Nd1-xEuxNiO2: Superconducting Nickelate

• Nd1-xEuxNiO2 (NENO) is an Eu-substituted infinite-layer nickelate characterized by mixed Eu valence, tunable hole concentration, and a broad superconducting dome.
• Thin-film synthesis via molecular beam epitaxy and high-oxygen-pressure chemical deposition enables controlled structure, stoichiometry, and reliable superconducting phase formation.
• Magnetic-field enhanced and reentrant superconductivity reveal a strong interplay between rare-earth 4f moments, exchange interactions, and unconventional pairing mechanisms.

Searching arXiv for the cited NENO papers to ground the article in current preprints. $\mathrm{Nd}_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2$, commonly abbreviated NENO, is a Eu-substituted Nd-based infinite-layer nickelate thin-film family in which Eu substitution changes both the nominal hole concentration and the rare-earth-layer magnetic environment. In the 2025 literature, NENO is presented as a superconducting nickelate platform that combines a broad superconducting composition range, a spectroscopically enlarged superconducting gap, strong violation of the weak-coupling Pauli limit, and magnetic-field-enhanced or field-reentrant superconductivity linked to rare-earth $4f$ moments (Vu et al., 21 Aug 2025, Han et al., 27 Nov 2025). A central theme is that Eu is not treated merely as a dopant: it is also a source of mixed valence and local magnetic exchange, so the Nd/Eu spacer layer becomes an active control parameter for the superconducting state.

1. Composition, valence, and material identity

NENO denotes the Eu-doped infinite-layer nickelate $\mathrm{Nd}_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2$. One 2025 study embeds it in the broader series

$$(\mathrm{Nd}_{1-y}\mathrm{RE}'_{y})_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2,\qquad \mathrm{RE}'=\mathrm{Pr,Nd,Sm,Gd,Dy},$$

with the fixed-$x=0.35$ subset

$$(\mathrm{Nd}_{1-y}\mathrm{RE}'_y)_{0.65}\mathrm{Eu}_{0.35}\mathrm{NiO}_2$$

used to vary the rare-earth $4f$ configuration without changing the nominal Eu level (Han et al., 27 Nov 2025).

Structurally, NENO consists of stacked $\mathrm{NiO}_2$ planes separated by Nd/Eu spacer layers. The rare-earth layer is treated as electronically consequential rather than inert. In the reported interpretation, unlike the usual cuprate analogy in which spacer layers play little direct role near the Fermi level, the rare-earth chemistry in nickelates can affect superconductivity through spin structure, exchange interactions, and Fermi surface changes (Vu et al., 21 Aug 2025).

A defining chemical feature is Eu mixed valence after reduction. XPS gives the estimate

$\mathrm{Eu}^{3+}:\mathrm{Eu}^{2+}\approx 1:1,$

and the paper therefore argues that only about half the Eu acts as $\mathrm{Eu}^{2+}$ hole dopant in the infinite-layer phase (Han et al., 27 Nov 2025). This mixed-valence picture is important because it separates nominal substitution $4f$0 from effective hole density. The same study estimates that the superconducting dome corresponds to an effective hole-doping range $4f$1–$4f$2, similar to $4f$3 (Han et al., 27 Nov 2025).

The magnetic role of Eu enters through the $4f$4 local moment. One paper emphasizes mixed $4f$5 valence together with the large local moment of $4f$6, $4f$7, while the other groups $4f$8 and $4f$9 together as half-filled $\mathrm{Nd}_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2$0 ions with large effective moments, written there as $\mathrm{Nd}_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2$1 (Vu et al., 21 Aug 2025, Han et al., 27 Nov 2025). This is the basis for treating NENO as a nickelate in which charge doping and rare-earth-moment physics are deliberately entangled.

2. Thin-film realization and synthesis routes

Two distinct thin-film routes are reported for NENO. One study uses molecular beam epitaxy to grow $\mathrm{Nd}_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2$2 precursor films of thickness 18–21 unit cells on commercial LSAT (001) substrates, cleaned at $\mathrm{Nd}_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2$3C in activated oxygen at $\mathrm{Nd}_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2$4 Torr; the films are then cooled in RF plasma oxygen to $\mathrm{Nd}_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2$5C to remove oxygen vacancies and reduced in situ using metallic Al to form the infinite-layer phase. The high-field transport films in that work are 6 nm thick and capped with 1 nm of $\mathrm{Nd}_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2$6 (Vu et al., 21 Aug 2025).

