Tunable superconductivity and spin density wave in La3Ni2O7/LaAlO3 thin films

Abstract: Recently, La3Ni2O7 thin film on the LaAlO3 substrate is shown to be superconducting, while the bulk La3Ni2O7 with the same in-plane lattice constant under pressure does not superconduct. This difference suggests the interlayer distance $d_{\rm Ni-Ni}$ is crucial to control superconductivity, and its variation under pressure may tune the ground state sensitively. We investigate systematically the La3Ni2O7/LaAlO3 thin films in a reasonable range of $d_{\rm Ni-Ni}$, by a combination of the first-principle calculations and the singular-mode functional renormalization group. For smaller (larger) $d_{\rm Ni-Ni}$, the ground state is a C-type (G-type) spin density wave with spins coupled ferromagnetically (antiferromagnetically) across the two layers. Between the two phases, $s_\pm$-wave superconductivity emerges with dominant pairings between nickel $3d_{3z<sup>2-r<sup>2}$ orbitals. The results explain the experimental superconductivity in the thin film under ambient pressure, and predict that the applied pressure will decrease the superconducting transition temperature, until the system enters the C-type spin density wave. Experimental verification would provide profound insights into the nature of electron correlations in this system, since the C-type spin density wave is achieved most naturally in the itinerant picture, while it would be hard in the local moment picture where spins are always coupled antiferromagnetically across the layers.

• The paper demonstrates that modifying the Ni–Ni distance in La3Ni2O7 films triggers transitions from C-type SDW to s₊₋ superconductivity to G-type SDW order.
• DFT and SM-FRG techniques reveal that orbital-selective effects and Fermi surface parity critically dictate the emergence of superconductivity and magnetism.
• The study offers practical insights into tuning electronic ground states via uniaxial stress, aligning theoretical predictions with experimental observations.

Tunable Superconductivity and Spin Density Wave Order in La₃Ni₂O₇/LaAlO₃ Thin Films

Introduction

This work presents a comprehensive theoretical study of La₃Ni₂O₇ (327) thin films grown on LaAlO₃ (LAO) substrates. The focus is on how superconductivity and spin density wave (SDW) orders can be controlled through the manipulation of the interlayer nickel-nickel distance ($d_{\mathrm{Ni-Ni}}$). Motivated by experimental observations of superconductivity in 327/LAO films under ambient pressure, as well as the contrasting absence of superconductivity in bulk 327 under similar in-plane lattice constraints, the authors systematically investigate the evolution of electronic structure and ordering instabilities as $d_{\mathrm{Ni-Ni}}$ is varied. The approach combines state-of-the-art density functional theory (DFT), maximally localized Wannier tight-binding construction, and the singular-mode functional renormalization group (SM-FRG) to analyze the emergence and competition of superconductivity and SDW states.

Electronic Structure and Model Construction

DFT calculations were performed for La₃Ni₂O₇ thin films under fixed in-plane compressive strain ($a=3.787$ Å, corresponding to 1.2% strain) and variable $d_{\mathrm{Ni-Ni}}$. Wannier90 was used to construct bilayer tight-binding models, including the Ni $3d_{x^2-y^2}$ ($x$) and $3d_{3z^2-r^2}$ ($z$) orbitals. This model accurately captures the bilayer splitting and orbital composition of Fermi surfaces.

Key findings are:

• Increasing $d_{\mathrm{Ni-Ni}}$ leads to a decrease in the $z$-orbital bandwidth and a significant increase in the $d_{\mathrm{Ni-Ni}}$0-orbital density of states at the Fermi energy.
• The Fermi surface consists of multiple pockets, with well-defined mirror parities due to the approximate electronic mirror symmetry retained even for the asymmetric LAO substrate.
• Compared to the bulk, film-specific features such as an additional pocket ($d_{\mathrm{Ni-Ni}}$1) arise, strengthening the case for orbital-selective effects.

FRG Analysis of Competing Instabilities

The correlated problem is tackled via SM-FRG, incorporating multi-orbital Coulomb interactions with realistic values ($d_{\mathrm{Ni-Ni}}$2 eV, $d_{\mathrm{Ni-Ni}}$3 eV, Kanamori relations). The FRG evolves the vertex function in the SDW, CDW, and superconducting (SC) channels as the infrared cutoff is decreased.

