A chemical avenue to manipulate field-reentrant superconducting rivalries in infinite layer nickelates

A chemical avenue to manipulate field-reentrant superconducting rivalries in infinite layer nickelates | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A chemical avenue to manipulate field-reentrant superconducting rivalries in infinite layer nickelates Jikun Chen, Haowen Han, Yusong Zhao, Yi Bian, Tong Ma, Wenlong Yang, and 11 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7803050/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Recently, preliminary magnetic field-reentrant superconductivity manifested in high-temperature (Tc) Eu-doped infinite-layer (IL) nickelates, beyond analogous discoveries exclusively in low-Tc systems. This evokes intriguing fundamental issues about potential quantum-phase boundary and criticality between unconventional superconductivity and field-reentrant-one, which are inexplicable owing to formidable challenges in growing IL-nickelates towards later-series rare-earths. Herein, we open up chemical avenues to enable effective growth of (RE1-yRE'y)1-xEuxNiO2 (RE/RE': Pr, Nd, Sm, Gd, Dy), giving rise to discoveries of RE-4f-related quantum rivalries between high-Tc and reentrant superconductivity. Robust magnetic-field-reentrant superconductivity with uniaxial anisotropy is observed at superconducting-dome boundaries, stemming from Eu2+-4f7 associated competitions between magnetic-fluctuation promoted pairing and exchange-field interactions. Their quantum-criticality is further modulable via RE(RE’)-magnetism, which either reinforces reentrancy or elevates Tc (~40.1 K) with more robust critical-current-density (~266 kA/cm2 at 2 K) beyond Sr-/Ca-doped counterparts. Our synthetic route enables the establishment of an ideal platform via IL-nickelates for studying 4f-related unconventional superconductivity and quantum-criticality. Physical sciences/Materials science/Condensed-matter physics/Superconducting properties and materials Physical sciences/Materials science Figures Figure 1 Figure 2 Figure 3 Figure 4 1.Introduction The participance of f -electrons in ferromagnetic coupling 1 , Kondo lattice 1,2 , and antiferromagnetic exchange mediated Cooper-pairing 3,4 , largely enriches the superconducting phase diagram, also giving rise to magnetic field-reentrant superconductivity 5 . Recently, preliminary sign of reentrant superconductivity was observed via introducing the half-filled Eu 2+ (4 f 7 ) as hole dopant for infinite-layer (IL) nickelates 6-8 , which belongs to a new family of high temperature superconductor 9 with T c near ~40 K 10 . This is in stark contrast to the analogous earlier discoveries in exclusive low- T c systems, such as UTe 2 5,11,12 , URhGe 13 , Eu-containing Chevrel phase compounds 14,15 , λ-(BETS) 2 FeCl 4 16,17 and moiré graphene 18 . It unveils a previously unexplored dimension associated with the rare-earth ( RE ) 4 f- orbital and/or magnetic effects that may exert a substantial effect on superconducting phase diagram of nickelates, beyond their conventional ionic size effects 19,20 . This observation further coincides with the distinct magnitude and anisotropy in the superconducting upper critical field as observed for IL nickelates with various magnetic contributions by the RE -4 f moments 21 . Also, it is more intriguing to note the generally elevated T c of ambient pressured nickelate superconductor via substituting their RE composition towards later lanthanide series, as presently valid for not only IL-nickelate 10,21,22 , but also thin film layered-perovskite nickelates 23-26 . In light of the prevailing trajectory of nickelate superconductors, venturing into heavier RE to map potential 4 f -orbital effects on superconducting phase diagram offers the prospect of groundbreaking superconductivities and fundamental elucidations of underlying mechanisms. Nevertheless, the key challenge in exploring nickelate superconductors towards heavier- RE lies in their material growths 10,22,27 . Presently, successful growths of IL-nickelates manifesting superconductivity were exclusively via vacuum epitaxy of perovskite nickelates precursors followed by topotactic reduction, limited to light- RE prior to Eu 27 . Owing to the lanthanide contraction, introducing heavier RE (e.g., behind Eu) with smaller ionic radius of RE ( r RE ) into perovskite nickelates is thermodynamically more difficult. This is because that a more distorted NiO 6 octahedra elevates the formation free energy (Δ G ) 19 of perovskite nickelates towards more positive magnitude, which is hardly stabilizable by coherent lattice with the substrate. Further obstacle is from the restriction in compositing the alkaline-earth ( AE ) hole dopants within perovskite nickelates, since conventional chemical process is incapable to form Ni 4+ in perovskites as major constituents even at extremely high p O2 of ~GPa 20,28 . Thus, perovskite nickelates containing AE constituents were likely to be heterogeneously formed via plasma or atomic beam interplays with the substrate, contingent upon precise and narrowly defined experimental window 10,22,27 . From these perspectives, the present strategy for growing IL-nickelates is insufficient to support further explorations pertaining to heavier RE , despite its strong likelihood to realize higher T c and/or unconventional superconductivity, e.g., field-reentry 6-8 . Here, we open up a simple high- p O2 assisted chemical avenue for growing IL nickelate superconductors toward heavier RE constituents with effectiveness in RE -substitutions, grounded in which their 4 f -orbital relevant field-reentrant superconducting phase diagram is elucidated. Robust uniaxially anisotropic superconducting reentrancy was validated to emerge at the quantum phase boundaries of the superconducting dome for both Nd 1-x Eu x NiO 2 and Pr 1-x Eu x NiO 2 systems. Their quantum criticality was further modulated via introducing RE' within (Nd 1-y RE' y ) 1-x Eu x NiO 2 ( RE' : Pr, Sm, Gd, Dy and Sm 1/2 Pr 1/2 ) to adjust the magnitude of exchange field associated with RE -magnetism. We highlight the further elevation in T c and critical current density ( J c ) for the Eu-doped IL-nickelates, exceeding previous layer spacing expectations developed from their counterpart systems doped by Sr/Ca. The root-cause was further elucidated, combining characterization of pairing strength via magneto-transport and localized magnetism via low-energy muon-spin spectroscopy (LE- μ SR). Our work unveils the pivotal role of magnetic fluctuations with close associations with RE -4 f in modulating the quantum criticality and pairing strength, beyond conventional BCS theory. Also, our MPa- p O2 assisted chemical synthetic route sheds a light on the capability to apply IL-nickelates as coated conductors analogous to high- T c cuprates 29 . 2. Results 2.1. A MPa-high p O2 assisted chemical avenue enables effective growth of IL-nickelates To reduce the positive Δ G of perovskite nickelates contracting with lanthanide contractions, we exploit a MPa-high p O2 assisted chemical strategy for thin film growth of IL-nickelate, illustrated in Fig. 1a. In brief, the chemical precursors of RE (NO 3 ) 3 and Ni(CH 3 COO) 2 were dissolved in ethylene glycol monomethyl ether (EGME), and spin coated on a NdGaO 3 (110) substrate. The spin coated films were crystallized into the perovskite precursor film by annealing at 700-900 ℃ under a high- p O2 within 1-20 MPa. Afterwards, the perovskite nickelates was transformed into infinite layer via soft chemical topotactic reduction based on CaH 2 co-anneals at a temperature between 260-320 ℃ for 0.5-4 hours. Instead of using conventional alkaline earth elements (e.g., Sr or Ca) 30,31 , herein the hole doping was realized via partially substituting their RE -constituents by Eu, which displays variable valance state from +3 in perovskites towards +2 upon topotactic reduction 22 . From the thermodynamic perspective, the metastable perovskite nickelates precursors containing later series RE -composition is preferentially stabilized at a high- p O2 within 10 0 -10 2 MPa 19,20 , as indicated by their equilibrium phase chart in Figure 1b (see more discussions in Supplementary Figs. 1-3). Hence, our strategy is capable to introduce later series RE further behind Eu into IL-nickelates, while the RE -constituent is simply and flexibly modulable manipulating the chemical solutions for spin coating. Efficient growth of IL-nickelates is firstly exemplified by Nd 1-x Eu x NiO 2 , covering a large variety in Eu-compositions. Via MPa-high p O2 anneals, the metastable Nd 1-x Eu x NiO 3 is well stabilized, as indicated by their abrupt metal-insulator transitions (see Fig. 1b and Supplementary Fig. 4) 32,33 . The accuracy in the stoichiometry controls for Eu is convinced by the linear increase in metal-insulator transition temperature ( T MIT ) with x (or average r RE ) in consistency with the previous reports 19,20 , as shown by the inset of Figure 1b. More details in determination of T MIT are shown in Supplementary Fig. 5. As shown in Fig. 1c, the X-ray diffraction patterns of the Nd 0.55 Eu 0.45 NiO 3 demonstrate their oriented perovskite crystal structure, which transformed to the Nd 0.55 Eu 0.45 NiO 2 infinite layers after the topotactic reduction, (see more XRD results in Supplementary Fig. 6). The reduction process may result in reduced crystallinity and interfacial coherency indicated by the broadened XRD peak, as also observed previously in vacuum deposited IL-nickelates 9,10 . The resultant variation in electronic structure, e.g., from Ni 3+ to Ni 1+ , is further confirmed by synchrotron-based X-ray absorption spectroscopy (XAS) analysis, as results shown in Supplementary Fig. 7. Figs. 1d-f show the archetypal cross-section morphology for Nd 1-x Eu x NiO 2 /NdGaO 3 (110) as probed by high-angle annular dark-field (HAADF), where a larger thickness of ~20 nm is observed compared with the vacuum deposited ones (e.g., 6-8 nm) 9,10,22,34 . More representative microscopic morphologies and elementary distributions are demonstrated in Supplementary Figs. 8-11. It is also worth noticing that the Nd 1-x Eu x NiO 3 precursor coherently grown on the NdGaO 3 substrate (see Supplementary Fig. 12), while the topotactic reduction slightly reduces the crystallinity and coherency of the interface. 