieved by using a sample probe with a rotator. Resistance was measured in Delta mode using a synchronized set of Keithley 6221 current source and Keithley 2812A nanovoltmeter (64). The magnetic field was swept from zero to maximum fields at the rate of 3 T per minute while voltage and current data were collected. Here, we define the upper critical field H as the magnetic field at which the resistance increases to 50% of the normal state resistance (Rn) just above the critical temperature (T ). Temperature was controlled using a PID controller with input from a capacitive thermometer mounted near the sample stage. This type of thermometer is known for having almost no field dependency, which is ideal for high magnetic field measurements.

The measurements in pulsed magnetic fields were conducted at NHMFL Pulsed Field Facility in Los Alamos National Laboratory. Four-wire electrical resistance measurements were performed in a 65 T short pulse magnet with He-4 cryostat on a probe with in situ rotating capabilities(65). The sample resistance was measured using pulsed direct current (DC) method based upon a modified form of the approach described in Ref. (66). Typical current durations were on the order of ~10 𝜇s.

Data presentation: For each Eu concentration and field orientation, magnetoresistance R(H) data were collected at 11-16 temperatures per data set (See Supplemental Information for R(H) data). For pulsed field measurement, each R(H) data curve was assigned the corresponding thermometer reading at the start of the pulse. For DC field measurement, we used temperature reading from a capacitive thermometer mounted near the sample stage. To facilitate direct comparison across samples and different measurement setup, we represented the data as the colormaps in Fig. 2. The R(H) curves were resampled onto a common field grid with 0.25 T steps by selecting the nearest measured point to each grid value. The resulting (T, B, R) triplets from all temperatures were combined and interpolated using a natural neighbor interpolation function, producing a smooth resistance surface R(T,B), which is then represented as colormaps as in Figure 2. The upper critical field H (T) was extracted for resistance thresholds corresponding to fractions of the normal-state resistance Rn by identifying all grid points where R(T,B) matched the target within ±0.001 of the target resistance.

The uncertainty from this process is checked by removing individual data points from the input set, re-interpolating R(T,B) and comparing the resulting H (T) values with the originals This measures the sensitivity of the interpolation to data sparsity and local irregularities in the sampling grid. This type of uncertainty becomes significant in regions where R(T) relationship becomes non-linear, i.e. in vicinity of the superconducting transition and near zero resistance and less significant at the middle of the transition where R(T) is almost linear and where we sample H (T) data.

X-Ray Diffraction

X-ray diffraction (XRD) of the samples is taken using a rotating anode high-resolution X-ray diffractometer (Rigaku SmartLab). The X-ray energy is fixed at the Cu-Kα energy of 8.04 keV.

Fourier-Transform Infrared Spectroscopy

We measured reflectivity spectra with a Bruker Vertex 80v Fourier transform spectrometer in quasi-normal incidence geometry. As a source, we used an in-built Hg arc lamp. The total measurement range of ~10 − 800 cm-1 was covered by detecting the far-infrared radiation with two different bolometers with working temperatures of 4.2 K and 1.6 K for the ranges above and below ~ 40 cm-1, respectively. The absolute reflectivities (see Supplemental Information) were obtained by taking the ratio at a given temperature between the reflected spectrum from the sample (either bare LSAT or NENO/LSAT) and that from a gold reference placed next to it. To this end, the sample holder was mounted on the cold finger of a He flow cryostat, equipped with a motorized stage.

In the case of temperature-dependent normalized reflectivity, to reduce the experimental error arising from changing the sample position, the spectra were measured on a fixed spot on the sample while the temperature was varied (54). Then, these were normalized by a reference spectrum taken at 22.5 K. This temperature was chosen to be slightly above 21 K, the onset temperature of superconductivity in NENO, identified by DC transport measurements.