The other study presents what it calls a “high-$\mathrm{Nd}_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2$7 chemical avenue.” In that route, perovskite precursor films $\mathrm{Nd}_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2$8 and $\mathrm{Nd}_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2$9 are synthesized by MPa-range oxygen-pressure-assisted chemical deposition and then topotactically reduced by $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_{y})_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2,\qquad \mathrm{RE}'=\mathrm{Pr,Nd,Sm,Gd,Dy},$$0 co-annealing to remove apical oxygen and convert the perovskite into the infinite-layer phase (Han et al., 27 Nov 2025). The paper states that heavy rare-earth perovskite nickelates become thermodynamically easier to stabilize at high oxygen pressure, in the range $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_{y})_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2,\qquad \mathrm{RE}'=\mathrm{Pr,Nd,Sm,Gd,Dy},$$1–$$(\mathrm{Nd}_{1-y}\mathrm{RE}'_{y})_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2,\qquad \mathrm{RE}'=\mathrm{Pr,Nd,Sm,Gd,Dy},$$2 MPa, whereas vacuum deposition faces formation-free-energy limitations for later-lanthanide precursors.

The structural characterization reported in the two studies is consistent with successful infinite-layer formation. In the MBE-grown films, XRD shows high crystallographic quality and a $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_{y})_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2,\qquad \mathrm{RE}'=\mathrm{Pr,Nd,Sm,Gd,Dy},$$3-axis lattice constant of about $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_{y})_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2,\qquad \mathrm{RE}'=\mathrm{Pr,Nd,Sm,Gd,Dy},$$4 Å with small doping dependence; the $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_{y})_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2,\qquad \mathrm{RE}'=\mathrm{Pr,Nd,Sm,Gd,Dy},$$5-axis lattice constant is also noted to be smaller by about $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_{y})_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2,\qquad \mathrm{RE}'=\mathrm{Pr,Nd,Sm,Gd,Dy},$$6 Å than in Sr-doped $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_{y})_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2,\qquad \mathrm{RE}'=\mathrm{Pr,Nd,Sm,Gd,Dy},$$7 (Vu et al., 21 Aug 2025). In the chemically synthesized series, XRD on $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_{y})_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2,\qquad \mathrm{RE}'=\mathrm{Pr,Nd,Sm,Gd,Dy},$$8 shows an oriented perovskite structure, and after reduction the pattern changes to that of $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_{y})_{1-x}\mathrm{Eu}_x\mathrm{NiO}_2,\qquad \mathrm{RE}'=\mathrm{Pr,Nd,Sm,Gd,Dy},$$9 with the expected infinite-layer reflections; synchrotron X-ray absorption spectroscopy shows the Ni valence change from nominal $x=0.35$0 in the precursor to $x=0.35$1 in the reduced film (Han et al., 27 Nov 2025).

The chemical route also changes the thickness regime. The reduced infinite-layer films are described as about $x=0.35$2 nm thick, larger than the $x=0.35$3–$x=0.35$4 nm typical of prior vacuum-grown films. Cross-sectional HAADF-STEM indicates that the perovskite precursor is coherently grown on the substrate, whereas the reduced infinite-layer film loses interfacial coherency and develops a “dead layer” near the interface (Han et al., 27 Nov 2025). That interfacial degradation is explicitly presented as a caveat for transport interpretation in ultrathin films.

A further internal stoichiometry check comes from the precursor phase. The $x=0.35$5 films show sharp metal-insulator transitions, and $x=0.35$6 increases linearly with $x=0.35$7, which the paper uses as evidence for reliable Eu stoichiometry control (Han et al., 27 Nov 2025).

