PrNiOₓ Thin Films: Structure & Superconductivity

• PrNiOₓ thin films are epitaxial nickelate materials with tunable oxygen stoichiometry that stabilize an infinite-layer phase similar to high-Tc cuprates.
• They are synthesized using techniques like PLD and MBE on lattice-matched substrates, followed by precise topotactic reduction with CaH₂ to ensure phase purity.
• Their electronic properties feature dome-shaped superconductivity, mixed carrier transport, and distinct magnetic excitations characterized by advanced spectroscopic methods.

PrNiO$_x$ thin films represent a family of epitaxial nickelate materials with tunable oxygen stoichiometry and electronic properties, including superconductivity in both undoped and Sr-doped compositions. Central to their significance is the ability to stabilize the infinite-layer phase (PrNiO$_2$) via topotactic reduction, yielding plane-coherent, square-planar NiO$_2$ sheets analogous to high-$T_c$ cuprates. Experimental advances over the past decade have detailed their synthesis, structural transitions, carrier dynamics, and magnetic excitations, elucidating both self-doping and defect-mediated hole doping mechanisms.

1. Synthesis Protocols and Phase Evolution

Thin-film PrNiO$_x$ compounds are typically synthesized by depositing perovskite PrNiO$_3$ on lattice-matched substrates, followed by topotactic reduction using CaH$_2$. Pulsed-laser deposition (PLD) and molecular beam epitaxy (MBE) are employed for film growth on SrTiO$_3$ (STO) or NdGaO$_3$ (NGO) substrates, with critical control over oxygen partial pressure and laser fluence to ensure phase purity and coherent strain (Osada et al., 2020, Sahib et al., 2024, Pons et al., 12 Jan 2026). Reduction is performed in sealed quartz tubes at 240–320 °C for 2–84 h, effectively extracting apical oxygen atoms and transforming the structure into the infinite-layer phase:

$$\mathrm{PrNiO}_3 + \mathrm{CaH}_2 \longrightarrow \mathrm{PrNiO}_2 + \mathrm{CaO} + \mathrm{H_2O}\uparrow$$

Direct reduction with full CaH$_2$ coverage yields highly crystalline PrNiO$_2$ (c ≈ 3.31–3.34 Å), while indirect, contactless reduction produces intermediate oxygen-deficient phases (x ≈ 2.3–2.9). No post-reduction oxidizing steps are applied.

2. Structural Characterization and Oxygen Stoichiometry

X-ray diffraction (XRD) and reciprocal-space mapping demonstrate that the infinite-layer PrNiO$_2$ phase adopts space group P4/mmm and maintains full in-plane coherence with the substrate (a$_{\rm STO}$ = 3.905 Å), absent any secondary orientations or relaxation. The c-axis lattice constant increases with Sr doping, transitioning from c = 3.310 Å for x = 0 to c = 3.440 Å for x = 0.32 in Sr-doped films (Osada et al., 2020), and contracts by ∼15% upon full reduction in undoped (x = 2.00 ± 0.02) films (Sahib et al., 2024). STEM–HAADF imaging confirms defect-free infinite-layer stacking with no apical/interstitial oxygen, while EELS reveals Pr/Ni ≃ 1, precluding accidental cation substitution (Sahib et al., 2024). The absence of O K-edge pre-edge features corroborates complete removal of apical oxygens.

3. Electronic and Magnetic Properties

3.1 Superconductivity and Transport

Electrical transport measurements reveal a dome-shaped superconducting phase in Sr-doped Pr$_{1-x}$Sr$_x$NiO$_2$ films for $0.12 \leq x \leq 0.28$, peaking at $T_c^{90\%}=14$ K for $x=0.18$; the superconducting transition is bounded by weakly insulating behavior at lower and higher $x$ values (Osada et al., 2020). The superconductivity manifests as a sharp drop in resistivity, with minimal localization at optimal doping. Undoped PrNiO$_2$ thin films also exhibit zero resistance up to $T_c^{\text{onset}}=7$–11 K, demonstrating that self-doping via Pr 5$d$–Ni 3$d$ hybridization is sufficient to populate the conduction band without external chemical dopants (Sahib et al., 2024).