2.2. Tunning the reentrant and high- T c superconductivity r ivalries for Nd(Pr) 1-x Eu x NiO 2 Robust superconducting behaviors are observed for Nd 1-x Eu x NiO 2 with x =0.25-0.55, with the highest T c,onset , T c,50% and T c,zero emerged at optimum Eu constituents (x=0.35-0.45) reaching ~37.6 K, ~27.3 K and ~22.2 K, respectively. The temperature dependence in resistivity ( ρ-T ) of archetypal Nd 1-x Eu x NiO 2 are shown in Figure 2a for optimum doping (x=0.45), underdoping (x=0.3), and overdoping (x=0.52), respectively; while the ρ-T tendencies for more Eu-doping constituents are provided in Supplementary Fig. 13. The optimum doped Nd 1-x Eu x NiO 2 (x=0.35-0.45) manifest expected high- T c superconductivity that is monotonically suppressed by magnetic fields up to 35 T with no signature of reentrance (see Supplementary Fig. 14). Supplementary Figs. 14J and 14K further demonstrate its high magnitude of J c reaching 266 kA/cm 2 at 2K, exceeding previous vacuum deposited Nd-Sr and Nd-Eu systems at the same temperature (e.g., J c =170 kA/cm 2 for Nd 0.8 Sr 0.2 NiO 2 9 , J c =237 kA/cm 2 for Nd 0.65 Eu 0.35 NiO 2 8 ). Only limited reduction in the magnitudes of J c is observed, even imparting cross-plane magnetic fields up to 9 T. In contrast, the magnetic field reentrant superconducting behaviors reaching zero-resistance are observed for Nd 1-x Eu x NiO 2 at both underdoped (x=0.2-0.3) and overdoped (x=0.52-0.6) regions. This is demonstrated by their ρ-B tendency in the insets of Figure 2a (also Supplementary Fig. 14), and also the crossing in their ρ-T tendencies as measured under different magnetic fields in Supplementary Fig. 15. The field-reentrant superconductivity emerging at both the underdoped and overdoped boundaries also holds for Pr 1-x Eu x NiO 2 /NdGaO 3 (110) and Nd 1-x Eu x NiO 2 /(LaAlO 3 ) 0.3 (Sr 2 TaAlO 6 ) 0.7 (100), as demonstrated in Supplementary Fig. 16. This indicates the rivalry between reentrant and high- T c superconductivity within Eu-doped IL-nickelates, giving rise to a more complicated superconducting phase diagram ( T c -x) compared to the Sr/Ca-doped ones, as shown in Figure 2c. We highlight that the superconducting reentry emerges exclusively at the superconducting boundaries, but is absent when the high- T c superconductivity is robust at optimum doping. This unveils the previously underestimated tunability in the quantum criticality by RE -4 f (particularly Eu-4 f 7 ) 6 , via the likelihood of a magnetic fluctuation modulated pairing in the neighborhoods of quantum phase transitions 11 . For example, in the underdoped region, the superconducting state has energy that is close to many competing states, such as charge order 35 , spin order 36 and/or oxygen order 37 . In the overdoped region near a hidden quantum critical point (QCP), the system exhibits a transition from non-Fermi liquid to Fermi liquid behavior 30 , triggering a sudden change in electronic state. Hence, potential RE -4 f modulated magnetic fluctuations and the suppression of superconductivity by the competing quantum states 34 may lead to the criticality between reentrant and high- T c superconductivity 11,36 . Of particular note is the broader superconducting dome extending to larger Eu compositions in Pr 1-x Eu x NiO 2 than in Nd 1-x Eu x NiO 2 , despite the similar magnitudes in their starting point (e.g., x=0.2) and maximum T c both of ~37.6 K. Further X-ray photoemission spectroscopy analysis as shown in Supplementary Figs. 18a-c indicate a higher Eu 2+ /Eu 3+ ratio for Nd 1-x Eu x NiO 2 (e.g., ~1/1) compared to Pr 1-x Eu x NiO 2 (e.g., ~2/3). Hence, estimating their practical hole doping range contributed by Eu 2+ indicates similarities to the previous reports for Nd 1-x Sr x NiO 2 30 and Pr 1-x Sr x NiO 2 38 , as more clearly demonstrated in Supplementary Figs. 17d and 17e. 2.3. Further modulations in the quantum criticality and T c via multiple RE -compositions To further elucidate the role of RE in rivalry between high- T c and reentrant superconductivity, we start with the matrix of optimum doped Nd 1-x Eu x NiO 2 (x: 0.35-0.45) without reentrancy and partially substitute Nd by RE ’ (e.g., Pr, Sm, Gd and Dy). The RE' substitution elicited corresponding changes in the T MIT of (Nd 1-y RE' y ) 0.65 Eu 0.35 NiO 3 (see Supplementary Fig. 18) and also lattice constants of (Nd 1-y RE' y ) 0.65 Eu 0.35 NiO 2 (see Supplementary Fig. 19). Fig. 3a (upper) shows the ρ -T tendencies for (Nd 0.9 Pr 0.1 ) 0.65 Eu 0.35 NiO 2 , (Nd 0.9 Sm 0.1 ) 0.65 Eu 0.35 NiO 2 and (Nd 0.9 Dy 0.1 ) 0.65 Eu 0.35 NiO 2 , where robust superconducting behaviors are observed, e.g., with T c,zero of ~20 K, 18 K and 14 K, respectively. As their ρ-B tendencies further demonstrated in the insets and also Supplementary Figs. 20a-c, these samples display no field-reentrant behaviors. In contrast, the reentrant superconductivity emerges for (Nd 1-y Gd y ) 0.65 Eu 0.35 NiO 2 (y=0.05, 0.1 and 0.2) as demonstrated in Fig. 3a (lower) and also the inset. Their ρ-B tendencies measured at more temperatures are further shown in Supplementary Figs. 20d and 20e. Also, the Gd substitution results in lower T c,zero compared to the ones substituted by other RE' (see Supplementary Fig. 21). To verify the zero-resistance for the Gd reinforced reentrant superconductivity and its secondary quench, we measured their ρ-B tendencies of (Nd 0.95 Gd 0.05 ) 0.65 Eu 0.35 NiO 2 up to higher magnetic fields at different temperatures, as shown in Fig. 3b. The reentrant superconductivity reaching zero resistances is observed from 5-10 T, 8-13 T and 10-15 T at 1.6 K, 2 K, and 3 K, respectively, afterwards quenching at 30 T, 25 T and 20 T. Further angular dependent magneto-transport measurements via altering the angle ( θ ) between H ext and c -axis indicates strong uniaxial cross-plane anisotropy in the superconducting reentrant behavior of (Nd 0.95 Gd 0.05 ) 0.65 Eu 0.35 NiO 2 . Their resistivity is mapped as a function of both magnetic field strength and θ in Fig. 3c at 2 K, 3 K and 5K, where more separated regions associated with the low field and reentrant field superconductivity are observed when imparting H ext along c- axis ( θ =0°). Also, elevating the temperature (e.g., from 2 K to 5 K) results in markedly contraction in the reentrant region. This should be attributed to the higher H c2 along the ab -plane compared to the c -axis, stemming from the Eu-4 f related anisotropy in orbital depairing 21 , as further discussed in Supplementary Fig. 22. Similar phenomenon was also observed for as-grown (Nd 0.9 Gd 0.1 ) 0.65 Eu 0.35 NiO 2 , Nd 0.48 Eu 0.52 NiO 2 and Nd 0.46 Eu 0.54 NiO 2 , as demonstrated in Supplementary Fig. 23. Hence, the Gd reinforced reentrant superconductivity is in consistency to ones observed for Nd-Eu and Sm-Eu systems grown by both vacuum depositions 6-8 . The preferential superconducting reentrancy via introducing Gd over other RE' (e.g., Pr, Sm and Dy) within (Nd 1-y RE' y ) 1-x Eu x NiO 2 was also verified in other compositions (e.g., x=0.35, y=0.2; x=0.45, y=0.2; x=0.5, y=0.1), as demonstrated in Supplementary Fig. 24. Instead of other proposed mechanisms (e.g., spin-triplet pairing 11 and metamagnetic criticality 39 ), the Jaccarino-Peter (J-P) effect 40,41 was more likely to explain the magnetic field induced reentrant superconductivity for Eu-doped IL-nickelates 6-8 . In sight of its half-filled 4 f 7 among RE 3+ (see details in Supplementary Table 1) 42,43 , introducing Gd 3+ is expected to enhance the internal exchange field ( H ex ) to partially against the external magnetic field ( H ext ), as illustrated in Figure 3c. In contrast, the Eu 2+ (also with 4 f 7 ) not only generates H ex , but also served as hole dopant that simultaneously contributes to transports, giving rise to more complicated impact beyond simply J-P effect. From a counterpoint compared to Gd, introducing RE' (e.g., Pr, Sm and Pr 1/2 Sm 1/2 ) to reduce the magnetism of rare-earth site within (Nd 1-y RE' y ) 0.65 Eu 0.35 NiO 2 sheds a light on further elevating T c beyond the superconducting dome of the matrix Nd 1-x Eu x NiO 2 with T c (e.g., peaking at ~37.6 K). This was confirmed by higher magnitudes of T c reaching 40.1 K, 38.1 K and 38.4 K as observed for (Nd 0.8 Pr 0.2 ) 0.65 Eu 0.35 NiO 2 , (Nd 0.6 Sm 0.4 ) 0.65 Eu 0.35 NiO 2 and (Nd 0.4 Pr 0.3 Sm 0.3 ) 0.65 Eu 0.35 NiO 2 , respectively, as demonstrated by Supplementary Figs. 24 and 25. Considering that Nd 3+ exhibits an ionic radius between Pr 3+ and Sm 3+ and a larger magnetic moment than both, the further elevation in T c is unlikely to be related to rare-earth size effect, but more associated with a weakened lattice magnetism via disturbing RE- 4 f spin ordering from RE -mixing. 2.4. Elevated T c coincide with promoted magnetic fluctuation at superconducting state Grounded in present large RE -compositional diversity, we summarized the T c plotted as a function of the c -axis lattice constants ( c ) for the present Eu-doped IL-nickelates showing robust superconductivity without reentrancy together with the reported ones 10,27 in Fig. 4a. This is further compared to the T c - c tendency developed from Sr-/Ca-doped IL-nickelates approaching to optimum doping 30,31,38,44-48 , as indicated by the dash line. The further elevation in T c is clearly observed for the optimum Eu-doped IL-nickelates transcending the Sr-/Ca-doped ones even at similar layer spacing. This unveils an extra pairing strengthening mechanism related to Eu 2+ -4 f 7 , as is further confirmed by performing magneto-electrical transport measurements shown in Supplementary Fig. 26 to estimate the paring strength summarized in Supplementary Table 2. It evokes closed associations with potential more complicated spin and orbital interactions with Eu 2+ -4 f 7 , which improves paring via potentially promoted magnetic fluctuation 49 , struggling for primacy with the J-P effects. Above viewpoint was supported by the abruptly promoted spin ordering below T c even for the optimum-doped Nd 0.6 Eu 0.4 NiO 2 with completely shielded reentrant superconductivity, as probed by LE- μ SR, as demonstrated in Fig. 4b. More detailed results are further shown in Supplementary Fig. 27 and 28. Descending temperature across 20-40 K (consistent to superconducting transition) results in an abrupt increase in the relaxation rate ( l ZF ), accompanied by reductions in the stretch parameter b down to a plateau magnitude of ~0.5-0.6 similar to spin-glass 48 . The magnitude of l ZF (e.g., 2.5 μs -1 ) in the superconducting state is much larger than that previously observed for the Sr-doped IL-nickelates (e.g., 0.22-0.48 μs -1 ) 48 . This indicates an Eu 2+ -enhanced spin ordering and magnetic fluctuations when entering the superconducting state, which may account for the large elevation in T c compared to Sr-doped IL-nickelates (e.g., ~10 K 9 ). 3. Conclusion In summary, grounded in the high- p O2 chemical avenue to effectively grow ( RE 1-y RE' y ) 1-x Eu x NiO 2 , we elucidate the enrichment in their superconducting phase diagram by field-reentrant superconducting states emerging at both quantum boundaries, competing for primacy. The quantum criticality between reentrant and high- T c superconductivity not only hinges on Eu-composition, but also displays associations with the RE ( RE ’) magnetism, which modulate the exchange field together with Eu 2+ . Furthermore, combining magneto-transport and LE- μ SR measurements unveils the concomitant occurrence of strengthened Cooper pairing and promoted magnetic fluctuation via optimum Eu 2+ -4 f 7 interactions. This counts for their further elevated T c beyond the Sr-/Ca-doped systems even at similar infinite layer-spacing, giving rise to higher T c up to ~40 K and more robust J c reaching 266 kA/cm 2 at 2 K. These discoveries highlight a new freedom from the overlooked RE -4 f orbital and spin interplays that further complicate the superconducting phase diagram of IL-nickelates in terms of quantum phase criticality modulation and pairing strengthening, beyond analogous cuprates with similar d -orbital frameworks. Furthermore, the non-vacuum growth of IL-nickelate with high effectiveness holds practical implications, particularly in potential to leverage coated-conductor technologies similar to cuprates. 