Anomalous Behavior of the Ni$^{1+}$ moment and interstitial band in bi-infinite-layered La$_3$Ni$_2$O$_5$F

Abstract: The discovery of superconductivity in hole-doped Ni$^{{1+}$ systems with "infinite layer" NiO$<em>2$ square-lattices analogous to the Cu$^{{2+}$ CaCuO$_2$ cuprate has renewed conflicting pictures of the Cu$^{{2+}$-$Ni$^{1+}}}similarityordistinction.RecentsynthesisofformalNi}</sup> similarity or distinction. Recent synthesis of formal Ni^{1+}</sup>La</sup> La_3NiNi{2}OO{5}FwithtwoinfiniteNiOF with two infinite NiO{2}layerspercellprovidesanovelmemberofthisclass.Firstprinciplesdensityfunctionaltheorystudiesrevealaninterstitialdensityderivedsingleband layers per cell provides a novel member of this class. First principles density functional theory studies reveal an interstitial density derived single band E^*</sup>inthreelayersunrelatedtoanyatom,whichprovidesself−dopingtoaNi</sup> in three layers unrelated to any atom, which provides self-doping to a Ni^{1.09+}</sup>ion.TheblockingLa(O/F)LaprovidesisolationoftheNiO</sup> ion.The blocking La(O/F)La provides isolation of the NiO_2bilayerandaninterstitial bilayer and an interstitial E^*$ density to strictly two-dimensional electronic and magnetic systems. Calculations of magnetic tendencies reveals behavior unlike previous nickelates, including vanishing susceptibility up to a large magnetic field. Two dimensional fluctuations and self-doping away from half-filling can account for the lack of observation of a magnetic transition.

• The paper demonstrates that La3Ni2O5F exhibits a self-doping interstitial E* band alongside a highly flexible Ni¹⁺ moment with minimal energy cost up to ~0.7 μB.
• It employs DFT, GGA+U, and fixed spin moment analyses to distinctly separate atomic dpσ bands from interstitial electronic states, emphasizing strict two-dimensionality.
• The findings suggest that the unique electronic structure and suppressed long-range magnetism could pave the way for exploring emergent quantum phases and unconventional superconductivity.

Anomalous Magnetic and Interstitial Electronic Behavior in Bi-Infinite-Layered La$_3$Ni$_2$O$_5$F

Introduction

This paper provides an in-depth first-principles investigation of the electronic and magnetic properties of bi-infinite-layered La$_3$Ni$_2$O$_5$F, a recently synthesized member of the Ni$^{1+}$ infinite-layer family that is structurally related to the high-$T_c$ cuprates but exhibits notable electronic distinctiveness. Through a combination of density functional theory (DFT), GGA+U, and fixed spin moment analyses, the work identifies and characterizes a unique interstitial band ($E^*$) that induces self-doping, as well as an anomalous, flexible behavior of the local Ni$^{1+}$ magnetic moment. This essay synthesizes the key findings and implications, with a focus on the separation between atomic and interstitial electronic degrees of freedom and the impact of strong two-dimensionality on magnetism.

Structure and Band Topology

La$_2$0Ni$_2$1O$_2$2F exhibits a body-centered tetragonal $_2$3 crystal structure, with NiO$_2$4 bilayers separated by a highly effective [La$_2$5] [O/F] [La$_2$6] blocking layer. Replacement of half the O with F results in bi-infinite stacking, providing near-complete electronic isolation between bilayers and enforcing strict two-dimensionality in the electronic structure.

Figure 1: (a) Crystal structure of La$_2$7Ni$_2$8O$_2$9F, highlighting the NiO$_5$0 bilayers and blocking layers. (b) Schematic orbital-projected DOS. (c,d) Fatband analysis showing Ni $_5$1 and interstitial $_5$2 band contributions. (e,f) Fermi surfaces.

The non-magnetic (NM) band structure near $_5$3 features both covalent $_5$4 bands (arising from Ni $_5$5 and O $_5$6) and a single, broad $_5$7 band, derived from interstitial charge density rather than atomic orbitals. This $_5$8 band is highly two-dimensional, with strictly vanishing $_5$9 dispersion over relevant energy scales. The electronic structure is thus composed of two nearly half-filled $_3$0 bands and the $_3$1 band, resulting in complex Fermiology and removal of the Fermi level from the $_3$2 van Hove singularity by self-doping.

Real-Space Characterization of the $_3$3 Band

The $_3$4 band presents an interstitial character, not confined to any particular atomic site but spatially distributed across the inter-bilayer region, especially at the vacant apical sites. Isocontour plots of the $_3$5 wavefunction reveal broad maxima at apical positions with "windmill"-like arms extending towards La ions, forming a quasi-molecular orbital distinct from s-like spherical electride states in other infinite-layer nickelates.

Figure 2: Isocontour plots of the $_3$6 band wavefunction at representative $_3$7-points, showing interstitial density without atomic participation.

This density topology directly modulates electronic screening and has implications for coupling to both transition metal and rare-earth $_3$8 states, though mixing near $_3$9 is minimized by large energy separations.