DFT calculations

All DFT calculations were performed using the Vienna ab initio simulation package (VASP) software (67) with ECUT=520eV, and 8×8×6 k-grid sampling for √2×√2×2 supercell, and the exchange-correlation effects were treated using the strongly-constrained-and-appropriately-normed (SCAN) meta-GGA functional (68). Spin-orbit coupling effects were included self-consistently. We use a √2×√2×2 supercell to allow spontaneous spin ordering along in-plane or out-of-plane directions. The ground state obtained in the DFT calculation is a C-AFM magnetic configuration (18). We then computed the tight-binding Kohn-Sham Hamiltonian on the maximally localized Wannier basis as extracted from our DFT calculations using the Wannier90 software (69). The Wannier basis includes all 3d- and the 4p -z orbitals of Ni, all p-orbitals of O, and all f-orbitals of Eu and Nd, which are sufficient to describe the bands near the Fermi level from -4eV to 2eV as well as the dominant magnetic moments (see Supplemental Information for details). Next, the Wannier tight-binding model was mapped to a Heisenberg model using the TB2J software (70), which directly provides the exchange interactions and allows us to compute the corresponding effective exchange field on the Ni band conduction electrons.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Question 1: OK.\nQuestion 2: OK.\nQuestion 3: Mostly OK. I appreciate the authors’ inclusion of additional details on the fitting procedure, which makes the\nanalysis much clearer. One remaining point of confusion concerns the second fitting approach referred to as the d-wave\nBCS model. I do not see the gap parameters explicitly appearing in the fitting functon(Eq. S5) in the Supplementary\nInformation. I assume these are included implicitly through σ_d (ω). If this is the case, I suggest the authors explicitly show\nthe expression and clarify the role of the gap parameters for readers who may not have a strong spectroscopy background. If\nthis assumption is incorrect, please clarify accordingly.\nQuestion 4: OK.\nQuestion 5: OK.\nQuestion 6: I understand that the authors may not feel comfortable commenting extensively on other groups’ results.\nHowever, given that similar samples are studied elsewhere and magnetism can play an important role in superconducting\nproperties, it would be helpful to include a brief acknowledgment of the relevant existing literature.\nMore comments: The figures would benefit from a careful cleanup to ensure consistent styling. Currently, different fonts are\nused across figures, and some labels are missing. For example, Fig. 4 lacks panel labels (a) and (b), and Fig. 3 appears to\nhave inconsistent fonts and aspect ratios.", "reviewer_2": "The authors have significantly improved the manuscript. I have no more comments. I recommend publication as it is.", "reviewer_3": "The authors have dramatically improved the quality of this manuscript in the previous stages of peer review. My opinion prior\nto the transfer of this manuscript was that the work is scientifically sound and will be of importance to the Nickelate\ncommunity. Therefore, I recommend publication of the work without extra modifications."}, "author_response": "We thank the reviewers again for the assessment of the work. With the transfer of the manuscript\nto Nature Communications, we enclose our point-by-point response to all the remaining comments\nhere, in blue, and provided a revised manuscript and Supplemental Information as separate files\nwith our changes in blue. We believe the manuscript and the attached response address all the\ncomments from the reviewers and that the manuscript is substantively improved and suitable for\npublication in Nature Communications.\n_______________\nReviewer #1 (Remarks to the Author):\nIn my original report, I raised several concerns regarding the impact, interpretation, rigor, and\nclarity of the manuscript relative to the standards expected by Nature Materials. I note that some\nof these issues were also highlighted by Referee #3. The revised version shows certain\nimprovements; however, there remain vague and sometimes evasive discussions that fail to\nadequately address the central scientific issues. While the work has potential, the current\nmanuscript still falls significantly short of Nature Materials standards in terms of impact, clarity,\nand robustness of results. Below I elaborate on my main points.\n1. The reported results represent an incremental advance over the group’s previous work (e.g.,\nextending magnetic field from 14 T to 60 T, identifying the Jaccarino–Peter effect, and reporting\na large superconducting gap). While these observations are of interest, they largely constitute\nadditional measurements rather than a conceptual breakthrough in materials physics. The DFT\ncalculations appear disconnected from the microscopic physics of the pairing symmetry. As I stated\nin my initial review, incremental progress could still be acceptable if the data and analysis were\nrigorous and conclusive; however, I remain concerned about these aspects.