4. Methods Sample preparation Thin films of (Nd 1-y RE' y ) 1-x Eu x NiO 2 ( RE' =Pr, Sm, Gd and Dy) were grown via a high-oxygen-pressure-assisted chemical route, followed by a soft topotactic reduction. Metal nitrate precursors, such as Nd(NO 3 ) 3 and Eu(NO 3 ) 3 , as well as the Ni(CH 3 COO) 2 (≥99.9%, Aladdin) were dissolved in ethylene glycol monomethyl ether (EGME) according to the target stoichiometry. For partial rare-earth substitutions, Pr(NO 3 ) 3 , Sm(NO 3 ) 3 , Gd(NO 3 ) 3 and Dy(NO 3 ) 3 were co-dissolved correspondingly. The precursor solution was spin-coated onto single-crystal NdGaO 3 (110) and LSAT(100) substrates and dried in air. As-deposited gel films were crystallized into perovskite-type nickelate precursors by annealing at 700-900 ℃ under oxygen pressures of 1-20 MPa in a custom-built high- p O2 tubular reactor. After cooling to room temperature, the perovskite films were sealed in a vacuum quartz tube together with CaH 2 powder and annealed at 260-320 ℃ for 0.5-4 h for topotactic reduction into the infinite-layer phase. This process simultaneously reduced Eu³⁺ to Eu²⁺, serving as the effective hole dopant. The resulting infinite-layer films had a typical thickness of ~20 nm. X-ray diffraction Crystal structures of the perovskite precursors and reduced infinite-layer nickelate films were characterized using X-ray diffraction (XRD, Bruker D8 Discover) with Cu K α1 radiation ( λ =1.5406 Å). The θ -2 θ scans were collected to identify phase purity, and reciprocal space mapping (RSM) of the (103) reflection was employed to verify the epitaxial quality and in-plane lattice coherence. Scanning transmission electron microscopy The cross-sectional morphologies and interfacial structures of the samples were characterized by scanning transmission electron microscopy (STEM) using an FEI Titan Themis Z microscope operated at 300 kV, equipped with a double aberration corrector and a high-angle annular dark-field (HAADF) detector. The convergence semi-angle for imaging is 25 mrad, and the collection semi-angle is 50-200 mrad for the HAADF imaging. The cross-sectional TEM lamellas were thinned to electron beam transparency at 30 kV by using Carl Zeiss Crossbeam 550L FIB-SEM, followed by the removal of the surface amorphous layer at 2 kV. The obtained HAADF-STEM images revealed atomically sharp interfaces between the Nd 1-x Eu x NiO 2 films and NdGaO 3 substrates and confirmed the topotactic structural transformation from the perovskite precursor to the infinite-layer phase after reduction. The electron energy-loss spectroscopy (EELS) and energy-dispersive X-ray spectroscopy (EDS) were performed to obtain chemical and electronic-structure information. The EELS spectrum-imaging was acquired with the post-column imaging filter fitted with a K3 direct electron detector. The STEM beam current was set to ~80 pA for spectrum imaging, the pixel dwell time was 1 ms, and the recorded pixel size was 0.5 Å. The EELS energy dispersion was of 0.35 eV per channel. The EDS elemental maps were collected with an acquisition current of ~100 pA. All EELS and EDS datasets were energy- and spatially-calibrated and processed using standard routines; elemental maps shown in the manuscript were optimized in Velox software (Thermo Fisher) with a light Gaussian blur applied for presentation. XPS and XAS measurements X-ray photoelectron spectroscopy (XPS, Thermo Scientific ESCALAB 250Xi) was used to determine the chemical states of Eu, Nd, and Ni ions, with Al K α (1486.6 eV) radiation. The binding energy was calibrated using the C 1 s peak at 284.8 eV. The Eu 3+ :Eu 2+ ratio was estimated by deconvolution of the Eu 3 d 3/2 and 3 d 5/2 peaks. The synchrotron-based X-ray absorption spectroscopy (XAS) at the Ni L -edge was carried out at the BL08U1A beamline of the Shanghai Synchrotron Radiation Facility (SSRF). Total electron yield (TEY) mode was used to probe the near-surface region, confirming the reduction of Ni valence from +3 in Nd 0.65 Eu 0.35 NiO 3 to +1 in Nd 0.65 Eu 0.35 NiO 2 . Electrical transport measurements Electrical transport properties were measured using a Quantum Design Physical Property Measurement System (PPMS). Standard four-probe geometry was used with aluminium ultrasonic wire bonds; contact resistances were typically below a few hundred ohms. Temperature-dependent resistivity ( ρ - T ) measurements were performed from 300 K to 2 K under magnetic fields up to 9 T. Angle-dependent transport was measured using a high-precision rotator (angular resolution 0.01°) to determine the anisotropy of reentrant superconductivity. The critical current density ( J c ) was measured using the Electrical Transport Option (ETO) module of the same PPMS from current-voltage ( I - V ) curves in a four-probe configuration. High-field magneto-transport High-magnetic-field resistance measurements were performed on the WM1 system at the Steady High Magnetic Field Facility, Chinese Academy of Sciences (Hefei). Magnetic fields up to 35 T and temperatures down to 1.6 K were achieved in a custom-built 4 He cryostat (Physike Instruments). A Keithley 6221 current source and SR830 lock-in amplifiers were used for low-noise data acquisition. The μ SR measurements The μ SR measurements were performed at the low-energy Muon Facility (LEM) at the μ E4 beam line of the Swiss muon source (S μ S) at Paul Scherrer Institut (PSI) in Villigen, Switzerland. Implantation energies were selected from TRIM.SP simulations to maximise muon stopping rates in the Nd 0.6 Eu 0.4 NiO 2 films. To exclude the possibility of stray magnetic field during the ZF- μ SR measurements, all the magnets were preliminarily degaussed, and an active field-compensating facility was used. For the wTF- μ SR measurements, the applied magnetic field (i.e., 10 mT) was perpendicular to the muon-spin direction, and the films were cooled in an applied magnetic field down to the base temperature (≈1.6 K). Six pieces of Nd 0.6 Eu 0.4 NiO 2 /LSAT(100) films (each has a dimension of 5´10 mm 2 ) were mounted on the non-magnetic Ag sample holder. The muon spin relaxation of Ag is less than 0.04 ms -1 at temperatures above 2 K, which is negligible compared with Nd 0.6 Eu 0.4 NiO 2 films. Declarations Competing interests: We declare no competing financial interest. Additional information : Supplementary Information is available for this manuscript. Correspondence s : Correspondence should be addressed: Prof. Jikun Chen ( [email protected] ), Prof. Jia-Cai Nie ( [email protected] ) and Prof. Binghui Ge ( [email protected] ). Author contributions: J.C. and J.N. conceived the project. H.H., Y.Z. and Y.B. contributed equally to this work. H.H. performed the soft chemical reduction experiments, transport measurements, and XRD characterizations, assisted by Y.B. and T.M.. Y.Z. synthesized the perovskite precursor films assisted by N.C. Y.B. and W.Y. assisted in the transport measurements. H.H., C.X., and Z.W. performed the high-field magneto-transport measurements. S.Y. and B.G. conducted the STEM experiments. H.D performed the XAS experiments assisted by K.M.; T.S. and Z. S. performed the LE- m SR measurements, while T.S. analysed the data. J.C, J.N. B.G, N.C and K.M. provided constructive experimental supports and discussions. All authors analysed and discussed the data. J.C. wrote the manuscript, assisted by H.H. and J.N, also with input from all authors. Acknowledgments: This work was supported the National Key Research and Development Program of China (No. 2021YFA0718900), the National Natural Science Foundation of China (No. 62474017, 92577108 and 12474001), the Natural Science Foundation of Guangdong Province of China (Grant No. 2025A1515011071) and the Guangdong Provincial Quantum Science Strategic Initiative (Grant No. GDZX2501006). We thank the BL08U1A beamline and the User Experiment Assist System of the Shanghai Synchrotron Radiation Facility (SSRF) for the assistance in characterizations. We also thank the staff members of the XMCD beamline at the NSRL in Hefei, for providing the technical support and assistance in XAS data collection and analysis. We also thank the WM1 of the Steady High Magnetic Field Facility, Chinese Academy of Sciences, for the assistance on the experiment. The muon measurements were performed at the µ E4 beamline of the Swiss Muon Source S µ S, Paul Scherrer Institute, Villigen, Switzerland. We also acknowledge the support from Dr. Andreas Suter and Dr. Thomas Proksha in PSI Center for Neutron and Muon Sciences, Paul Scherrer Institute, Switzerland. Also, we acknowledge the constructive discussions with Dr. Ivan Božović. References Shen, B. et al. Strange-metal behaviour in a pure ferromagnetic Kondo lattice. Nature 579 , 51-55 (2020). Iglesias, J. R., Lacroix, C. & Coqblin, B. 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Intrinsic magnetism in superconducting infinite-layer nickelates. Nature Physics 18 , 1043-1047 (2022). Petrich, G., Von Molnár, S. & Penney, T. Exchange-induced autoionization in Eu-rich EuO. Physical Review Letters 26 , 885 (1971). Additional Declarations There is NO Competing Interest. Supplementary Files supplementarymaterials.pdf The Supplementary Information available online includes 28 composite figures and 2 tables. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7803050","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":632811550,"identity":"6085b185-0240-4e78-b3ab-0fbd2c911aa5","order_by":0,"name":"Jikun Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVRIiWNgGAWjYBACxmY2EHWAgYG9AchrgLCJ1MIDxAeJ0cLAANMikUCkFuZ2tjTpgpo7cuaSb4w/f9zBIMd3I4HxcwF+hx2TnnHsmbHl7BwziYNnGIwlbyQwS8/Aq4W9TZq34XDihts5ZgwH2xgSN9xIYGPmIUJL/YabZ4w/ALXUE6EF6DCglgSDGzwGEkAtQAZhLcnWPMcOG244k1YmcfaMhOHMMw+bpfFpMew/Znibp+awvMHxw5s/VO6wkec7nnzwM14tDah8CQZoGsAN5PHKjoJRMApGwSgAAQDe2E9g6MXIZgAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-0860-5106","institution":"University of Science and Technology Beijing","correspondingAuthor":true,"prefix":"","firstName":"Jikun","middleName":"","lastName":"Chen","suffix":""},{"id":632811551,"identity":"96635edb-858e-4e81-bf30-07bf09c53a19","order_by":1,"name":"Haowen Han","email":"","orcid":"","institution":"University of Science and Technology Beijing","correspondingAuthor":false,"prefix":"","firstName":"Haowen","middleName":"","lastName":"Han","suffix":""},{"id":632811552,"identity":"57e7bb77-638c-45e0-9db1-9e48bf543a8e","order_by":2,"name":"Yusong Zhao","email":"","orcid":"","institution":"University of Science and Technology Beijing","correspondingAuthor":false,"prefix":"","firstName":"Yusong","middleName":"","lastName":"Zhao","suffix":""},{"id":632811553,"identity":"0e9b37d5-2d52-4c34-998c-61fd2544ed50","order_by":3,"name":"Yi Bian","email":"","orcid":"","institution":"School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China","correspondingAuthor":false,"prefix":"","firstName":"Yi","middleName":"","lastName":"Bian","suffix":""},{"id":632811554,"identity":"0d61cff9-3cee-4de0-8e4a-395f59a60400","order_by":4,"name":"Tong Ma","email":"","orcid":"","institution":"University of Science and Technology Beijing","correspondingAuthor":false,"prefix":"","firstName":"Tong","middleName":"","lastName":"Ma","suffix":""},{"id":632811555,"identity":"b4714b28-3d98-410e-a8ff-85399ddc7e5e","order_by":5,"name":"Wenlong Yang","email":"","orcid":"","institution":"Beijing Normal University","correspondingAuthor":false,"prefix":"","firstName":"Wenlong","middleName":"","lastName":"Yang","suffix":""},{"id":632811556,"identity":"325da1f2-f36f-480d-9fce-e528c432e5ff","order_by":6,"name":"Shaohua Yang","email":"","orcid":"","institution":"Anhui University","correspondingAuthor":false,"prefix":"","firstName":"Shaohua","middleName":"","lastName":"Yang","suffix":""},{"id":632811557,"identity":"71d4514e-d2b6-4fc5-b682-4d3249ba418d","order_by":7,"name":"Binghui Ge","email":"","orcid":"https://orcid.org/0000-0002-6470-6278","institution":"Anhui University","correspondingAuthor":false,"prefix":"","firstName":"Binghui","middleName":"","lastName":"Ge","suffix":""},{"id":632811558,"identity":"0d913b69-8966-46af-82a8-a30bdc07b165","order_by":8,"name":"Hongliang Dong","email":"","orcid":"","institution":"Center for High Pressure Science and Technology Advanced Research (HPSTAR)","correspondingAuthor":false,"prefix":"","firstName":"Hongliang","middleName":"","lastName":"Dong","suffix":""},{"id":632811559,"identity":"b250f4bc-c522-4628-b27a-7ef43692ca67","order_by":9,"name":"Chuanying Xi","email":"","orcid":"","institution":"Anhui Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, HFIPS, Anhui, Chinese Academy of Sciences, Hefei 230031, P. 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Also, other rare-earth elements, e.g., Pr, Sm, Gd and Dy, were also introduced to partially substitute Nd. As obtained solution was spin coated on NdGaO\u003csub\u003e3\u003c/sub\u003e(110) and LSAT(100) single crystal substrates and dried. II, A post annealing process was further performed under a high oxygen pressure (\u003cem\u003ep\u003c/em\u003e\u003csub\u003eO2\u003c/sub\u003e) to crystallize the spin coated film into the 113-typed perovskite precursor film. III, Finally, as-obtained perovskite nickelate precursor film was annealed together with CaH\u003csub\u003e2\u003c/sub\u003e powder to be topotactical reduced into infinite layer. \u003cstrong\u003eb\u003c/strong\u003e,\u0026nbsp;The pressure-temperature (\u003cem\u003ep\u003c/em\u003e-\u003cem\u003eT\u003c/em\u003e) phase diagram for the formation of perovskite nickelates with different rare-earth elements under high oxygen pressure is depicted. The red region outlines the range of synthesis conditions encompassed by our method, with the slash area indicating the specific parameters employed in this work. The purple region represents the typical synthesis conditions for vacuum deposition of perovskite nickelate thin films.