Magnetic Order in bilayer Ruddlesden-Popper Nickelates

Summary

Based on experimental evidence of orbital-selective electronic correlations, this work proposes a new magnetic description framework for bilayer nickelate La₃Ni₂O₇. In the bad-metal regime of the normal state, the system lies close to an orbital-selective Mott phase, with the electronic spectrum decomposing into coherent d_(x²-y²) quasiparticles and incoherent d_(z²) local moments. An effective spin model incorporating superexchange between local moments and RKKY interactions mediated by coherent electrons is constructed, where the RKKY contribution dominates third-neighbor coupling and introduces magnetic frustration. The model naturally stabilizes a noncoplanar antiferromagnetic ground state with a wavevector near (π/2, π/2) and antiferromagnetic interlayer stacking, consistent with neutron scattering experiments. The calculated spin-wave spectrum contains low-frequency acoustic and high-frequency optical branches, with the acoustic branch softening at the ordering wavevector and an overall bandwidth of about 80 meV, in agreement with resonant inelastic X-ray scattering data. These results reveal that orbital-selective correlations are the essential ingredient determining magnetism in bilayer nickelates and indicate that low-energy magnetic fluctuations and short-range exchange interactions may provide the pairing glue for unconventional superconductivity.

Materials

• La₃Ni₂O₇

Methods

• Slave-spin approach
• Luttinger–Tisza method
• Variational optimization
• Spin-wave theory
• Bilayer two-orbital Hubbard model

Keywords

• orbital selective correlations
• rkky interaction
• superexchange
• incommensurate antiferromagnetism
• spin wave spectrum
• high temperature superconductivity

Highlights

• The magnetic order is described in a conceptually new way via a combination of RKKY and superexchange interactions among effective local moments.
• The model yields an incommensurate antiferromagnetic ground state with interlayer antiferromagnetic stacking and wave vector near (π/2,π/2) without fine-tuning.
• The spin-wave spectrum reveals intense low-energy fluctuations and optical modes, suggesting these magnetic correlations may drive superconducting pairing.

Conclusions

• A theoretical framework based on orbital-selective electronic correlations is developed to understand the magnetic properties of La₃Ni₂O₇.
• The effective spin Hamiltonian, comprising RKKY and superexchange couplings, stabilizes an incommensurate antiferromagnetic order with wave vector near (π/2,π/2).
• The calculated spin-wave spectrum shows an acoustic branch softening at the ordering wave vector and an overall bandwidth of about 80 meV, consistent with RIXS and neutron scattering experiments.
• Orbital-selective correlations are essential for the magnetism in bilayer nickelates.

Main claims

• Orbital-selective correlations in the bad-metal regime give rise to a combination of RKKY and superexchange interactions that determine the magnetic properties of La₃Ni₂O₇.
  • Evidence: Abstract: 'Based on the accumulated experimental evidence for a bad metal state in proximity to an orbital-selective Mott phase, here we describe magnetic correlations … in terms of effective local moments experiencing a combination of RKKY and superexchange interactions.',Models section: 'the spectral weight of the d_(x²-y²) orbital resides more in the coherent part, while that of the d_(z²) orbital mainly populates the incoherent part' and 'Two distinct processes contribute to the exchange coupling … superexchange … and RKKY coupling.'
• The effective spin model stabilizes an incommensurate antiferromagnetic order with wavevector near (π/2,π/2), consistent with neutron scattering.
  • Evidence: Magnetic order section: 'the ground state is an antiferromagnet … magnetic order is stabilized at the wave vector Q. At U=3 eV, Q≈(0.24,0.24) … close to (π/2,π/2)',Ibid: 'consistent with the magnetic order observed experimentally' and references to neutron diffraction (Refs. 57–59).
• The calculated spin-wave spectrum has acoustic branch softening at Q and an overall bandwidth of ≈80 meV, matching RIXS and inelastic neutron scattering data.
  • Evidence: Magnetic order and excitations section: 'the calculated spin-wave spectrum … comprises a low-energy acoustic branch and a higher-energy optical branch; the acoustic branch softens at the ordering wave vector Q … overall bandwidth of the calculated spectrum is approximately 80 meV, in good agreement with the energy scale observed in recent RIXS experiments [73].'
• Orbital-selective correlations are an essential ingredient for magnetism in bilayer nickelates and may provide the pairing glue for superconductivity.
  • Evidence: Introduction: 'Our results underscore the essential role of orbital-selective electron correlations in determining the magnetic properties of the bilayer nickelate and provide direct insight into understanding the origin of high-temperature superconductivity',Discussions: 'the relatively short-range exchange interactions can drive superconducting pairing … tuning a non-thermal parameter … weakens the long-range magnetic order and allows the same electrons to instead develop superconducting pairing.'

Workflow

• orbital-selective renormalization — Orbital-selective correlations justify low-energy description: local moments from d_z2 coupled to itinerant dx2-y2 electrons.
  • Materials: bilayer two-orbital Hubbard model; DFT-based tight-binding parameters; slave-spin mean-field approach
  • Methods: renormalization of hopping and onsite energies using slave-spin; separation into coherent (dx2-y2) and incoherent (d_z2) sectors
  • Observations: dx2-y2 orbital mostly coherent; d_z2 orbital largely incoherent, forming local moments
• exchange interaction derivation — Frustrated RKKY interactions are the dominant intralayer couplings; combined with superexchange they define the magnetic Hamiltonian.
  • Materials: renormalized quasiparticle Hamiltonian; static susceptibility formula; inter-orbital exchange coupling J_cf
  • Methods: RKKY interaction via susceptibility and Fourier transform; superexchange estimate from slave-spin weights
  • Observations: third-nearest-neighbor RKKY coupling J₃ dominates (J₃/J₁ > 1); interlayer superexchange J_perp ≈ 23 meV
• magnetic ground state analysis — The model naturally stabilizes an antiferromagnetic order with wavevector near (π/2,π/2), consistent with neutron diffraction.
  • Materials: effective J₁-J₃ bilayer spin model; Luttinger-Tisza method; variational optimization
  • Methods: minimization of classical magnetic energy; wavevector refinement
  • Observations: noncoplanar antiferromagnetic ground state; ordering wavevector Q near (π/2,π/2); gradual shift of Q with correlation strength
• spin-wave dispersion calculation — The calculated spin-wave spectrum matches RIXS and inelastic neutron scattering data, confirming the magnetic model.
  • Materials: optimized classical ground state; linear spin-wave theory
  • Methods: dispersion calculation with incommensurate order and zone folding
  • Observations: acoustic and optical branches; acoustic mode softening at Q; overall bandwidth ≈80 meV