Magnetic Response and Fixed Spin Moment Behavior

Unlike other nickelates or cuprates, La$_2$0Ni$_2$1O$_2$2F exhibits anomalous rigid moment behavior. Fixed spin moment calculations within GGA demonstrate that modest polarization of Ni$_2$3 states incurs almost no energy cost up to $_2$4 per formula unit. Only beyond this threshold does the magnetic energy increase steeply, indicating a highly flexible Ni moment and negligible magnetic susceptibility at zero field. The $_2$5 band remains impervious to exchange splitting, separating the itinerant interstitial carriers from the atomic magnetism.

Figure 3: Total energy variation as a function of constrained spin moment, showing a flat energy landscape up to $_2$6, and exchange splitting in the FM band structure inset.

Self-consistent calculations reveal that AFM alignment is energetically favored over FM or C-type ordering, with G-AFM lower by up to 159 meV/f.u. at the GGA level. The AFM solution hosts large local Ni moments ($_2$7), and displays a large exchange splitting in $_2$8 bands, with the $_2$9 band traversing the Mott-like gap and maintaining self-doping.

Correlation Effects and the $_5$0–$_5$1 Semimetal

Inclusion of GGA+U correlation enlarges the magnetic splitting and further localizes the Ni moments (approaching $_5$2). However, a genuine Mott gap does not open until $_5$3 eV. For intermediate $_5$4, the system transitions to a semimetallic regime in which the $_5$5 band defines the conduction edge, rather than the split $_5$6. The exchange parameters extracted from energy differences suggest robust in-plane coupling ($_5$7 118 meV), but with severely reduced inter-bilayer interactions ($_5$8).

Figure 4: GGA+U ($_5$9=3 eV) band structure for G-AFM, showing $^{1+}$0–$^{1+}$1 band overlap and extreme flatness of $^{1+}$2 along $^{1+}$3–$^{1+}$4.

Raising $^{1+}$5 eventually isolates a zero-gap or small-gap semiconducting state, but the fundamental gap is between the $^{1+}$6 valence and $^{1+}$7 conduction band, not a canonical Mott insulator. This contrasts with both cuprate and other nickelate analogs, reinforcing the unique self-doped, interstitially mediated electronic regime.

Dimensionality Effects and Theoretical Implications

Perfect two-dimensionality is enforced both structurally (due to the blocking layer) and electronically (vanishing $^{1+}$8 dispersion). This places the system squarely in the regime where long-range magnetic order is suppressed by thermal and quantum fluctuations, as dictated by the Mermin-Wagner theorem. Magnetic ordering is observed neither experimentally nor in the calculated susceptibility, with the observed moments likely manifesting only as short-range AFM correlations.

The interplay between two-dimensionality, interstitial self-doping, and suppressed magnetic ordering—in conjunction with the proximity of the formal Ni$^{1+}$9 valence to the superconducting regime in other nickelates—creates a platform for emergent physics absent in cuprates or previously studied nickelates. Notably, the $T_c$0 band’s linear dispersion and interlayer connected density evoke analogies to topological bands in skutterudites and 3D Dirac systems, although arising here within a layered oxide context.

Implications for Nickelate Superconductivity and Open Questions

The findings support several robust or contrasting statements:

• The Ni$T_c$1 moment in La$T_c$2Ni$T_c$3O$T_c$4F is highly flexible, exhibiting vanishing energy cost for moderate spin polarization in a metal with no long-range order, defying expectations based on standard Stoner or Heisenberg models.
• A unique, partially occupied interstitial $T_c$5 band enforces significant self-doping ($T_c$60.09 electrons per Ni), producing a Ni$T_c$7 state without external chemical doping.
• Extreme two-dimensionality fundamentally inhibits magnetic order via fluctuation effects, making La$T_c$8Ni$T_c$9O$E^*$0F a paradigmatic platform to study strictly 2D quantum magnets with itinerant self-doping.

Practically, these results imply that La$E^*$1Ni$E^*$2O$E^*$3F may serve as a new test bed for fluctuation-driven phenomena, competing orders, and possibly unconventional superconductivity. Theoretically, these findings motivate extended models that explicitly include interstitial, non-atomic bands and their influence on both magnetism and pairing, moving beyond the traditional $E^*$4 Hubbard or $E^*$5-$E^*$6 models common to oxides.

Future research directions include:

• Exploration of superconducting instabilities in the presence of the $E^*$7 band via many-body extensions of DFT, with attention to twinned orbital and real-space (interstitial) channels.
• Inelastic neutron and ARPES probes to resolve the nature and extent of magnetic and charge correlations.
• Synthetic analogs with controlled dimensionality or blocking layer composition to manipulate $E^*$8 band occupation and Ni valence.

Conclusion

This work elucidates the electronic and magnetic anomalies in La$E^*$9Ni$^{1+}$0O$^{1+}$1F, identifying a highly unusual interplay of interstitial-derived self-doping, robust but fluctuation-suppressed local moments, and ideally two-dimensional magnetism. These phenomena distinguish La$^{1+}$2Ni$^{1+}$3O$^{1+}$4F not only from cuprates but also from its nickelate congeners, opening conceptual space for further exploration of emergent quantum phases in oxide heterostructures and for theoretical frameworks that accommodate non-atomic, interstitial degrees of freedom (2606.28735).