3. Superconducting composition range and gap phenomenology

In the chemically synthesized NENO series, superconductivity is observed over a broad Eu-substitution range $x=0.35$8–$x=0.35$9, with the highest values around $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_y)_{0.65}\mathrm{Eu}_{0.35}\mathrm{NiO}_2$$0–$$(\mathrm{Nd}_{1-y}\mathrm{RE}'_y)_{0.65}\mathrm{Eu}_{0.35}\mathrm{NiO}_2$$1. The reported peak values are

• $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_y)_{0.65}\mathrm{Eu}_{0.35}\mathrm{NiO}_2$$2 K,
• $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_y)_{0.65}\mathrm{Eu}_{0.35}\mathrm{NiO}_2$$3 K, which define a superconducting dome in Eu content (Han et al., 27 Nov 2025).

The transport-based and optical study focuses on the superconducting range $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_y)_{0.65}\mathrm{Eu}_{0.35}\mathrm{NiO}_2$$4, $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_y)_{0.65}\mathrm{Eu}_{0.35}\mathrm{NiO}_2$$5, and $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_y)_{0.65}\mathrm{Eu}_{0.35}\mathrm{NiO}_2$$6, with infrared spectroscopy on $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_y)_{0.65}\mathrm{Eu}_{0.35}\mathrm{NiO}_2$$7. For the $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_y)_{0.65}\mathrm{Eu}_{0.35}\mathrm{NiO}_2$$8 optical sample, the quoted transition temperatures are $$(\mathrm{Nd}_{1-y}\mathrm{RE}'_y)_{0.65}\mathrm{Eu}_{0.35}\mathrm{NiO}_2$$9 K and $4f$0 K. That paper defines $4f$1 through the criterion $4f$2, corresponding to $4f$3 in its field-dependent plots (Vu et al., 21 Aug 2025).

The definitions used in the phase-diagram work are explicit:

• $4f$4: where resistivity first deviates from normal-state behavior;
• $4f$5: where resistivity falls to 50% of the normal-state value;
• $4f$6: where resistivity drops below the experimental detection limit (Han et al., 27 Nov 2025).

The most direct gap measurement comes from far-infrared reflectivity on $4f$7. The normalized reflectivity develops a dip near $4f$8 and a sharp low-frequency upturn below the superconducting transition; the feature disappears above about 15 K and is flattened by 20 K. The robust extracted gap is

$4f$9

which yields

$\mathrm{NiO}_2$0

The paper identifies this ratio as substantially above the weak-coupling BCS value $\mathrm{NiO}_2$1 and roughly twice the gap scale reported for Sr-doped $\mathrm{NiO}_2$2, where most prior optical and related data suggest $\mathrm{NiO}_2$3–$\mathrm{NiO}_2$4 (Vu et al., 21 Aug 2025).

Modeling of the optical response is not unique. A dirty-limit Mattis-Bardeen $\mathrm{NiO}_2$5-wave model reproduces the spectra with the same gap but gives a fitted normal-state conductivity of about $\mathrm{NiO}_2$6, more than an order of magnitude below the $\mathrm{NiO}_2$7 inferred from electrical transport. A dirty nodal $\mathrm{NiO}_2$8-wave superconductor plus a residual Drude peak from uncondensed quasiparticles gives a better fit with the same gap and a larger conductivity, $\mathrm{NiO}_2$9; with spatial inhomogeneity and coexisting normal and superconducting regions, the spectra can be reconciled with $\mathrm{Eu}^{3+}:\mathrm{Eu}^{2+}\approx 1:1,$0 (Vu et al., 21 Aug 2025). The paper therefore treats the enlarged gap scale as robust but stops short of claiming definitive pairing symmetry.