Crucial results include:

• C-type SDW ground state emerges for small $d_{\mathrm{Ni-Ni}}$4. This phase features ferromagnetic spin alignment across layers (interlayer FM), a configuration that is not favored by local-moment (superexchange-based) models, but arises naturally from itinerant (Fermi surface nesting) physics due to parity selection rules.
• $d_{\mathrm{Ni-Ni}}$5-wave superconductivity with dominant $d_{\mathrm{Ni-Ni}}$6-orbital pairing materializes at intermediate $d_{\mathrm{Ni-Ni}}$7. The gap structure changes sign between sets of Fermi pockets with different parities; interlayer pairing between $d_{\mathrm{Ni-Ni}}$8 orbitals is the leading component, with a significant intralayer contribution. SC is triggered by G-type (AFM) SDW fluctuations connecting Fermi pockets of opposite mirror parity.
• G-type SDW order dominates at large $d_{\mathrm{Ni-Ni}}$9, where the SDW features antiferromagnetic coupling both in-plane and across layers. The transition between these phases can be controlled by uniaxial (out-of-plane) stress, offering a practical means to tune ground state properties.

Parity, Magnetism, and the FM-AFM Selection Rule

A central conceptual advancement is the clarification of how Fermi surface parity underpins the interlayer magnetic order, encapsulated in the FM-AFM selection rule:

• Interlayer FM (C-type SDW) is favored when SDW fluctuations connect Fermi pockets of the same parity.
• Interlayer AFM (G-type SDW and SC-promoting fluctuations) is stabilized when nesting involves pockets of opposite parity.

This selection rule is formalized in the parity decomposition of the effective order parameters and generalized for SC, SDW, and CDW channels. The unique structure of the $a=3.787$0 superconducting gap in this bilayer system, distinct from both cuprate and iron-based analogs, is a direct consequence of the parity-induced selection.

Phase Diagram and Experimental Relevance

The computed phase diagram reveals a tunable sequence: as $a=3.787$1 increases, the system transitions from C-type SDW to $a=3.787$2 SC to G-type SDW. The superconducting $a=3.787$3 is non-monotonic with $a=3.787$4, peaking where magnetic fluctuations cross from FM to AFM character. These trends match recent experiments showing a suppression of SC under applied pressure, as increased pressure decreases $a=3.787$5, driving the system into the C-type SDW regime.

The dominance of the $a=3.787$6 orbital is further substantiated by its increasing density of states and leading role in both SC and magnetism, reaffirming the importance of orbital-selective physics in RP nickelate heterostructures.

Theoretical and Practical Implications

The findings consolidate the paradigm that SC in RP nickelate films is fundamentally itinerant and parity-selective, with the proximity to magnetic order setting the pairing glue, analogous but not identical to iron-based and cuprate SCs. The FM-AFM selection rule provides a powerful theoretical tool for predicting and engineering phase diagrams in multi-layer nickelates and perhaps other correlated layered oxides with broken local symmetry.

Experimental implications are direct:

• Pressure-induced tuning (out-of-plane) should drive transitions through the sequence of C-type SDW, SC, and G-type SDW.
• Observation of interlayer FM SDW would provide unambiguous evidence for itinerant magnetism, challenging strong-coupling, local-moment-based theories.
• The structure of spin susceptibilities and impurity-induced quasiparticle interference should be sensitive to the parity structure of the gap, motivating spectroscopic and neutron studies.

Conclusion

This study establishes a detailed, first-principles-grounded phase diagram for 327/LAO thin films, revealing a tunable interplay of superconductivity and SDW orders dictated by Fermi surface parity and interlayer coupling. The theoretical framework leveraging the SM-FRG and emphasizing the FM-AFM selection rule advances the understanding of superconductivity and magnetism in RP nickelates and provides a blueprint for engineering new quantum phases in oxide heterostructures (2604.05590). Future work should pursue the experimental confirmation of the predicted interlayer FM phase and probe the detailed momentum- and parity-resolved structure of the SC state.