\nWe respectfully do not agree with the description of our work as merely incremental. Our results\nrepresent significant experimental evidence that challenges prior results about nickelate\nsuperconductivity:\nFirst, the discovery of strong-coupling superconductivity in nickelates directly contradicts the\nweak-coupling picture established by all prior studies, including the recent Nature Materials paper\n(Nature Materials 23, 775–781 (2024)). These are not just \"additional measurements\", they\nfundamentally change our understanding of the pairing mechanism. While it is still inconclusive\non exactly how the presence of Eu affects coupling strength, the results will substantially impact\nfuture theoretical studies aimed at understanding the microscopic mechanism of superconductivity\nin nickelates and its relationship to cuprates.\nSecond, the observation of magnetic-field-induced re-entrant superconductivity via the Jaccarino-\nPeter mechanism represents a rare and striking phenomenon. Among known superconductors, only\na handful of systems exhibit this behavior (e.g., certain heavy fermion compounds). Our work\nestablishes nickelates as a new platform for studying the interplay between magnetism and\nsuperconductivity, a central problem in condensed matter physics. The fact that competing groups\nhave now reported similar findings (arXiv:2508.14666 and arXiv:2508.16290) utilizing highly-\nsought-after resources such as pulsed high magnetic field facilities underscores the significance\nand timeliness of this discovery.\nRegarding the DFT calculations, we note that these provide crucial microscopic support for the\nJaccarino-Peter mechanism by demonstrating how Eu substitution introduces the necessary\nmagnetic exchange field. While they do not address effect of Eu substitution on pairing symmetry,\nthey are essential for validating the proposed mechanism.\n2. The measurement of the superconducting gap is important, but not sufficiently novel on its\nown. The data do not convincingly demonstrate the fraction of uncondensed quasiparticles—\nwhile the fitting suggests a possible hint, it does not distinguish clearly between s-wave and d-\nwave symmetry.\nThe purpose of the optical measurements is to measure the size of the superconducting gap which\nrepresents a major finding: 𝟐∆⁄𝒌 𝑻 ≃𝟓−𝟔, indicative of strong-coupling\n𝑩 𝐜\nsuperconductivity. As we have stated explicitly in our previously revised manuscript: Optical\nspectroscopy, not being a momentum-resolved technique, is unable to provide definitive\nconclusions about the symmetry of the superconducting gap.\nAs discussed in the previous rebuttal, the magnitude of the fit parameters remains a significant\nobservation. The s-wave fit requires a normal-state conductivity more than one order of magnitude\nlower than the value measured via DC transport. The reflectivity spectra can be fitted with\nreasonable s values only if a substantial portion of the spectral weight in σ₁ below the gap persists\nDC\nto the lowest temperatures. This behavior is inconsistent with the complete suppression expected\nfor a fully gapped s-wave superconductor and is naturally explained by the presence of nodes in\nthe superconducting gap, where residual quasiparticle would accumulate. To make it clearer, we\ntabulated the obtained fit parameters in tables S4, S5 of the Supplemental Information Section S7.\nMoreover, the assumption of inhomogeneous or filamentary superconductivity appears ad hoc.\nAn effective medium approach was employed to consistently fit the reflectivity spectra using the\nexact value of the normal-state conductivity measured via DC transport.\nAs discussed in the manuscript, in spite of possible inclusion of normal regions, the observation\nof robust zero resistance at high magnetic fields, along with a high critical current density and a\nlarge diamagnetic screening signal, demonstrates the bulk nature of superconductivity in our\nsamples.\nThe references cited in response to my earlier comment (#2) show optical conductivity both\nbelow and above, which is missing here and is essential for a complete analysis.\nThe work referred to by the reviewer was carried out with a different technique than ours, namely\nTHz time-domain spectroscopy. This technique allows, after appropriate modeling of the substrate\nresponse, to directly extract both the real and imaginary part of the optical conductivity of the thin\nfilm.\nOur measurements were performed instead with Fourier Transform Infrared Spectroscopy, such\nas those on LSNO in Cervasio et al., ACS Applied Electronic Materials 5, 4770-4777 (2023).