4. Magnetic-field-enhanced and field-reentrant superconductivity

A central feature of NENO is its nonmonotonic magnetic-field response. In the transport study, magnetoresistance was measured up to 41 T for both $\mathrm{Eu}^{3+}:\mathrm{Eu}^{2+}\approx 1:1,$1 and $\mathrm{Eu}^{3+}:\mathrm{Eu}^{2+}\approx 1:1,$2, and up to 60 T in pulsed fields for the $\mathrm{Eu}^{3+}:\mathrm{Eu}^{2+}\approx 1:1,$3 sample. Instead of monotonic suppression, $\mathrm{Eu}^{3+}:\mathrm{Eu}^{2+}\approx 1:1,$4 first increases at low field and then decreases again over an extended field range centered near 20 T. For $\mathrm{Eu}^{3+}:\mathrm{Eu}^{2+}\approx 1:1,$5, the low-temperature $\mathrm{Eu}^{3+}:\mathrm{Eu}^{2+}\approx 1:1,$6 curve shows a maximum at low field and a minimum near $\mathrm{Eu}^{3+}:\mathrm{Eu}^{2+}\approx 1:1,$7 T, where the resistance returns to zero; the extracted $\mathrm{Eu}^{3+}:\mathrm{Eu}^{2+}\approx 1:1,$8 therefore contains inflection points and field-enhanced superconductivity (Vu et al., 21 Aug 2025).

The later phase-diagram study sharpens this phenomenon into magnetic-field reentrant superconductivity. In that paper, reentrant superconductivity is defined operationally as a state in which superconductivity is destroyed at low field and then reappears at higher field over a finite field window, often recovering zero resistance before final quenching at still higher field. Its transport signatures are nonmonotonic $\mathrm{Eu}^{3+}:\mathrm{Eu}^{2+}\approx 1:1,$9 at fixed low temperature and crossing behavior in $\mathrm{Eu}^{2+}$0 curves taken at different fields. For the underdoped and overdoped NENO compositions, at $\mathrm{Eu}^{2+}$1–$\mathrm{Eu}^{2+}$2 K superconductivity is first quenched at about $\mathrm{Eu}^{2+}$3–$\mathrm{Eu}^{2+}$4 T and then reappears beyond roughly $\mathrm{Eu}^{2+}$5–$\mathrm{Eu}^{2+}$6 T, with zero resistance recovered (Han et al., 27 Nov 2025).

Composition	Regime	Reported field response
$\mathrm{Eu}^{2+}$7	Near optimal	No reentrance up to 35 T
$\mathrm{Eu}^{2+}$8	Underdoped edge	Quenched at $\mathrm{Eu}^{2+}$9–2 T, reenters above $4f$00–8 T at 2 K
$4f$01	Overdoped edge	Quenched at $4f$02–2 T, reenters above $4f$03–8 T at 3 K
$4f$04	Gd-enhanced reentry	$4f$05–10 T at 1.6 K; $4f$06–13 T at 2 K; $4f$07–15 T at 3 K

The field orientation is decisive. In the phase-diagram study, the high-field reentrant region appears preferentially for $4f$08-axis and is strongly suppressed as the field is rotated toward the $4f$09 plane. Angular magnetotransport on $4f$10 shows deep-blue zero-resistance regions at high field near $4f$11 ($4f$12), shrinking rapidly from 2 K to 5 K and absent by 10 K (Han et al., 27 Nov 2025). In the transport study, $4f$13 produces broadened transitions interpreted as a vortex-liquid regime, whereas $4f$14 gives sharper transitions with greater paramagnetic character; $4f$15 is much larger than $4f$16, yet both orientations exceed the nominal weak-coupling Pauli limit (Vu et al., 21 Aug 2025).

For a singlet superconductor, that paper writes the paramagnetic limit as

$4f$17

with the weak-coupling relation

$4f$18

so that for $4f$19,

$4f$20

NENO is reported to violate this weak-coupling bound strongly, and even after subtracting exchange-field enhancement the inferred Pauli-limit violation ratio remains $4f$21 (Vu et al., 21 Aug 2025).

5. Rare-earth substitution, $4f$22 moments, and exchange pathways

The comparative substitution series shows that NENO cannot be reduced to a simple ionic-size or carrier-density problem. At fixed Eu content $4f$23, replacing 10% of Nd by Pr, Sm, or Dy yields

$4f$24

all of which remain conventionally superconducting with no reentrance, with $4f$25 about $4f$26, $4f$27, and $4f$28 K, respectively. By contrast,

$4f$29

does show reentrant superconductivity, and increasing Gd appears to reinforce the effect while lowering $4f$30 (Han et al., 27 Nov 2025).