\u003cstrong\u003e c\u003c/strong\u003e, Temperature dependence of resistivity measured for Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e3\u003c/sub\u003e thin films with various Eu-substituting compositions (\u003cem\u003ex\u003c/em\u003e), convincing their abrupt metal-insulator transition behavior. The inset shows their metal-insulator transition temperature (\u003cem\u003eT\u003c/em\u003e\u003csub\u003eMIT\u003c/sub\u003e) versus \u003cem\u003ex\u003c/em\u003e. \u003cstrong\u003ed\u003c/strong\u003e, The X-ray diffraction patterns for Nd\u003csub\u003e0.55\u003c/sub\u003eEu\u003csub\u003e45\u003c/sub\u003eNiO\u003csub\u003e3\u003c/sub\u003e perovskite precursor and the Nd\u003csub\u003e0.55\u003c/sub\u003eEu\u003csub\u003e0.45\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e infinite layer.\u003cstrong\u003e e\u003c/strong\u003e, Cross-sectional HAADF-STEM image of Nd\u003csub\u003e0.7\u003c/sub\u003eEu\u003csub\u003e0.3\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e on NdGaO\u003csub\u003e3\u003c/sub\u003e(110).\u003cstrong\u003e f, g,\u003c/strong\u003e Magnified HAADF-STEM images of \u003cstrong\u003ef,\u003c/strong\u003e the interfacial region and \u003cstrong\u003eg,\u003c/strong\u003e the film surface.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7803050/v1/70f583f1bc68eb5c1af2eb5f.png"},{"id":108406094,"identity":"7acfc0b8-4de9-44a0-b97f-6961692a446c","added_by":"auto","created_at":"2026-05-04 09:41:20","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":140874,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDiscovery of\u003c/strong\u003e \u003cstrong\u003efield reentrant superconductivity at the quantum boundaries of superconducting dome. a\u003c/strong\u003e, The temperature-dependent resistivity (\u003cem\u003eρ\u003c/em\u003e-\u003cem\u003eT\u003c/em\u003e) measured for: the optimally doped Nd\u003csub\u003e0.55\u003c/sub\u003eEu\u003csub\u003e0.45\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e, with the inset showing the corresponding magnetic field dependent resistivity (\u003cem\u003eρ\u003c/em\u003e-\u003cem\u003eB\u003c/em\u003e) at 5 K that demonstrated conventional superconductivity;\u003cstrong\u003e \u003c/strong\u003ethe underdoped Nd\u003csub\u003e0.7\u003c/sub\u003eEu\u003csub\u003e0.3\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e, with the inset showing \u003cem\u003eρ\u003c/em\u003e-\u003cem\u003eB\u003c/em\u003e at 2 K that demonstrates reentrance;\u003cstrong\u003e \u003c/strong\u003ethe overdoped Nd\u003csub\u003e0.48\u003c/sub\u003eEu\u003csub\u003e0.52\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e, with the inset showing \u003cem\u003eρ\u003c/em\u003e-\u003cem\u003eB\u003c/em\u003e curve at 3 K that demonstrates reentrance.\u003cstrong\u003e b\u003c/strong\u003e, \u003cstrong\u003ec\u003c/strong\u003e, Superconducting phase diagram for \u003cstrong\u003eb\u003c/strong\u003e, Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e and \u003cstrong\u003ec\u003c/strong\u003e, Pr\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e plotted as a function of Eu substituting composition, \u003cem\u003ex\u003c/em\u003e. The blue region represents the high-\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e superconducting region without reentry, while the orange-shaded regions represent the emergence of magnetic field-reentrant superconductivity. The onset critical temperature (\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec,onset\u003c/sub\u003e) is corresponding to the temperature where the electrical resistivity begins to deviate notably from its normal-state behavior. The midpoint transition temperature (\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec,50%\u003c/sub\u003e) represents the temperature where the resistivity drops to 50% of its normal-state value under zero magnetic field (typically referenced to the value at \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec,onset\u003c/sub\u003e). The zero-resistance temperature (\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec,zero\u003c/sub\u003e) is defined as the temperature where the electrical resistivity drops below the experimental detection limit. The dome is established from samples at more Eu-substituting compositions, as shown by Supplementary Figs. 13 and 16.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7803050/v1/ba4c4b72a8fc5ac9e4e01b27.png"},{"id":108406086,"identity":"6f8d4d3f-9608-436c-b3a6-2cc7eb4e23eb","added_by":"auto","created_at":"2026-05-04 09:41:19","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":259445,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFurther modification in criticality with field-reentrant superconductivity via introducing other rare-earth substituents. a\u003c/strong\u003e, The normalized temperature dependent resistivity (\u003cem\u003eρ\u003c/em\u003e-\u003cem\u003eT\u003c/em\u003e) measured for (Nd\u003csub\u003e0.9\u003c/sub\u003e\u003cem\u003eRE'\u003c/em\u003e\u003csub\u003e0.1\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e (\u003cem\u003eRE'\u003c/em\u003e=Pr, Sm and Dy), displaying robust conventional superconductivity. The inset shows their corresponding magnetic field dependent resistivity (\u003cem\u003eρ\u003c/em\u003e-\u003cem\u003eB\u003c/em\u003e) measured at 2 K. The normalized \u003cem\u003eρ-T \u003c/em\u003eas measured for (Nd\u003csub\u003e1-y\u003c/sub\u003eGd\u003csub\u003ey\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e (y=0.05, 0.1 and 0.2), showing clear field-reentrant superconductivity. The inset shows their corresponding \u003cem\u003eρ\u003c/em\u003e-\u003cem\u003eB\u003c/em\u003e measured at 2 K.\u003cstrong\u003e b\u003c/strong\u003e, Schematic illustration of the proposed mechanism: the 4\u003cem\u003ef\u003c/em\u003e\u003csup\u003e7 \u003c/sup\u003emoments of Gd\u003csup\u003e3+\u003c/sup\u003e located at deeper energy level generate an internal exchange field (\u003cem\u003eH\u003c/em\u003e\u003csub\u003eex\u003c/sub\u003e) that partially compensates the external magnetic field (\u003cem\u003eH\u003c/em\u003e\u003csub\u003eext\u003c/sub\u003e) via the Jaccarino-Peter effect\u003csup\u003e40\u003c/sup\u003e, giving rise to reentrant superconductivity.\u003cstrong\u003e \u003c/strong\u003e\u003cem\u003eρ\u003c/em\u003e-\u003cem\u003eB\u003c/em\u003e measurements of (Nd\u003csub\u003e0.95\u003c/sub\u003eGd\u003csub\u003e0.05\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e up to higher magnetic fields at different temperature.\u003cstrong\u003e c\u003c/strong\u003e, Resistivity of (Nd\u003csub\u003e0.95\u003c/sub\u003eGd\u003csub\u003e0.05\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e measured for various angles between the external magnetic field and \u003cem\u003ec\u003c/em\u003e-axis at: 2 K, 3 K and 5 K. The bottom projection shows the colored mapping of the resistivity, where the deep blue regions of zero resistance (reentrant superconductivity) emerging at high fields when\u0026nbsp;\u003cem\u003eH\u003c/em\u003e\u003csub\u003eext\u003c/sub\u003e is near the\u0026nbsp;\u003cem\u003ec\u003c/em\u003e-axis (\u003cem\u003eθ\u003c/em\u003e≈0°), revealing strong uniaxial anisotropy. In addition, elevating the temperature progressively suppresses the reentrant superconducting phase, constraining it within a narrow range of angles and fields.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7803050/v1/8c0a8e0d5dd93b5a77538256.png"},{"id":108406101,"identity":"a8c29329-0cc2-4ccc-a339-d8ee6bdd49d4","added_by":"auto","created_at":"2026-05-04 09:41:22","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":126108,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFurther elevation in \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eT\u003c/strong\u003e\u003c/em\u003e\u003csub\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e concomitant with promoted magnetic fluctuations in Eu-doped infinite-layer nickelates. a,\u003c/strong\u003e The \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec,onset\u003c/sub\u003e plotted as a function of the -axis lattice constant for the present and reported\u003csup\u003e10,22,27\u003c/sup\u003e Eu-doped infinite-layer nickelates without reentrancy together with ones doped by Sr/Ca\u003csup\u003e30,31,38,44-48\u003c/sup\u003e. The dashed line is a guide to the \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e-\u003cem\u003ec\u003c/em\u003e trend fitted from the Sr-/Ca-doped systems. \u003cstrong\u003eb,\u003c/strong\u003e The zero-field muon spin relaxation rate (\u003cem\u003eλ\u003c/em\u003e\u003csub\u003eZF\u003c/sub\u003e) fitted from the zero-field (ZF-) \u003cem\u003eμ\u003c/em\u003eSR spectra plotted as a function of temperature for the optimum-doped Nd\u003csub\u003e0.6\u003c/sub\u003eEu\u003csub\u003e0.4\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e films grown on the LSAT (100) substrates, compared to the reported ones for Nd\u003csub\u003e1-x\u003c/sub\u003eSr\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e (hollow dots)\u003csup\u003e48\u003c/sup\u003e. Descending temperature across \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e results in abrupt elevation in \u003cem\u003eλ\u003c/em\u003e\u003csub\u003eZF\u003c/sub\u003e, indicating promoted spin ordering and magnetic fluctuation. The inset demonstrates the temperature dependence of the stretch exponent \u003cem\u003eβ\u003c/em\u003e (solid dots), showing similar temperature dependence compared with the previous report for Nd\u003csub\u003e1-x\u003c/sub\u003eSr\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e (hollow dots)\u003csup\u003e48\u003c/sup\u003e. The magnitude of \u003cem\u003eβ\u003c/em\u003e saturates to ~0.5-0.6 below 50 K, indicating a possible spin glass-like state, as \u003cem\u003eT\u003c/em\u003e\u003csub\u003esg\u003c/sub\u003e marked by the arrow.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7803050/v1/f4292a1607fc12ac95e354e3.png"},{"id":108703439,"identity":"2aa87192-90f6-49c3-9989-58c1c117d18e","added_by":"auto","created_at":"2026-05-07 12:57:58","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1401902,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7803050/v1/08a60a58-bf88-4344-8c57-52d11b944e5b.pdf"},{"id":108406054,"identity":"fdab3cef-ac8f-4192-a366-e1e1c3f7d709","added_by":"auto","created_at":"2026-05-04 09:41:08","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":6268849,"visible":true,"origin":"","legend":"The Supplementary Information available online includes 28 composite figures and 2 tables.","description":"","filename":"supplementarymaterials.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7803050/v1/447dcae31ea59e12c9170add.