\nWhile through reflectivity ratios at various temperatures we are sensitive to very small changes\nacross the superconducting transition, in order to extract the complex optical conductivity, we\nwould have to rely on Kramers-Kronig transformations. This procedure, given the limited\nmeasurement range, would introduce considerable uncertainties. To avoid unwanted uncertainties,\nfollowing the same standard approach as that of Cervasio et al., as well as that of other works using\nthe same technique, we directly fitted the reflectivity ratios with a multilayer model, thus extracting\nthe parameters related to the response of the superconducting film. Overall, the information\nobtained from our experiment (superconducting gap, normal state conductivity, quasiparticle\ncontribution) is the same as that from the other works mentioned.\n3. I remain disappointed by the authors’ response to my suggestion for a more systematic\npresentation of the optical conductivity fitting. At a minimum, the manuscript should list all key\nequations in a logically consistent manner, include detailed descriptions of fitting parameters, and\ntabulate the extracted values.\nWe have followed the referee's suggestion and improved the discussion related to the various fit\nmodels in the revised version of Section S7 of the Supplemental Information. We have also\nincluded tables S4 and S5 with fit parameters.\nCurrently, the discussion remains fragmented and overly general, with statements such as:\n“This approach involves calculating Fresnel reflection and transmission coefficients at each\ninterface...” and “Due to the lack of interference effects...the interfaces were assumed to be\nincoherent.”\nThese claims raise concerns. For instance, it is unclear how a film only 6 nm thick could reasonably\nfall into the incoherent Fresnel reflection limit.\nThere was a misunderstanding here. The absence of interference effects referred to the response\nof the substrate and in particular to the absence of a reflected signal from its back surface, which\nwas not polished in our sample. In contrast, the coherent effects at the Al O /NENO and\n2 3\nNENO/LSAT interfaces were correctly accounted for in the model.\nTo clarify, we have modified the sentence in question in section S6 of the Supplemental\nInformation, which now reads:\n“Note that the coherent effects at the Al O /NENO and NENO/LSAT interfaces were taken into\n2 3\naccount in the model. In contrast, the contribution from the back surface of the substrate (not\npolished in our sample) was neglected.”\n4. I strongly recommend additional measurements across different doping levels and Tc values.\nGiven the modest novelty and inconclusive evidence so far, these are essential. For example, the\ngap size versus temperature (Fig. 4b) shows no systematic variation within experimental\nuncertainty, suggesting inadequate sampling. The authors dismiss this by stating that the optical\nmeasurements were performed at too low a temperature; however, the data shown are at 4 K,\nwhereas other dopings exhibit Tc > 10 K. This rationale is unconvincing and does not meet the\nlevel of experimental rigor expected for Nature Materials.\nWe agree that a broader doping-dependent optical spectroscopy dataset would be good to have and\nis a clear priority for future work, possibly with an improved experimental setup. We reiterate here\nhow the need to use windows limits the ability to cool the samples to the lowest temperatures to\nperform optical experiments that can resolve features of the superconducting gap, which are\ngenerally harder than transport measurements.\nSpecifically, optical measurements on samples with lower critical temperatures would have a high\nchance of failure. A direct measurement of features related to the superconducting gap would be\nmade extremely challenging for both lower and high doping levels (i) by the fact that the gap itself,\ngiven the lower T , would be smaller and likely fall below our measurement range and (ii) by not\nC\nbeing able to reach sufficiently low temperatures, ideally below ~T /2, to observe the response of\nC\na fully developed order parameter. As a result, we present optical spectroscopy data only for the\noptimally doped sample with the highest critical temperature.\n5. To convincingly demonstrate that the observed superconductivity is of bulk rather than\nfilamentary nature, clear and quantitative evidence of Meissner diamagnetism is essential. This\nconstitutes the bare minimum standard for establishing bulk superconductivity, yet such evidence\nis currently absent.\nAs discussed in the Supplemental Information Section S8, the observation of robust zero resistance\nat high magnetic fields, along with a high critical current density and a large diamagnetic screening\nsignal from mutual inductance measurements, demonstrates the bulk nature of superconductivity\nin our samples. These multiple independent measurements provide compelling evidence against\nfilamentary superconductivity.\n6. Several recent studies have proposed a key role of ferromagnetism in the re-entrant\nsuperconducting behavior. For instance, a recent arXiv report (2508.14666) attributes the effect to\nferromagnetism of the Eu²⁺ sublattice. In contrast, the present manuscript does not report any\nferromagnetic order. It would be desirable, though not strictly essential, for the authors to clarify\nthis apparent inconsistency and discuss how their findings relate to those reports.