The paper interprets this comparison as evidence that rare-earth $4f$31 physics, not merely ionic size, controls the reentrant behavior. Its ion-specific argument distinguishes $4f$32 from $4f$33: both are half-filled $4f$34 ions with large moments, but $4f$35 has shallower $4f$36 levels that are argued to be more likely to hybridize or exchange-couple with the $4f$37-derived conduction states, whereas $4f$38 has deeper $4f$39 levels and mainly contributes a stronger localized on-site moment without analogous $4f$40-band interplay (Han et al., 27 Nov 2025). This is used to explain why Eu near optimal content supports stronger conventional high-$4f$41 superconductivity, while added Gd reinforces reentrance.

A complementary microscopic argument comes from DFT. The Eu $4f$42 contribution is neglected because its local moment is only about $4f$43, much smaller than the Eu $4f$44 moment of about $4f$45. The calculations find antiferromagnetic Eu exchange with Ni $4f$46 and Ni $4f$47, and ferromagnetic coupling to Ni $4f$48. The corresponding exchange fields are reported as $4f$49 on Ni $4f$50, $4f$51 on Ni $4f$52, and $4f$53 on Ni $4f$54, while the exchange fields from Nd and Sr substitution are negligible, $4f$55 for Nd and $4f$56 for Sr (Vu et al., 21 Aug 2025). The paper therefore argues that Eu substitution matters qualitatively, not just quantitatively, and infers that the carriers in Ni $4f$57 are the ones most directly responsible for superconductivity in NENO.

6. Mechanistic interpretations, phase boundaries, and unresolved issues

The main exchange-field interpretation is Jaccarino-Peter-type compensation. One paper writes the exchange Hamiltonian as

$4f$58

with a total field acting on superconducting carriers

$4f$59

and, in the paramagnetic case used in its modeling,

$4f$60

where $4f$61 is the saturated exchange field and $4f$62 is the Brillouin function for the $4f$63 moments (Vu et al., 21 Aug 2025). Fits to $4f$64 give

$4f$65

a scale that matches both the magnetoresistance minimum near 20 T and the DFT estimate of $4f$66 on Ni $4f$67. In that paper, NENO is placed in a magnetic-field-enhanced regime with $4f$68, rather than in a fully overcompensated regime (Vu et al., 21 Aug 2025).

The later phase-diagram work uses a related but broader framework. It presents the high-$4f$69 dome and the field-reentrant superconducting state as rival orders near quantum phase boundaries and states that reentrance fringes the dome on both the underdoped and overdoped sides rather than appearing at optimal Eu content (Han et al., 27 Nov 2025). On the underdoped side, the possible competing states mentioned are charge order, spin order, or oxygen order; on the overdoped side, the paper refers to a hidden quantum critical point associated with a change from non-Fermi-liquid to Fermi-liquid transport, by analogy with Sr-doped $4f$70. This suggests a picture in which competing states weaken conventional superconductivity while magnetic fluctuations are enhanced.

Neither study presents the mechanism as uniquely settled. The Gd-enhanced phase-diagram work explicitly states that Jaccarino-Peter-like compensation does not exclude alternative mechanisms, especially in view of the strong anisotropy and possible oxygen-vacancy effects introduced by topotactic reduction; it also suggests that exchange-induced competition between singlet and triplet pairing channels might be relevant (Han et al., 27 Nov 2025). The transport-and-optics study reports low-temperature upturns in $4f$71 above both of its fitting forms and notes that similar upturns in NSNO and LSNO could arise from multiband superconductivity or another unconventional electronic state; it also remarks that neglected higher-order field terms in the Ginzburg-Landau expansion may contribute (Vu et al., 21 Aug 2025).

Several caveats recur across the literature. These include thin-film sample dependence, interfacial dead layers after reduction, incomplete Eu valence control, possible oxygen-vacancy effects, and the absence in the supplied description of full structural refinement or thermodynamic probes (Han et al., 27 Nov 2025). Accordingly, the secure empirical conclusions are narrower than the full interpretive program: NENO is a superconducting infinite-layer nickelate family in which Eu substitution enlarges the superconducting gap scale relative to Sr-doped $4f$72, drives strong Pauli-limit violation, and creates a composition- and field-orientation-dependent landscape of magnetic-field-enhanced or field-reentrant superconductivity (Vu et al., 21 Aug 2025, Han et al., 27 Nov 2025).