3.2 Hall Effect and Carrier Balance

Normal-state Hall coefficient measurements indicate mixed electron and hole carrier bands, with sign changes in $R_H(T,x)$ as a function of temperature and doping (Osada et al., 2020). Under optimal conditions, $R_H(T)$ approaches zero near $T_c$, aligning with the lowest normal-state resistivity. The two-band model captures this competition:

$$R_H = \frac{\mu_h^2\,p - \mu_e^2\,n}{e(\mu_h\,p + \mu_e\,n)^2}$$

where $n$, $p$ denote carrier densities and $\mu_e$, $\mu_h$ their respective mobilities. In undoped PrNiO$_2$, $R_H(T)$ remains negative, revealing differences in band occupation compared to Sr-doped systems (Sahib et al., 2024).

3.3 Magnetic Excitations

Resonant inelastic x-ray scattering (RIXS) spectra in undoped PrNiO$_2$ films detect sharp single-magnon excitations at $E_m\approx200$ meV at the Brillouin zone boundary, resonant at the Ni$^{1+}$ absorption peak (Sahib et al., 2024). The magnon dispersion and bandwidth match other infinite-layer nickelates, emphasizing robust superexchange and magnetic order in the square-planar NiO$_2$ sheets.

4. Electronic Structure and Hole Doping Mechanisms

Soft x-ray absorption spectroscopy (XAS) at the Ni $L_{3,2}$-edge reveals pronounced linear dichroism, indicating strong hole occupation of Ni 3$d_{x^2−y^2}$ orbitals. The charge sum rule analysis yields an average Ni$^{3d}$ hole count $h_{3d}$ decreasing from $\sim2.2$ (perovskite, x ≈ 3) to $\sim1.6$ in maximally reduced infinite-layer films, with superconductivity appearing around $h_{3d}\approx1.55$–1.60 (Pons et al., 12 Jan 2026). Remarkably, no samples attain the pure $d^9$ configuration. O K-edge spectra show collapse of the ligand-hole pre-peak but persistence of O 2$p$–Ni 3$d$/Pr 5$d$ hybridization in most reduced films. This suggests a complex ground state comprising both $d^9L$ (Ni$^{1+}$) and $d^8$ high-spin (Ni$^{2+}$) local environments, driven by both self-doping and oxygen non-stoichiometry. Oxygen vacancies provide two electrons per missing oxygen, converting Ni$^{3+}$ to Ni$^{2+}$, while rare-earth 5$d$–Ni 3$d$ hybridization self-dopes the NiO$_2$ planes.

c (Å)	n$_{3d}$	h$_{3d}$
3.80	7.78	2.22
3.31	8.45	1.55

Superconductivity appears for $h_{3d}$ between 1.55–1.60; pure $d^9$ ($h=1.0$) is not realized.

5. Influence of Rare-Earth Site Chemistry and Disorder

The radius of Pr$^{3+}$ (113 pm, CN = 9) exceeds that of Nd$^{3+}$ (111 pm), resulting in increased perovskite tolerance factor, reduced lattice mismatch with STO, and improved film crystallinity (Osada et al., 2020). This enables a broader superconducting dome ($\Delta x\approx0.16$ for Pr versus $\Delta x\approx0.075$ for Nd). Comparison across rare-earth elements shows analogous phase diagrams: dome-like $T_c(x)$, sign-reversing Hall effect, and transport minima in superconducting compositions. These features underscore the dominance of the NiO$_2$ planes in low-energy physics, relegating the rare-earth site to a role of chemical pressure and disorder.

6. Comparisons and Current Controversies

Direct imaging confirms that undoped PrNiO$_2$ thin films possess no unintended oxygen or Sr content, differentiating them from NdNiO$_2$ and LaNiO$_2$, which often suffer from interstitial oxygen or charge order (Sahib et al., 2024). The emergence of superconductivity at higher $3d$ hole occupation in PrNiO$_2$ than expected from Sr-doping studies calls into question models assuming strict stoichiometry. A plausible implication is that both oxygen-defect disorder and rare-earth self-doping are essential for stabilizing superconductivity in these nickelates (Pons et al., 12 Jan 2026).

7. Outlook and Benchmarks

Infinite-layer PrNiO$_x$ thin films, when precisely reduced and structurally optimized, display reproducible superconducting transitions, T-linear metallicity, dome-like $T_c$ behavior, and distinct mixed-carrier effects. Quantitative XAS and ligand-field benchmarks inform ongoing investigations into correlated electron phenomena, pairing mechanisms, and doping strategies in nickelate superconductors. Future studies are expected to address the electron configuration, defect landscape, and subtle interplay between rare-earth and oxygen contributions to the electronic ground state.