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"A chemical avenue to manipulate field-reentrant superconducting rivalries in infinite layer nickelates","fulltext":[{"header":"1.Introduction","content":"\u003cp\u003eThe participance of \u003cem\u003ef\u003c/em\u003e-electrons in ferromagnetic coupling\u003csup\u003e1\u003c/sup\u003e, Kondo lattice\u003csup\u003e1,2\u003c/sup\u003e, and antiferromagnetic exchange mediated Cooper-pairing\u003csup\u003e3,4\u003c/sup\u003e, largely enriches the superconducting phase diagram, also giving rise to magnetic field-reentrant superconductivity\u003csup\u003e5\u003c/sup\u003e. Recently, preliminary sign of reentrant superconductivity was observed via introducing the half-filled Eu\u003csup\u003e2+\u003c/sup\u003e (4\u003cem\u003ef\u003c/em\u003e\u003csup\u003e\u0026nbsp;7\u003c/sup\u003e) as hole dopant for infinite-layer (IL) nickelates\u003csup\u003e6-8\u003c/sup\u003e, which belongs to a new family of high temperature superconductor\u003csup\u003e9\u003c/sup\u003e with \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e near ~40 K\u003csup\u003e10\u003c/sup\u003e. This is in stark contrast to the analogous earlier discoveries in exclusive low-\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e systems, such as UTe\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e5,11,12\u003c/sup\u003e, URhGe\u003csup\u003e13\u003c/sup\u003e, Eu-containing Chevrel phase compounds\u003csup\u003e14,15\u003c/sup\u003e, \u0026lambda;-(BETS)\u003csub\u003e2\u003c/sub\u003eFeCl\u003csub\u003e4\u003c/sub\u003e\u003csup\u003e16,17\u003c/sup\u003e and moir\u0026eacute; graphene\u003csup\u003e18\u003c/sup\u003e. It unveils a previously unexplored dimension associated with the rare-earth (\u003cem\u003eRE\u003c/em\u003e) 4\u003cem\u003ef-\u003c/em\u003eorbital and/or magnetic effects that may exert a substantial effect on superconducting phase diagram of nickelates, beyond their conventional ionic size effects\u003csup\u003e19,20\u003c/sup\u003e. This observation further coincides with the distinct magnitude and anisotropy in the superconducting upper critical field as observed for IL nickelates with various magnetic contributions by the \u003cem\u003eRE\u003c/em\u003e-4\u003cem\u003ef\u003c/em\u003e moments\u003csup\u003e21\u003c/sup\u003e. Also, it is more intriguing to note the generally elevated \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e of ambient pressured nickelate superconductor via substituting their \u003cem\u003eRE\u003c/em\u003e composition towards later lanthanide series, as presently valid for not only IL-nickelate\u003csup\u003e10,21,22\u003c/sup\u003e, but also thin film layered-perovskite nickelates\u003csup\u003e23-26\u003c/sup\u003e. In light of the prevailing trajectory of nickelate superconductors, venturing into heavier \u003cem\u003eRE\u003c/em\u003e to map potential 4\u003cem\u003ef\u003c/em\u003e-orbital effects on superconducting phase diagram offers the prospect of groundbreaking superconductivities and fundamental elucidations of underlying mechanisms.\u003c/p\u003e\n\u003cp\u003eNevertheless, the key challenge in exploring nickelate superconductors towards heavier-\u003cem\u003eRE\u003c/em\u003e lies in their material growths\u003csup\u003e10,22,27\u003c/sup\u003e. Presently, successful growths of IL-nickelates manifesting superconductivity were exclusively via vacuum epitaxy of perovskite nickelates precursors followed by topotactic reduction, limited to light-\u003cem\u003eRE\u003c/em\u003e prior to Eu\u003csup\u003e27\u003c/sup\u003e. Owing to the lanthanide contraction, introducing heavier \u003cem\u003eRE\u003c/em\u003e (e.g., behind Eu) with smaller ionic radius of \u003cem\u003eRE\u003c/em\u003e (\u003cem\u003er\u003csub\u003eRE\u003c/sub\u003e\u003c/em\u003e) into perovskite nickelates is thermodynamically more difficult. This is because that a more distorted NiO\u003csub\u003e6\u003c/sub\u003e octahedra elevates the formation free energy (\u0026Delta;\u003cem\u003eG\u003c/em\u003e) \u003csup\u003e19\u003c/sup\u003e of perovskite nickelates towards more positive magnitude, which is hardly stabilizable by coherent lattice with the substrate. Further obstacle is from the restriction in compositing the alkaline-earth (\u003cem\u003eAE\u003c/em\u003e) hole dopants within perovskite nickelates, since conventional chemical process is incapable to form Ni\u003csup\u003e4+\u003c/sup\u003e in perovskites as major constituents even at extremely high \u003cem\u003ep\u003c/em\u003e\u003csub\u003eO2\u003c/sub\u003e of ~GPa\u003csup\u003e20,28\u003c/sup\u003e. Thus, perovskite nickelates containing \u003cem\u003eAE\u003c/em\u003e constituents were likely to be heterogeneously formed via plasma or atomic beam interplays with the substrate, contingent upon precise and narrowly defined experimental window\u003csup\u003e10,22,27\u003c/sup\u003e. From these perspectives, the present strategy for growing IL-nickelates is insufficient to support further explorations pertaining to heavier \u003cem\u003eRE\u003c/em\u003e, despite its strong likelihood to realize higher \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e and/or unconventional superconductivity, e.g., field-reentry\u003csup\u003e6-8\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eHere, we open up a simple high-\u003cem\u003ep\u003c/em\u003e\u003csub\u003eO2\u003c/sub\u003e assisted chemical avenue for growing IL nickelate superconductors toward heavier \u003cem\u003eRE\u003c/em\u003e constituents with effectiveness in \u003cem\u003eRE\u003c/em\u003e-substitutions, grounded in which their 4\u003cem\u003ef\u003c/em\u003e-orbital relevant field-reentrant superconducting phase diagram is elucidated. Robust uniaxially anisotropic superconducting reentrancy was validated to emerge at the quantum phase boundaries of the superconducting dome for both Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e and Pr\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e systems. Their quantum criticality was further modulated via introducing \u003cem\u003eRE\u0026apos;\u003c/em\u003e within (Nd\u003csub\u003e1-y\u003c/sub\u003e\u003cem\u003eRE\u0026apos;\u003c/em\u003e\u003csub\u003ey\u003c/sub\u003e)\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e (\u003cem\u003eRE\u0026apos;\u003c/em\u003e: Pr, Sm, Gd, Dy and Sm\u003csub\u003e1/2\u003c/sub\u003ePr\u003csub\u003e1/2\u003c/sub\u003e) to adjust the magnitude of exchange field associated with \u003cem\u003eRE\u003c/em\u003e-magnetism. We highlight the further elevation in \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e and critical current density (\u003cem\u003eJ\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e) for the Eu-doped IL-nickelates, exceeding previous layer spacing expectations developed from their counterpart systems doped by Sr/Ca. The root-cause was further elucidated, combining characterization of pairing strength via magneto-transport and localized magnetism via low-energy muon-spin spectroscopy (LE-\u003cem\u003e\u0026mu;\u003c/em\u003eSR). Our work unveils the pivotal role of magnetic fluctuations with close associations with \u003cem\u003eRE\u003c/em\u003e-4\u003cem\u003ef\u003c/em\u003e in modulating the quantum criticality and pairing strength, beyond conventional BCS theory. Also, our MPa-\u003cem\u003ep\u003c/em\u003e\u003csub\u003eO2\u003c/sub\u003e assisted chemical synthetic route sheds a light on the capability to apply IL-nickelates as coated conductors analogous to high-\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e cuprates\u003csup\u003e29\u003c/sup\u003e.\u003c/p\u003e"},{"header":"2.\tResults","content":"\u003cp\u003e\u003cstrong\u003e2.1. A MPa-high \u003cem\u003ep\u003c/em\u003e\u003csub\u003eO2\u003c/sub\u003e assisted chemical avenue enables effective growth of IL-nickelates\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo reduce the positive \u0026Delta;\u003cem\u003eG\u003c/em\u003e of perovskite nickelates contracting with lanthanide contractions, we exploit a MPa-high \u003cem\u003ep\u003c/em\u003e\u003csub\u003eO2\u003c/sub\u003e assisted chemical strategy for thin film growth of IL-nickelate, illustrated in Fig. 1a. In brief, the chemical precursors of \u003cem\u003eRE\u003c/em\u003e(NO\u003csub\u003e3\u003c/sub\u003e)\u003csub\u003e3\u003c/sub\u003e and Ni(CH\u003csub\u003e3\u003c/sub\u003eCOO)\u003csub\u003e2\u003c/sub\u003e were dissolved in ethylene glycol monomethyl ether (EGME), and spin coated on a NdGaO\u003csub\u003e3\u003c/sub\u003e (110) substrate. The spin coated films were crystallized into the perovskite precursor film by annealing at 700-900 ℃ under a high-\u003cem\u003ep\u003c/em\u003e\u003csub\u003eO2\u003c/sub\u003e within 1-20 MPa. Afterwards, the perovskite nickelates was transformed into infinite layer via soft chemical topotactic reduction based on CaH\u003csub\u003e2\u003c/sub\u003e co-anneals at a temperature between 260-320 ℃ for 0.5-4 hours. Instead of using conventional alkaline earth elements (e.g., Sr or Ca)\u003csup\u003e30,31\u003c/sup\u003e, herein the hole doping was realized via partially substituting their \u003cem\u003eRE\u003c/em\u003e-constituents by Eu, which displays variable valance state from +3 in perovskites towards +2 upon topotactic reduction\u003csup\u003e22\u003c/sup\u003e. From the thermodynamic perspective, the metastable perovskite nickelates precursors containing later series \u003cem\u003eRE\u003c/em\u003e-composition is preferentially stabilized at a high-\u003cem\u003ep\u003c/em\u003e\u003csub\u003eO2\u003c/sub\u003e within 10\u003csup\u003e0\u003c/sup\u003e-10\u003csup\u003e2\u003c/sup\u003e MPa\u003csup\u003e19,20\u003c/sup\u003e, as indicated by their equilibrium phase chart in Figure 1b (see more discussions in Supplementary Figs. 1-3). Hence, our strategy is capable to introduce later series \u003cem\u003eRE\u003c/em\u003e further behind Eu into IL-nickelates, while the \u003cem\u003eRE\u003c/em\u003e-constituent is simply and flexibly modulable manipulating the chemical solutions for spin coating.\u003c/p\u003e\n\u003cp\u003eEfficient growth of IL-nickelates is firstly exemplified by Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e, covering a large variety in Eu-compositions. Via MPa-high \u003cem\u003ep\u003c/em\u003e\u003csub\u003eO2\u003c/sub\u003e anneals, the metastable Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e3\u003c/sub\u003e is well stabilized, as indicated by their abrupt metal-insulator transitions (see Fig. 1b and Supplementary Fig. 4)\u003csup\u003e32,33\u003c/sup\u003e. The accuracy in the stoichiometry controls for Eu is convinced by the linear increase in metal-insulator transition temperature (\u003cem\u003eT\u003c/em\u003e\u003csub\u003eMIT\u003c/sub\u003e) with \u003cem\u003ex\u003c/em\u003e (or average \u003cem\u003er\u003csub\u003eRE\u003c/sub\u003e\u003c/em\u003e) in consistency with the previous reports\u003csup\u003e19,20\u003c/sup\u003e, as shown by the inset of Figure 1b. More details in determination of \u003cem\u003eT\u003c/em\u003e\u003csub\u003eMIT\u003c/sub\u003e are shown in Supplementary Fig. 5. As shown in Fig. 1c, the X-ray diffraction patterns of the Nd\u003csub\u003e0.55\u003c/sub\u003eEu\u003csub\u003e0.45\u003c/sub\u003eNiO\u003csub\u003e3\u003c/sub\u003e demonstrate their oriented perovskite crystal structure, which transformed to the Nd\u003csub\u003e0.55\u003c/sub\u003eEu\u003csub\u003e0.45\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e infinite layers after the topotactic reduction, (see more XRD results in Supplementary Fig. 6). The reduction process may result in reduced crystallinity and interfacial coherency indicated by the broadened XRD peak, as also observed previously in vacuum deposited IL-nickelates\u003csup\u003e9,10\u003c/sup\u003e. The resultant variation in electronic structure, e.g., from Ni\u003csup\u003e3+\u003c/sup\u003e to Ni\u003csup\u003e1+\u003c/sup\u003e, is further confirmed by synchrotron-based X-ray absorption spectroscopy (XAS) analysis, as results shown in Supplementary Fig. 7. Figs. 1d-f show the archetypal cross-section morphology for Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e/NdGaO\u003csub\u003e3\u003c/sub\u003e (110) as probed by high-angle annular dark-field (HAADF), where a larger thickness of ~20 nm is observed compared with the vacuum deposited ones (e.g., 6-8 nm)\u003csup\u003e9,10,22,34\u003c/sup\u003e. More representative microscopic morphologies and elementary distributions are demonstrated in Supplementary Figs. 8-11. It is also worth noticing that the Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e3\u003c/sub\u003e precursor coherently grown on the NdGaO\u003csub\u003e3\u003c/sub\u003e substrate (see Supplementary Fig. 12), while the topotactic reduction slightly reduces the crystallinity and coherency of the interface.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.2.