\nWhile ferromagnetism remains a possibility that warrants further investigation, the magnetic\nmeasurements in arXiv:2508.14666 show features that suggest contributions beyond simple Eu2+\nordering. Specifically, that report shows magnetic moments reaching up to 400 μB/Eu in their\nx=0.22 sample and >10 μB/Eu in x=0.34 and x=0.55 samples, values much higher than the\nexpected saturated moment of 7.94 μB/Eu for Eu2+. This indicates that the magnetic moment may\noriginate from sources other than Eu2+. Additionally, without temperature-dependent\nmagnetization data and given the absence of hysteresis in Hall and magnetoresistance\nmeasurements (which would be expected for intrinsic ferromagnetism), we find the evidence for\nferromagnetic order inconclusive at this stage. Prior studies have also pointed toward spin-glass\nstates or NiO inclusions as possible sources of magnetic hysteresis. We refrain from claims of\nmagnetic ordering in our system until more definitive experimental evidence is available.\n_______________\nReviewer #2 (Remarks to the Author):\nI have read the modified manuscript by the Ahn team, as well as their descriptive response to\neach point raised by the reviewers. Going point by point through the response provided by the\nauthors:\n1) The removal of kinks is good in Fig.2, but I still don’t like this data presentation style as it is\nnot visually clear how many sweeps there are. At a bare minimum, all sweeps should be shown\nin the SI.\nFollowing the reviewer’s suggestion, we now include all sweeps in the Supplemental Information,\nSection S9.\n2) These statements based on models may be plausible, but I still only consider it to be valid if\nadditional thickness samples were investigated due to the large number of parameters used in all\nfitting procedures.\nWhile the analysis is plausible, it is best to validate using experimental study of thickness\ndependence, as the reviewer suggests. We thank the reviewer for this idea and will work on that in\nfuture studies.\n3) Thank you for clarifying this.\n4) Thank you for expanding on the discussion on the fitting procedure, which is very helpful. I\nfind it surprising that \\lamba_SO is so small, but as the authors note, it is connected to \\alpha,\nwhich makes the fitting procedure challenging.\n5) Thank you for clarifying this section, which is now significantly improved.\n6) Thank you for clarifying this point.\nWe appreciate the reviewer's comments on the improvements and clarifications we have made.\nIn summary, I think the work is scientifically sound, especially given the challenges associated\nwith accessing the high magnetic field lab for experiments. But there remains the question of\nwhy this work is significant beyond the niche case of nickelates.\nWe thank the reviewer for their careful evaluation and constructive feedback.\nRegarding the significance of this work beyond nickelates, recently there has been increasing\nattention to studies of upper critical fields in different materials, with a special emphasis on Pauli-\nlimit violation.\nA few examples include graphene-based superconductors and UTe . For example, in UTe there\n2 2\nare 3 distinctively different superconducting phases, which behave very differently under the\napplication of the external magnetic field: some superconducting phases are suppressed by the\nfield, some are enhanced, and some exist only in ultra-high magnetic fields. Understanding which\nmechanisms lead to field-induced superconductivity is a fundamental question with potential for\ndiscovering new superconducting materials and states with practical applications.\nThe Jaccarino-Peter mechanism is among a few known microscopic mechanisms to maintain\nsuperconductivity at very high magnetic fields. Our work aims towards a Jaccarino-Peter-like\nscenario in NENO. This finding establishes a synergetic relationship between local magnetism and\nsuperconductivity in a way that parallels heavy-fermion and uranium-based superconductors, but\nin a chemically and structurally distinct platform. Therefore, beyond the specific case of nickelates,\nour results contribute to the fundamental understanding of how magnetism and superconductivity,\ntypically antagonistic phenomena, coexist and even reinforce each other, aiding the engineering of\nnew field-tunable or magnetically mediated superconductors across a wide range of materials.\n_______________\nReviewer #3 (Remarks to the Author):\nIn the revised version, the authors have significantly improved the quality of the manuscript.\nBelow I provide two more comments:\n1. High Tc superconductivity is usually associated with strong coupling and a large\nsuperconducting gap. In this manuscript, the authors found that the substitution of Eu strengthens\nthe superconducting gap of Nd-based nickelate superconductors. However, the Tc of these samples\nare similar to those of Nd1-xSrxNiO2 (15-20 K). They seem inconsistent.