Unusual Behavior of the Ni1+ moment and interstitial band in bi-infinite-layered La3Ni2O5F

Technical Summary: Unusual Behavior of the Ni1+ Moment and Interstitial Band in Bi-Infinite-Layered La3Ni2O5F

Problem Statement
The discovery of superconductivity in hole-doped infinite-layer nickelates (RNiO2) has renewed interest in the comparison between Ni1+ and Cu2+ systems. However, the origin of superconductivity and the specific behavior of the Ni moment remain elusive, particularly regarding the role of interstitial electride-like bands ("E-bands") and the necessity of strong correlation corrections to describe magnetic moments. Recently, the bi-infinite-layered compound La3Ni2O5F was synthesized, featuring two NiO2 layers per unit cell separated by a blocking layer with mixed O/F anions. While its structure is established, its magnetic behavior remains unclear due to experimental difficulties (e.g., ferromagnetic inclusions) and the lack of observed antiferromagnetic (AFM) transitions. This study investigates the electronic and magnetic properties of La3Ni2O5F to understand the Ni1+ moment, the nature of the interstitial band, and the material's dimensionality.

Methodology
The authors employed first-principles calculations using all-electron full-potential codes (WIEN2k and FPLO).

1. Exchange-Correlation Functionals: Calculations were performed using the Generalized Gradient Approximation (GGA) as the baseline for non-magnetic (NM) and magnetic states.
2. Correlation Effects: To address electron-electron interactions, the GGA+U approach was applied to Ni 3d orbitals with effective Hubbard repulsion values ($U_{eff} = U - J_H$) ranging from 3 to 5 eV, a range established as appropriate for nickelates.
3. Magnetic Configurations: Three distinct spin-ordered states were analyzed: Ferromagnetic (FM), C-type AFM (checkerboard in-plane, aligned between planes), and G-type AFM (checkerboard in-plane, antialigned between planes).
4. Fixed Spin Moment (FSM): FSM calculations were utilized to map the energy landscape $\Delta E(M)$ as a function of the magnetic moment to probe the stability of magnetic ordering without relying on self-consistent convergence alone.

Key Contributions and Results

• Interstitial E-Band Characteristics:
  The study identifies a distinct interstitial electron band (E-band) that provides intrinsic electron self-doping. Unlike the E-band in single-layer RNiO2 (which has a minimum at the $\Gamma$ point), the E-band in La3Ni2O5F exhibits unique features:

  • Dispersion: It has a deep, sharp minimum at the M point (zone corner) rather than $\Gamma$.
  • Linearity: The band is remarkably linear from its bottom at -0.5 eV (at M) upward for 1.5 eV, implying a divergent longitudinal effective mass and an off-diagonal effective mass tensor.
  • Symmetry and Density: The wavefunction is nodeless within the unit cell ("s-like" symmetry) but highly anisotropic, forming "fat arms" along the [110] directions toward La ions. It is impervious to magnetic splitting.
  • Self-Doping: This band dips below the Fermi level ($E_F$), donating approximately 0.18 electrons per formula unit to the NiO2 layers, resulting in a formal Ni valence of Ni$^{1.18+}$. This places the system near the peak of the superconducting dome in nickelate phase diagrams.

• Unusual Magnetic Behavior of Ni1+:

  • Spontaneous Moment without U: In contrast to LaNiO2 and CaCuO2, where magnetic order typically requires the inclusion of Hubbard $U$, conventional GGA calculations for La3Ni2O5F already predict a substantial magnetic moment. The system exhibits a large exchange splitting (~0.7 eV in FM, ~2 eV in G-AFM) and a Mott-like splitting of the $d_{x^2-y^2}$ orbitals even without correlation corrections.
  • Metastability and Energy Landscape: Fixed spin moment calculations reveal a peculiar energy landscape where the energy remains nearly constant up to a moment of $M \approx 0.75 \mu_B$. The energy only rises sharply beyond $M = 0.8 \mu_B$. This suggests a flexible Ni moment with negligible energy cost to induce magnetization, rendering a standard Ginzburg-Landau expansion in the magnetic order parameter impossible.
  • AFM Preference: The G-AFM state is the ground state, lower in energy than NM, FM, and C-AFM states by approximately 155–159 meV/f.u. in GGA. The calculated Ni moment in the AFM state is $0.68 \mu_B$.

• Dimensionality and Interlayer Coupling:
  The structure features a PbO-type blocking layer with vacant apical sites, leading to extreme two-dimensionality.

  • Dispersion: The electronic bands show virtually vanishing $k_z$ dispersion.
  • Exchange Parameters: Estimated exchange parameters indicate a strong in-plane coupling ($J_{\parallel} \approx 118$ meV) but extremely weak interlayer coupling ($J_{\perp} \approx 4.5$ meV, roughly 4% of $J_{\parallel}$).
  • Mermin-Wagner Implications: The negligible interlayer coupling places La3Ni2O5F in the regime of strictly 2D magnetic systems. The authors suggest that the lack of observed magnetic phase transitions in experimental data may be attributed to the Mermin-Wagner theorem, where 2D fluctuations prevent long-range magnetic order at finite temperatures.

• Effect of Hubbard U:
  Applying $U_{eff}$ (3–5 eV) primarily increases the Mott-like splitting of the $d_{x^2-y^2}$ bands, increasing the Ni moment toward $1 \mu_B$. It also slightly reduces the self-doping level by shifting the majority $d_{p\sigma}$ band down relative to the E-band. At $U_{eff} \approx 3$ eV, the system approaches a semimetal-to-insulator transition where the gap opens between the $d_{p\sigma}$ and E-bands rather than a standard Mott gap.

Significance
The paper establishes that La3Ni2O5F presents a unique case in nickelate physics where:

1. Ni1+ behaves differently from Cu2+: The system exhibits strong magnetic tendencies and large exchange splitting within standard DFT, unlike cuprates where correlations are essential to generate moments.
2. The E-band is distinct: The interstitial band in this bi-layer system is linear, centered at the M point, and highly anisotropic, differing significantly from the $\Gamma$-centered bands in single-layer analogs.
3. Extreme 2D Physics: The material serves as a model for studying the interplay between self-doping by an interstitial band and the suppression of magnetic order due to extreme two-dimensionality.
4. Valence and Superconductivity: The calculated formal valence of Ni$^{1.18+}$ aligns with the optimal doping range for superconductivity in nickelates, suggesting that understanding the interplay between the E-band and the Ni $d$-orbitals is crucial for elucidating the mechanism of superconductivity in this family of materials.

The authors conclude that while the theoretical framework provides a consistent picture of the electronic structure, the extreme two-dimensionality and the role of fluctuations require further experimental and theoretical investigation to fully explain the absence of magnetic ordering and the potential for superconductivity.