\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eTunning the\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003ereentrant and high-\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e superconductivity\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003er\u003c/strong\u003e\u003cstrong\u003eivalries for\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;Nd(Pr)\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eRobust superconducting behaviors are observed for Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e with \u003cem\u003ex\u003c/em\u003e=0.25-0.55, with the highest \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec,onset\u003c/sub\u003e, \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec,50%\u003c/sub\u003e and \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec,zero\u003c/sub\u003e emerged at optimum Eu constituents (x=0.35-0.45) reaching ~37.6 K, ~27.3 K and ~22.2 K, respectively. The temperature dependence in resistivity (\u003cem\u003e\u0026rho;-T\u003c/em\u003e) of archetypal Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e are shown in Figure 2a for optimum doping (x=0.45), underdoping (x=0.3), and overdoping (x=0.52), respectively; while the \u003cem\u003e\u0026rho;-T\u003c/em\u003e tendencies for more Eu-doping constituents are provided in Supplementary Fig. 13. The optimum doped Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e (x=0.35-0.45) manifest expected high-\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e superconductivity that is monotonically suppressed by magnetic fields up to 35 T with no signature of reentrance (see Supplementary Fig. 14). Supplementary Figs. 14J and 14K further demonstrate its high magnitude of \u003cem\u003eJ\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e reaching 266 kA/cm\u003csup\u003e2\u003c/sup\u003e at 2K, exceeding previous vacuum deposited Nd-Sr and Nd-Eu systems at the same temperature (e.g., \u003cem\u003eJ\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e=170 kA/cm\u003csup\u003e2\u003c/sup\u003e for Nd\u003csub\u003e0.8\u003c/sub\u003eSr\u003csub\u003e0.2\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e9\u003c/sup\u003e, \u003cem\u003eJ\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e=237 kA/cm\u003csup\u003e2\u003c/sup\u003e for Nd\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e8\u003c/sup\u003e). Only limited reduction in the magnitudes of \u003cem\u003eJ\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e is observed, even imparting cross-plane magnetic fields up to 9 T. In contrast, the magnetic field reentrant superconducting behaviors reaching zero-resistance are observed for Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e at both underdoped (x=0.2-0.3) and overdoped (x=0.52-0.6) regions. This is demonstrated by their \u003cem\u003e\u0026rho;-B\u0026nbsp;\u003c/em\u003etendency in the insets of Figure 2a (also Supplementary Fig. 14), and also the crossing in their \u003cem\u003e\u0026rho;-T\u003c/em\u003e tendencies as measured under different magnetic fields in Supplementary Fig. 15.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe field-reentrant superconductivity emerging at both the underdoped and overdoped boundaries also holds for Pr\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e/NdGaO\u003csub\u003e3\u003c/sub\u003e (110) and Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e/(LaAlO\u003csub\u003e3\u003c/sub\u003e)\u003csub\u003e0.3\u003c/sub\u003e(Sr\u003csub\u003e2\u003c/sub\u003eTaAlO\u003csub\u003e6\u003c/sub\u003e)\u003csub\u003e0.7\u003c/sub\u003e (100), as demonstrated in Supplementary Fig. 16. This indicates the rivalry between reentrant and high-\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e superconductivity within Eu-doped IL-nickelates, giving rise to a more complicated superconducting phase diagram (\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e-x) compared to the Sr/Ca-doped ones, as shown in Figure 2c. We highlight that the superconducting reentry emerges exclusively at the superconducting boundaries, but is absent when the high-\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e superconductivity is robust at optimum doping. This unveils the previously underestimated tunability in the quantum criticality by \u003cem\u003eRE\u003c/em\u003e-4\u003cem\u003ef\u003c/em\u003e (particularly Eu-4\u003cem\u003ef\u003c/em\u003e\u003csup\u003e7\u003c/sup\u003e)\u003csup\u003e6\u003c/sup\u003e, via the likelihood of a magnetic fluctuation modulated pairing in the neighborhoods of quantum phase transitions\u003csup\u003e11\u003c/sup\u003e. For example, in the underdoped region, the superconducting state has energy that is close to many competing states, such as charge order\u003csup\u003e35\u003c/sup\u003e, spin order\u003csup\u003e36\u003c/sup\u003e and/or oxygen order\u003csup\u003e37\u003c/sup\u003e. In the overdoped region near a hidden quantum critical point (QCP), the system exhibits a transition from non-Fermi liquid to Fermi liquid behavior\u003csup\u003e30\u003c/sup\u003e, triggering a sudden change in electronic state. Hence, potential \u003cem\u003eRE\u003c/em\u003e-4\u003cem\u003ef\u003c/em\u003e modulated magnetic fluctuations and the suppression of superconductivity by the competing quantum states\u003csup\u003e34\u003c/sup\u003e may lead to the criticality between reentrant and high-\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e superconductivity\u003csup\u003e11,36\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eOf particular note is the broader superconducting dome extending to larger Eu compositions in Pr\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e than in Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e, despite the similar magnitudes in their starting point (e.g., x=0.2) and maximum \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e both of ~37.6 K. Further X-ray photoemission spectroscopy analysis as shown in Supplementary Figs. 18a-c indicate a higher Eu\u003csup\u003e2+\u003c/sup\u003e/Eu\u003csup\u003e3+\u003c/sup\u003e ratio for Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e (e.g., ~1/1) compared to Pr\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e (e.g., ~2/3). Hence, estimating their practical hole doping range contributed by Eu\u003csup\u003e2+\u003c/sup\u003e indicates similarities to the previous reports for Nd\u003csub\u003e1-x\u003c/sub\u003eSr\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e30\u003c/sup\u003e and Pr\u003csub\u003e1-x\u003c/sub\u003eSr\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e38\u003c/sup\u003e, as more clearly demonstrated in Supplementary Figs. 17d and 17e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.3.\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eFurther modulations in the\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003equantum criticality and \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e via multiple \u003cem\u003eRE\u003c/em\u003e-compositions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo further elucidate the role of \u003cem\u003eRE\u003c/em\u003e in rivalry between high-\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e and reentrant superconductivity, we start with the matrix of optimum doped Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e (x: 0.35-0.45) without reentrancy and partially substitute Nd by \u003cem\u003eRE\u003c/em\u003e\u0026rsquo; (e.g., Pr, Sm, Gd and Dy). The \u003cem\u003eRE\u0026apos;\u003c/em\u003e substitution elicited corresponding changes in the \u003cem\u003eT\u003c/em\u003e\u003csub\u003eMIT\u003c/sub\u003e of (Nd\u003csub\u003e1-y\u003c/sub\u003e\u003cem\u003eRE\u0026apos;\u003c/em\u003e\u003csub\u003ey\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e3\u003c/sub\u003e (see Supplementary Fig. 18) and also lattice constants of (Nd\u003csub\u003e1-y\u003c/sub\u003e\u003cem\u003eRE\u0026apos;\u003c/em\u003e\u003csub\u003ey\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e (see Supplementary Fig. 19). Fig. 3a (upper) shows the \u003cem\u003e\u0026rho;\u003c/em\u003e\u003cem\u003e-T\u003c/em\u003e tendencies for (Nd\u003csub\u003e0.9\u003c/sub\u003ePr\u003csub\u003e0.1\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e, (Nd\u003csub\u003e0.9\u003c/sub\u003eSm\u003csub\u003e0.1\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e and (Nd\u003csub\u003e0.9\u003c/sub\u003eDy\u003csub\u003e0.1\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e, where robust superconducting behaviors are observed, e.g., with \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec,zero\u003c/sub\u003e of ~20 K, 18 K and 14 K, respectively. As their \u003cem\u003e\u0026rho;-B\u003c/em\u003e tendencies further demonstrated in the insets and also Supplementary Figs. 20a-c, these samples display no field-reentrant behaviors. In contrast, the reentrant superconductivity emerges for (Nd\u003csub\u003e1-y\u003c/sub\u003eGd\u003csub\u003ey\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e (y=0.05, 0.1 and 0.2) as demonstrated in Fig. 3a (lower) and also the inset. Their \u003cem\u003e\u0026rho;-B\u003c/em\u003e tendencies measured at more temperatures are further shown in Supplementary Figs. 20d and 20e. Also, the Gd substitution results in lower \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec,zero\u003c/sub\u003e compared to the ones substituted by other \u003cem\u003eRE\u0026apos;\u003c/em\u003e (see Supplementary Fig. 21).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo verify the zero-resistance for the Gd reinforced reentrant superconductivity and its secondary quench, we measured their \u003cem\u003e\u0026rho;-B\u003c/em\u003e tendencies of (Nd\u003csub\u003e0.95\u003c/sub\u003eGd\u003csub\u003e0.05\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e up to higher magnetic fields at different temperatures, as shown in Fig. 3b. The reentrant superconductivity reaching zero resistances is observed from 5-10 T, 8-13 T and 10-15 T at 1.6 K, 2 K, and 3 K, respectively, afterwards quenching at 30 T, 25 T and 20 T. Further angular dependent magneto-transport measurements via altering the angle (\u003cem\u003e\u0026theta;\u003c/em\u003e) between \u003cem\u003eH\u003c/em\u003e\u003csub\u003eext\u003c/sub\u003e and \u003cem\u003ec\u003c/em\u003e-axis indicates strong uniaxial \u003cem\u003ecross-plane\u003c/em\u003e anisotropy in the superconducting reentrant behavior of (Nd\u003csub\u003e0.95\u003c/sub\u003eGd\u003csub\u003e0.05\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e. Their resistivity is mapped as a function of both magnetic field strength and \u003cem\u003e\u0026theta;\u003c/em\u003e in Fig. 3c at 2 K, 3 K and 5K, where more separated regions associated with the low field and reentrant field superconductivity are observed when imparting \u003cem\u003eH\u003c/em\u003e\u003csub\u003eext\u003c/sub\u003e along \u003cem\u003ec-\u003c/em\u003eaxis (\u003cem\u003e\u0026theta;\u003c/em\u003e=0\u0026deg;). Also, elevating the temperature (e.g., from 2 K to 5 K) results in markedly contraction in the reentrant region. This should be attributed to the higher \u003cem\u003eH\u003c/em\u003e\u003csub\u003ec2\u003c/sub\u003e along the \u003cem\u003eab\u003c/em\u003e-plane compared to the \u003cem\u003ec\u003c/em\u003e-axis, stemming from the Eu-4\u003cem\u003ef\u003c/em\u003e related anisotropy in orbital depairing\u003csup\u003e21\u003c/sup\u003e, as further discussed in Supplementary Fig.\u0026nbsp;22. Similar phenomenon was also observed for as-grown (Nd\u003csub\u003e0.9\u003c/sub\u003eGd\u003csub\u003e0.1\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e, Nd\u003csub\u003e0.48\u003c/sub\u003eEu\u003csub\u003e0.52\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e and Nd\u003csub\u003e0.46\u003c/sub\u003eEu\u003csub\u003e0.54\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e, as demonstrated in Supplementary Fig. 23. Hence, the Gd reinforced reentrant superconductivity is in consistency to ones observed for Nd-Eu and Sm-Eu systems grown by both vacuum depositions\u003csup\u003e6-8\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe preferential superconducting reentrancy via introducing Gd over other \u003cem\u003eRE\u0026apos;\u0026nbsp;\u003c/em\u003e(e.g., Pr, Sm and Dy) within (Nd\u003csub\u003e1-y\u003c/sub\u003e\u003cem\u003eRE\u0026apos;\u003c/em\u003e\u003csub\u003ey\u003c/sub\u003e)\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e was also verified in other compositions (e.g., x=0.35, y=0.2; x=0.45, y=0.2; x=0.5, y=0.1), as demonstrated in Supplementary Fig. 24. Instead of other proposed mechanisms (e.g., spin-triplet pairing\u003csup\u003e11\u003c/sup\u003e and metamagnetic criticality\u003csup\u003e39\u003c/sup\u003e), the Jaccarino-Peter (J-P) effect\u003csup\u003e40,41\u003c/sup\u003e was more likely to explain the magnetic field induced reentrant superconductivity for Eu-doped IL-nickelates\u003csup\u003e6-8\u003c/sup\u003e. In sight of its half-filled 4\u003cem\u003ef\u003c/em\u003e\u003csup\u003e7\u003c/sup\u003e among \u003cem\u003eRE\u003c/em\u003e\u003csup\u003e3+\u003c/sup\u003e (see details in Supplementary Table 1)\u003csup\u003e42,43\u003c/sup\u003e, introducing Gd\u003csup\u003e3+\u003c/sup\u003e is expected to enhance the internal exchange field (\u003cem\u003eH\u003c/em\u003e\u003csub\u003eex\u003c/sub\u003e) to partially against the external magnetic field (\u003cem\u003eH\u003c/em\u003e\u003csub\u003eext\u003c/sub\u003e), as illustrated in Figure 3c. In contrast, the Eu\u003csup\u003e2+\u003c/sup\u003e (also with 4\u003cem\u003ef\u003c/em\u003e\u003csup\u003e7\u003c/sup\u003e) not only generates \u003cem\u003eH\u003c/em\u003e\u003csub\u003eex\u003c/sub\u003e, but also served as hole dopant that simultaneously contributes to transports, giving rise to more complicated impact beyond simply J-P effect.