\nThank you for the insightful comment. The observation of a larger superconducting gap in Eu\nsubstituted Nd-based nickelates, together with a moderate T similar to that of Nd Sr NiO ,\nC 1-x x 2\nis not inconsistent with unconventional strong-coupling superconductivity. Such a disproportionate\nincrease of gap-over-Tc ratio is a hallmark of strong coupling superconductivity. For example, in\nLa Sr CuO (LSCO), the gap-to-Tc ratio in underdoped LSCO can reach ~8, with a moderate\n2-x x 4\nT often below 40 K; the ratio in over doped Bi-2212 can reach ~10 near optimal doping (Science\nC\n362,62-65(2018)); and this ratio also reaches 4.6 in Pb - an archetypal strong coupling\nsuperconductor with modest T of 7.2K.\nC\nThese examples illustrate that strongly coupled superconductors could produce larger gaps at the\nsame Tc of their weaker coupled counterparts. Notably, this is also seen in iron-based\nsuperconductors, which is in a similarly intermediate coupling regime to NENO (see Figure 25,\nReviews of Modern Physics 93, 025006 (2021)).\n2. Figures 2g,h need some improvement. A zoom-in figure would help to show if zero resistance\nis achieved under high fields (re-entrant superconductivity).\nFollowing the reviewer’s suggestion, we revised Figures 2g,h to show the achieved zero resistance\nunder high fields.\nRESPONSE TO REFEREE REPORTS\nWe thank the reviewers again for the assessment of the work. We enclose our point-by-point\nresponse to all the remaining comments here, in blue, and provided a revised manuscript and\nSupplemental Information as separate files. We believe the manuscript and the attached response\naddress all the comments from the reviewers and that the manuscript is suitable for publication in\nNature Communications.\n_______________\nReviewer #1 (Remarks to the Author):\nQuestion 1: OK.\nQuestion 2: OK.\nQuestion 3: Mostly OK. I appreciate the authors’ inclusion of additional details on the fitting\nprocedure, which makes the analysis much clearer. One remaining point of confusion concerns\nthe second fitting approach referred to as the d-wave BCS model. I do not see the gap parameters\nexplicitly appearing in the fitting functon(Eq. S5) in the Supplementary Information. I assume\nthese are included implicitly through σ_d (ω). If this is the case, I suggest the authors explicitly\nshow the expression and clarify the role of the gap parameters for readers who may not have a\nstrong spectroscopy background. If this assumption is incorrect, please clarify accordingly.\nResponse: Following the reviewer’s suggestion, we have included the formula for the d-wave\nMattis-Bardeen model in the revised manuscript (lines 334-345 in the Supplementary Information)\nand clarified the role of the gap parameters. This explicit inclusion will assist readers who may not\nhave a strong background in spectroscopy.\nQuestion 4: OK.\nQuestion 5: OK.\nQuestion 6: I understand that the authors may not feel comfortable commenting extensively on\nother groups’ results. However, given that similar samples are studied elsewhere and magnetism\ncan play an important role in superconducting properties, it would be helpful to include a brief\nacknowledgment of the relevant existing literature.\nResponse: We have now incorporated our previous response to the reviewer’s comment on\nmagnetism in similar samples into the revised manuscript (lines 53-60 in the Supplementary\nInformation) to acknowledge the relevant existing literature.\nMore comments: The figures would benefit from a careful cleanup to ensure consistent styling.\nCurrently, different fonts are used across figures, and some labels are missing. For example, Fig.\n4 lacks panel labels (a) and (b), and Fig. 3 appears to have inconsistent fonts and aspect ratios.\nResponse: We appreciate the reviewer’s attention to detail. We have carefully reviewed and edited\nthe figures to ensure consistent styling and proper labeling. The revised figures are submitted as\neditable files for editorial purposes.\n_______________\nReviewer #2 (Remarks to the Author):\nThe authors have significantly improved the manuscript. I have no more comments. I\nrecommend publication as it is.\nResponse: We sincerely thank the reviewer for their careful evaluation and constructive feedback,\nwhich have significantly improved the quality of the manuscript.\n_______________\nReviewer #3 (Remarks to the Author):\nThe authors have dramatically improved the quality of this manuscript in the previous stages of\npeer review. My opinion prior to the transfer of this manuscript was that the work is scientifically\nsound and will be of importance to the Nickelate community. Therefore, I recommend publication\nof the work without extra modifications.\nResponse: We thank the reviewer for their thoughtful evaluation and constructive feedback. We\nare pleased that our manuscript has met their expectations and appreciate their support for its\npublication."}]

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