Summary
This study employs a multi-orbital itinerant electron framework, combined with Hartree-Fock and random phase approximation methods, to systematically analyze the magnetic ground states and transverse spin excitations of bilayer and trilayer nickelates. For the bilayer system, although the double-stripe order has slightly lower energy, the excitation spectrum of the single-stripe state exhibits anisotropic low-energy cone-shaped dispersion at the wavevector Q_BL and isotropic high-energy excitations near the Γ point, showing qualitative consistency with resonant inelastic X-ray scattering and neutron scattering experiments; it is also found that the energy of the mirror-even interlayer optical mode at Q_BL coincides with that of the mirror-odd mode at Γ. In the trilayer system, both mirror-odd and mirror-even spin-density wave orders can be stabilized, with the mirror-odd state having lower energy and hosting a near-zero-gap mode predominantly from the middle layer, whereas the mirror-even state supports only one acoustic mode and two gapped optical modes; comparison with experimental data supports the mirror-odd order picture. The results demonstrate that magnetic excitations can serve as a sensitive probe to distinguish magnetic order configurations and reinforce the conclusion that the magnetism in multilayer nickelates shares a common itinerant origin.
Materials
Methods
Keywords
- high temperature superconductivity
- spin density wave
- magnetic excitations
- mirror parity
- single stripe order
- double stripe order
- interlayer coupling
- itinerant magnetism
Highlights
- Identification of mirror-even optical interlayer modes at the ordering wavevector in bilayer nickelates, with energies matching those of mirror-odd modes at the zone center.
- The mirror-odd spin-density-wave state in trilayer nickelates hosts an additional nearly gapless mode dominated by the middle layer, reflecting the absence of a static moment on that layer.
- The single-stripe order in bilayer nickelates yields an anisotropic low-energy spin-wave cone and an isotropic high-energy ring around the Γ point, consistent with neutron scattering.
- Calculated excitation spectra differentiate between competing magnetic configurations, providing a theoretical basis for experimental distinction.
Conclusions
- The excitation spectrum of the single-stripe state in bilayer nickelates is qualitatively consistent with RIXS and neutron scattering experiments, supporting the single-stripe magnetic order.
- The mirror-odd spin-density-wave state is energetically favored over the mirror-even state in trilayer nickelates, and its excitation spectrum compares favorably with available RIXS data.
- Magnetic excitation spectra serve as a sensitive probe to distinguish between magnetic ground states in multilayer nickelates.
- The magnetism in bilayer and trilayer nickelates can be understood within a unified itinerant framework, where spin-density-wave order and superconductivity both originate from Fermi surface scattering between bands of opposite mirror parity.
Main claims
- In bilayer nickelates, the single-stripe magnetic order, despite being slightly higher in energy, produces an excitation spectrum that qualitatively matches experimental RIXS and neutron scattering data.
- Evidence: the calculated excitation spectrum of the single-stripe state, characterized by an anisotropic low-energy cone at Q_BL and isotropic high-energy excitations near Γ, exhibits good qualitative agreement with recent RIXS and neutron scattering experiments (from abstract).,The observed slight gap feature around 25 meV at Q_BL can be captured in a magnetic configuration with a small φ, where the spinless site have a small moment (from full text).
- For trilayer nickelates, the mirror-odd spin-density-wave state is energetically preferred and its excitation spectrum, featuring an additional nearly gapless middle-layer mode, is more consistent with RIXS data than the mirror-even state.
- Evidence: both mirror-odd and mirror-even spin-density-wave states can be stabilized near Q_TL, with the mirror-odd state lower in energy (from abstract).,Comparison with available RIXS data favors the mirror-odd spin-density-wave scenario (from abstract).,The mirror-odd SDW hosts an additional, nearly gapless mode dominated by the middle layer; the mirror-even SDW contains only one acoustic branch together with two gapped optical modes (from abstract).
- Magnetic excitations provide a sensitive probe to identify the underlying magnetic order in multilayer nickelates and support a common itinerant origin for both magnetism and high-Tc superconductivity.
- Evidence: Our results show that magnetic excitations provide a sensitive probe of the magnetic order and support a common itinerant origin of magnetism in multilayer nickelates (from abstract).,Together with the itinerant pairing scenario driven by scattering between Fermi pockets of opposite mirror parity, our work supports a unified itinerant description (from conclusion).
Workflow
- model_setup — The low-energy electronic structure supports magnetic instabilities driven by scattering between bands of opposite mirror parity.
- Materials: Multi-orbital tight-binding Hamiltonian for bilayer and trilayer nickelates; Hubbard-Kanamori interaction parameters (U, J_H); Mirror-parity basis for electronic states
- Methods: Construction of kinetic Hamiltonian with layer and orbital flavors; Onsite interactions written in particle-hole channel; Classification of bands by mirror parity
- ground_state_determination — Hartree-Fock calculations show that the double-stripe order is favored in the bilayer, while the mirror-odd SDW is favored in the trilayer.
- Materials: Hartree-Fock mean-field method; Spin-density-wave (SDW) order parameter ansatz with layer-dependent phase φ
- Methods: Self-consistent solution of HF equations in folded Brillouin zone; Energy minimization over order parameter phase for bilayer and trilayer
- Observations: Bilayer: double-stripe (φ≈π/2) has lower HF energy than single-stripe (φ=0); Trilayer: mirror-odd SDW is the robust ground state, with energy minimum at φ≈0 (single-stripe-like with spinless sites); Mirror-odd SDW has zero static moment on middle layer
- excitation_spectra_calculation — The calculated spin excitation spectra reveal distinct signatures—number of gapless modes, optical branches, and anisotropy—that distinguish competing magnetic orders.
- Materials: Transverse spin susceptibility within random phase approximation (RPA); Coherence factors from HF quasiparticle states; Projection operators onto layer-resolved and mirror-parity channels
- Methods: Computation of bare particle-hole bubble using SDW-state vertices; RPA summation of ladder diagrams in the transverse spin channel; Spectral weight projection onto outer-layer mirror-odd/even and middle-layer channels
- Observations: Bilayer SS: Gapless anisotropic cone at Q_BL, isotropic high-energy ring near Γ, mirror-even optical mode at Q_BL degenerate with mirror-odd at Γ; Bilayer DS: Additional downward feature along Γ-X, cone splitting near Q_BL, asymmetry along M-X; Trilayer mirror-odd: Two nearly gapless modes (outer-layer Goldstone and middle-layer soft mode) and one optical mode; Trilayer mirror-even: One gapless mode and two gapped optical modes near Q_TL
- experimental_comparison_and_interpretation — The single-stripe order in bilayer and mirror-odd SDW in trilayer are the magnetic ground states consistent with experiments, supporting a unified itinerant picture for magnetism and superconductivity.
- Materials: Reported RIXS spectra; Reported neutron scattering data
- Methods: Qualitative comparison of low-energy ring anisotropy, high-energy ring isotropy, and optical modes
- Observations: Bilayer SS excitations: anisotropic low-energy ring and isotropic high-energy ring match neutron scattering features; DS excitations are inconsistent; Trilayer mirror-odd: one optical mode consistent with RIXS; mirror-even would predict two optical modes; The mirror-odd SDW's nearly gapless middle-layer mode may be observable under pressure