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFrom a counterpoint compared to Gd, introducing \u003cem\u003eRE\u0026apos;\u003c/em\u003e (e.g., Pr, Sm and Pr\u003csub\u003e1/2\u003c/sub\u003eSm\u003csub\u003e1/2\u003c/sub\u003e) to reduce the magnetism of rare-earth site within (Nd\u003csub\u003e1-y\u003c/sub\u003e\u003cem\u003eRE\u0026apos;\u003c/em\u003e\u003csub\u003ey\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e sheds a light on further elevating \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e beyond the superconducting dome of the matrix Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e with \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e (e.g., peaking at ~37.6 K). This was confirmed by higher magnitudes of \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e reaching 40.1 K, 38.1 K and 38.4 K as observed for (Nd\u003csub\u003e0.8\u003c/sub\u003ePr\u003csub\u003e0.2\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e, (Nd\u003csub\u003e0.6\u003c/sub\u003eSm\u003csub\u003e0.4\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e and (Nd\u003csub\u003e0.4\u003c/sub\u003ePr\u003csub\u003e0.3\u003c/sub\u003eSm\u003csub\u003e0.3\u003c/sub\u003e)\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e, respectively, as demonstrated by Supplementary Figs. 24 and 25. Considering that Nd\u003csup\u003e3+\u003c/sup\u003e exhibits an ionic radius between Pr\u003csup\u003e3+\u003c/sup\u003e and Sm\u003csup\u003e3+\u003c/sup\u003e and a larger magnetic moment than both, the further elevation in \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e is unlikely to be related to rare-earth size effect, but more associated with a weakened lattice magnetism via disturbing \u003cem\u003eRE-\u003c/em\u003e4\u003cem\u003ef\u003c/em\u003e spin ordering from \u003cem\u003eRE\u003c/em\u003e-mixing.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.4. Elevated \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e coincide with promoted magnetic fluctuation at superconducting state\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eGrounded in present large \u003cem\u003eRE\u003c/em\u003e-compositional diversity, we summarized the \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e plotted as a function of the \u003cem\u003ec\u003c/em\u003e-axis lattice constants (\u003cem\u003ec\u003c/em\u003e) for the present Eu-doped IL-nickelates showing robust superconductivity without reentrancy together with the reported ones\u003csup\u003e10,27\u003c/sup\u003e in Fig. 4a. This is further compared to the \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e-\u003cem\u003ec\u003c/em\u003e tendency developed from Sr-/Ca-doped IL-nickelates approaching to optimum doping\u003csup\u003e30,31,38,44-48\u003c/sup\u003e, as indicated by the dash line. The further elevation in \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e is clearly observed for the optimum Eu-doped IL-nickelates transcending the Sr-/Ca-doped ones even at similar layer spacing. This unveils an extra pairing strengthening mechanism related to Eu\u003csup\u003e2+\u003c/sup\u003e-4\u003cem\u003ef\u003c/em\u003e\u003csup\u003e7\u003c/sup\u003e, as is further confirmed by performing magneto-electrical transport measurements shown in Supplementary Fig. 26 to estimate the paring strength summarized in Supplementary Table 2. It evokes closed associations with potential more complicated spin and orbital interactions with Eu\u003csup\u003e2+\u003c/sup\u003e-4\u003cem\u003ef\u003c/em\u003e\u003csup\u003e7\u003c/sup\u003e, which improves paring via potentially promoted magnetic fluctuation\u003csup\u003e49\u003c/sup\u003e, struggling for primacy with the J-P effects.\u003c/p\u003e\n\u003cp\u003eAbove viewpoint was supported by the abruptly promoted spin ordering below \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e even for the optimum-doped Nd\u003csub\u003e0.6\u003c/sub\u003eEu\u003csub\u003e0.4\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e with completely shielded reentrant superconductivity, as probed by LE-\u003cem\u003e\u0026mu;\u003c/em\u003eSR, as demonstrated in Fig. 4b. More detailed results are further shown in Supplementary Fig. 27 and 28. Descending temperature across 20-40 K (consistent to superconducting transition) results in an abrupt increase in the relaxation rate (\u003cem\u003el\u003c/em\u003e\u003csub\u003eZF\u003c/sub\u003e), accompanied by reductions in the stretch parameter \u003cem\u003eb\u003c/em\u003e down to a plateau magnitude of ~0.5-0.6 similar to spin-glass\u003csup\u003e48\u003c/sup\u003e. The magnitude of \u003cem\u003el\u003c/em\u003e\u003csub\u003eZF\u003c/sub\u003e (e.g., 2.5 \u0026mu;s\u003csup\u003e-1\u003c/sup\u003e) in the superconducting state is\u0026nbsp;much\u0026nbsp;larger than that previously observed for\u0026nbsp;the Sr-doped IL-nickelates (e.g., 0.22-0.48\u0026nbsp;\u0026mu;s\u003csup\u003e-1\u003c/sup\u003e)\u003csup\u003e48\u003c/sup\u003e.\u0026nbsp;This indicates\u0026nbsp;an Eu\u003csup\u003e2+\u003c/sup\u003e-enhanced spin ordering and magnetic fluctuations when entering the superconducting state, which may account for the large elevation in \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e compared to Sr-doped IL-nickelates (e.g., ~10 K\u003csup\u003e9\u003c/sup\u003e).\u0026nbsp;\u003c/p\u003e"},{"header":"3.\tConclusion","content":"\u003cp\u003eIn summary, grounded in the high-\u003cem\u003ep\u003c/em\u003e\u003csub\u003eO2\u003c/sub\u003e chemical avenue to effectively grow (\u003cem\u003eRE\u003c/em\u003e\u003csub\u003e1-y\u003c/sub\u003e\u003cem\u003eRE\u0026apos;\u003c/em\u003e\u003csub\u003ey\u003c/sub\u003e)\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e, we elucidate the enrichment in their superconducting phase diagram by field-reentrant superconducting states emerging at both quantum boundaries, competing for primacy. The quantum criticality between reentrant and high-\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e superconductivity not only hinges on Eu-composition, but also displays associations with the \u003cem\u003eRE\u003c/em\u003e (\u003cem\u003eRE\u003c/em\u003e\u0026rsquo;) magnetism, which modulate the exchange field together with Eu\u003csup\u003e2+\u003c/sup\u003e. Furthermore, combining magneto-transport and LE-\u003cem\u003e\u0026mu;\u003c/em\u003eSR measurements unveils the concomitant occurrence of strengthened Cooper pairing and promoted magnetic fluctuation via optimum Eu\u003csup\u003e2+\u003c/sup\u003e-4\u003cem\u003ef\u003c/em\u003e\u003csup\u003e7\u003c/sup\u003e interactions. This counts for their further elevated \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e beyond the Sr-/Ca-doped systems even at similar infinite layer-spacing, giving rise to higher \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e up to ~40 K and more robust \u003cem\u003eJ\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e reaching 266 kA/cm\u003csup\u003e2\u003c/sup\u003e at 2 K. These discoveries highlight a new freedom from the overlooked \u003cem\u003eRE\u003c/em\u003e-4\u003cem\u003ef\u003c/em\u003e orbital and spin interplays that further complicate the superconducting phase diagram of IL-nickelates in terms of quantum phase criticality modulation and pairing strengthening, beyond analogous cuprates with similar \u003cem\u003ed\u003c/em\u003e-orbital frameworks. Furthermore, the non-vacuum growth of IL-nickelate with high effectiveness holds practical implications, particularly in potential to leverage coated-conductor technologies similar to cuprates.\u003c/p\u003e"},{"header":"4. Methods ","content":"\u003cp\u003e\u003cstrong\u003eSample preparation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThin films of (Nd\u003csub\u003e1-y\u003c/sub\u003e\u003cem\u003eRE\u0026apos;\u003c/em\u003e\u003csub\u003ey\u003c/sub\u003e)\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e (\u003cem\u003eRE\u0026apos;\u003c/em\u003e=Pr, Sm, Gd and Dy) were grown via a high-oxygen-pressure-assisted chemical route, followed by a soft topotactic reduction. Metal nitrate precursors, such as Nd(NO\u003csub\u003e3\u003c/sub\u003e)\u003csub\u003e3\u003c/sub\u003e and Eu(NO\u003csub\u003e3\u003c/sub\u003e)\u003csub\u003e3\u003c/sub\u003e, as well as the Ni(CH\u003csub\u003e3\u003c/sub\u003eCOO)\u003csub\u003e2\u003c/sub\u003e (\u0026ge;99.9%, Aladdin) were dissolved in ethylene glycol monomethyl ether (EGME) according to the target stoichiometry. For partial rare-earth substitutions, Pr(NO\u003csub\u003e3\u003c/sub\u003e)\u003csub\u003e3\u003c/sub\u003e, Sm(NO\u003csub\u003e3\u003c/sub\u003e)\u003csub\u003e3\u003c/sub\u003e, Gd(NO\u003csub\u003e3\u003c/sub\u003e)\u003csub\u003e3\u003c/sub\u003e and Dy(NO\u003csub\u003e3\u003c/sub\u003e)\u003csub\u003e3\u003c/sub\u003e were co-dissolved correspondingly. The precursor solution was spin-coated onto single-crystal NdGaO\u003csub\u003e3\u003c/sub\u003e(110) and LSAT(100) substrates and dried in air.\u003c/p\u003e\n\u003cp\u003eAs-deposited gel films were crystallized into perovskite-type nickelate precursors by annealing at 700-900\u0026thinsp;℃ under oxygen pressures of 1-20\u0026thinsp;MPa in a custom-built high-\u003cem\u003ep\u003c/em\u003e\u003csub\u003eO2\u003c/sub\u003e tubular reactor. After cooling to room temperature, the perovskite films were sealed in a vacuum quartz tube together with CaH\u003csub\u003e2\u003c/sub\u003e powder and annealed at 260-320\u0026thinsp;℃ for 0.5-4\u0026thinsp;h for topotactic reduction into the infinite-layer phase. This process simultaneously reduced Eu\u0026sup3;⁺ to Eu\u0026sup2;⁺, serving as the effective hole dopant. The resulting infinite-layer films had a typical thickness of ~20\u0026thinsp;nm.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eX-ray diffraction\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCrystal structures of the perovskite precursors and reduced infinite-layer nickelate films were characterized using X-ray diffraction (XRD, Bruker D8 Discover) with Cu \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u0026alpha;1\u003c/sub\u003e radiation (\u003cem\u003e\u0026lambda;\u003c/em\u003e=1.5406\u0026thinsp;\u0026Aring;). The \u003cem\u003e\u0026theta;\u003c/em\u003e-2\u003cem\u003e\u0026theta;\u003c/em\u003e scans were collected to identify phase purity, and reciprocal space mapping (RSM) of the (103) reflection was employed to verify the epitaxial quality and in-plane lattice coherence.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eScanning transmission electron microscopy\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe cross-sectional morphologies and interfacial structures of the samples were characterized by scanning transmission electron microscopy (STEM) using an FEI Titan Themis Z microscope operated at 300 kV, equipped with a double aberration corrector and a high-angle annular dark-field (HAADF) detector. The convergence semi-angle for imaging is 25 mrad, and the collection semi-angle is 50-200 mrad for the HAADF imaging. The cross-sectional TEM lamellas were thinned to electron beam transparency at 30 kV by using Carl Zeiss Crossbeam 550L FIB-SEM, followed by the removal of the surface amorphous layer at 2 kV. The obtained HAADF-STEM images revealed atomically sharp interfaces between the Nd\u003csub\u003e1-x\u003c/sub\u003eEu\u003csub\u003ex\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e films and NdGaO\u003csub\u003e3\u003c/sub\u003e substrates and confirmed the topotactic structural transformation from the perovskite precursor to the infinite-layer phase after reduction. The electron energy-loss spectroscopy (EELS) and energy-dispersive X-ray spectroscopy (EDS) were performed to obtain chemical and electronic-structure information. The EELS spectrum-imaging was acquired with the post-column imaging filter fitted with a K3 direct electron detector. The STEM beam current was set to ~80 pA for spectrum imaging, the pixel dwell time was 1 ms, and the recorded pixel size was 0.5 \u0026Aring;. The EELS energy dispersion was of 0.35 eV per channel. The EDS elemental maps were collected with an acquisition current of ~100 pA. All EELS and EDS datasets were energy- and spatially-calibrated and processed using standard routines; elemental maps shown in the manuscript were optimized in Velox software (Thermo Fisher) with a light Gaussian blur applied for presentation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eXPS and XAS measurements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eX-ray photoelectron spectroscopy (XPS, Thermo Scientific ESCALAB 250Xi) was used to determine the chemical states of Eu, Nd, and Ni ions, with Al \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u0026alpha;\u003c/sub\u003e (1486.6 eV) radiation. The binding energy was calibrated using the C 1\u003cem\u003es\u003c/em\u003e peak at 284.8 eV. The Eu\u003csup\u003e3+\u003c/sup\u003e:Eu\u003csup\u003e2+\u003c/sup\u003e ratio was estimated by deconvolution of the Eu 3\u003cem\u003ed\u003c/em\u003e\u003csub\u003e3/2\u003c/sub\u003e and 3\u003cem\u003ed\u003c/em\u003e\u003csub\u003e5/2\u003c/sub\u003e peaks. The synchrotron-based X-ray absorption spectroscopy (XAS) at the Ni \u003cem\u003eL\u003c/em\u003e-edge was carried out at the BL08U1A beamline of the Shanghai Synchrotron Radiation Facility (SSRF). Total electron yield (TEY) mode was used to probe the near-surface region, confirming the reduction of Ni valence from +3 in Nd\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e3\u003c/sub\u003e to +1 in Nd\u003csub\u003e0.65\u003c/sub\u003eEu\u003csub\u003e0.35\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eElectrical transport measurements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eElectrical transport properties were measured using a Quantum Design Physical Property Measurement System (PPMS). Standard four-probe geometry was used with aluminium ultrasonic wire bonds; contact resistances were typically below a few hundred ohms. Temperature-dependent resistivity (\u003cem\u003e\u0026rho;\u003c/em\u003e-\u003cem\u003eT\u003c/em\u003e) measurements were performed from 300\u0026thinsp;K to 2\u0026thinsp;K under magnetic fields up to 9\u0026thinsp;T. Angle-dependent transport was measured using a high-precision rotator (angular resolution 0.01\u0026deg;) to determine the anisotropy of reentrant superconductivity. The critical current density (\u003cem\u003eJ\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e) was measured using the Electrical Transport Option (ETO) module of the same PPMS from current-voltage (\u003cem\u003eI\u003c/em\u003e-\u003cem\u003eV\u003c/em\u003e) curves in a four-probe configuration.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eHigh-field magneto-transport\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eHigh-magnetic-field resistance measurements were performed on the WM1 system at the Steady High Magnetic Field Facility, Chinese Academy of Sciences (Hefei). Magnetic fields up to 35\u0026thinsp;T and temperatures down to 1.6\u0026thinsp;K were achieved in a custom-built \u003csup\u003e4\u003c/sup\u003eHe cryostat (Physike Instruments). A Keithley 6221 current source and SR830 lock-in amplifiers were used for low-noise data acquisition.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe \u003cem\u003e\u0026mu;\u003c/em\u003eSR measurements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe \u003cem\u003e\u0026mu;\u003c/em\u003eSR measurements were performed at the low-energy Muon Facility (LEM) at the \u003cem\u003e\u0026mu;\u003c/em\u003eE4 beam line of the Swiss muon source (S\u003cem\u003e\u0026mu;\u003c/em\u003eS) at Paul Scherrer Institut (PSI) in Villigen, Switzerland. Implantation energies were selected from TRIM.SP simulations to maximise muon stopping rates in the Nd\u003csub\u003e0.6\u003c/sub\u003eEu\u003csub\u003e0.4\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e films. To exclude the possibility of stray magnetic field during the ZF-\u003cem\u003e\u0026mu;\u003c/em\u003eSR measurements, all the magnets were preliminarily degaussed, and an active field-compensating facility was used. For the wTF-\u003cem\u003e\u0026mu;\u003c/em\u003eSR measurements, the applied magnetic field (i.e., 10 mT) was perpendicular to the muon-spin direction, and the films were cooled in an applied magnetic field down to the base temperature (\u0026asymp;1.6 K). Six pieces of Nd\u003csub\u003e0.6\u003c/sub\u003eEu\u003csub\u003e0.4\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e/LSAT(100) films (each has a dimension of 5\u0026acute;10 mm\u003csup\u003e2\u003c/sup\u003e) were mounted on the non-magnetic Ag sample holder. The muon spin relaxation of Ag is less than 0.04 ms\u003csup\u003e-1\u003c/sup\u003e at temperatures above 2 K, which is negligible compared with Nd\u003csub\u003e0.6\u003c/sub\u003eEu\u003csub\u003e0.4\u003c/sub\u003eNiO\u003csub\u003e2\u003c/sub\u003e films. \u0026nbsp;\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eCompeting interests:\u0026nbsp;\u003c/strong\u003eWe declare no competing financial interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAdditional information\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eSupplementary\u0026nbsp;Information is available for this manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorrespondence\u003c/strong\u003e\u003cstrong\u003es\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Correspondence should be addressed: Prof. Jikun Chen ([email protected]), Prof. Jia-Cai Nie ([email protected]) and Prof. Binghui Ge ([email protected]).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions:\u0026nbsp;\u003c/strong\u003eJ.C. and J.N. conceived the project. H.H., Y.Z. and Y.B. contributed equally to this work. H.H. performed the soft chemical reduction experiments, transport measurements, and XRD characterizations, assisted by Y.B. and T.M.. Y.Z. synthesized the perovskite precursor films assisted by N.C. Y.B. and W.Y. assisted in the transport measurements. H.H., C.X., and Z.W. performed the high-field magneto-transport measurements. S.Y. and B.G. conducted the STEM experiments. H.D performed the XAS experiments assisted by K.M.; T.S. and Z. S. performed the LE-\u003cem\u003em\u003c/em\u003eSR measurements, while T.S. analysed the data. J.C, J.N. B.G, N.C and K.M. provided constructive experimental supports and discussions. All authors analysed and discussed the data. J.C. wrote the manuscript, assisted by H.H. and J.N, also with input from all authors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments:\u0026nbsp;\u003c/strong\u003eThis work was supported the National Key Research and Development Program of China (No. 2021YFA0718900), the National Natural Science Foundation of China (No. 62474017, 92577108 and 12474001), the Natural Science Foundation of Guangdong Province of China (Grant No. 2025A1515011071) and the Guangdong Provincial Quantum Science Strategic Initiative (Grant No. GDZX2501006). We thank the BL08U1A beamline and the User Experiment Assist System of the Shanghai Synchrotron Radiation Facility (SSRF) for the assistance in characterizations. We also thank the staff members of the XMCD beamline at the NSRL in Hefei, for providing the technical support and assistance in XAS data collection and analysis. We also thank the\u0026ensp;WM1\u0026ensp;of the Steady High Magnetic Field Facility, Chinese Academy of Sciences,\u0026ensp;for the\u0026ensp;assistance\u0026ensp;on\u0026ensp;the\u0026ensp;experiment. The muon measurements were performed at the \u003cem\u003e\u0026micro;\u003c/em\u003eE4 beamline of the Swiss Muon Source S\u003cem\u003e\u0026micro;\u003c/em\u003eS, Paul Scherrer Institute, Villigen, Switzerland. We also acknowledge the support from Dr. Andreas Suter and Dr. Thomas Proksha in PSI Center for Neutron and Muon Sciences, Paul Scherrer Institute, Switzerland. Also, we acknowledge the constructive discussions with Dr. Ivan Božović.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eShen, B.\u003cem\u003e et al.\u003c/em\u003e Strange-metal behaviour in a pure ferromagnetic Kondo lattice. \u003cem\u003eNature\u003c/em\u003e \u003cstrong\u003e579\u003c/strong\u003e, 51-55 (2020).\u003c/li\u003e\n\u003cli\u003eIglesias, J. 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Exchange-induced autoionization in Eu-rich EuO. \u003cem\u003ePhysical Review Letters\u003c/em\u003e \u003cstrong\u003e26\u003c/strong\u003e, 885 (1971).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7803050/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7803050/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Recently, preliminary magnetic field-reentrant superconductivity manifested in high-temperature (Tc) Eu-doped infinite-layer (IL) nickelates, beyond analogous discoveries exclusively in low-Tc systems. This evokes intriguing fundamental issues about potential quantum-phase boundary and criticality between unconventional superconductivity and field-reentrant-one, which are inexplicable owing to formidable challenges in growing IL-nickelates towards later-series rare-earths. Herein, we open up chemical avenues to enable effective growth of (RE1-yRE'y)1-xEuxNiO2 (RE/RE': Pr, Nd, Sm, Gd, Dy), giving rise to discoveries of RE-4f-related quantum rivalries between high-Tc and reentrant superconductivity. Robust magnetic-field-reentrant superconductivity with uniaxial anisotropy is observed at superconducting-dome boundaries, stemming from Eu2+-4f7 associated competitions between magnetic-fluctuation promoted pairing and exchange-field interactions. Their quantum-criticality is further modulable via RE(RE’)-magnetism, which either reinforces reentrancy or elevates Tc (~40.1 K) with more robust critical-current-density (~266 kA/cm2 at 2 K) beyond Sr-/Ca-doped counterparts. Our synthetic route enables the establishment of an ideal platform via IL-nickelates for studying 4f-related unconventional superconductivity and quantum-criticality.","manuscriptTitle":"A chemical avenue to manipulate field-reentrant superconducting rivalries in infinite layer nickelates","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-04 09:40:34","doi":"10.21203/rs.3.rs-7803050/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"3da57356-7ab9-4617-b965-0a97ff7d90c6","owner":[],"postedDate":"May 4th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Reject before peer review","date":"2026-05-07T12:54:11+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-05-01T05:55:50+00:00","index":"","fulltext":""},{"type":"submitted","content":"Nature Synthesis","date":"2026-04-30T12:01:08+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":67358170,"name":"Physical sciences/Materials science/Condensed-matter physics/Superconducting properties and materials"},{"id":67358171,"name":"Physical sciences/Materials science"}],"tags":[],"updatedAt":"2026-05-07T12:57:46+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-04 09:40:34","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7803050","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7803050","identity":"rs-7803050","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}