Direct imaging of the Ni e_g hole orbitals in the bilayer nickelate La₂SmNi₂O₇

Summary

This study used Ni M₁-edge s-core-level nonresonant inelastic X-ray scattering (s-NIXS), a bulk-sensitive method, to determine the angular distribution of Ni 3d holes in the ambient-pressure single-crystal bilayer nickelate La₂SmNi₂O₇. Fitting yielded an e_g hole occupancy ratio h_z/h_x = 0.94 ± 0.06, significantly higher than the 2/3 expected from the model of a fully occupied d_z² bonding band and close to the picture of approximately one hole per e_g orbital under Hund coupling, and consistent with DMFT charge-transfer calculations for the high-pressure phase. On this basis, it is argued that the superconducting pairing scenario for this material should allow both e_g orbitals to participate in electron pairing rather than being dominated solely by a single d_z² orbital; however, this constitutes experimental support for the relevant pairing theory and does not directly establish the pairing mechanism.

Materials

• La₂SmNi₂O₇
• La₃Ni₂O₇
• La₂PrNi₂O₇
• La_1.57Sm_1.43Ni₂O_7−δ
• La_2−xSr_xCuO₄

Methods

• s-core-level non-resonant inelastic x-ray scattering (s-NIXS) at the Ni M₁ edge
• x-ray diffraction
• DMFT calculations
• DFT
• ARPES
• EELS
• RIXS
• x-ray linear dichroism
• polarization-dependent x-ray absorption

Keywords

• hund's coupling
• charge transfer
• ligand holes
• orbital hole occupancy
• bilayer nickelate superconductivity
• electron pairing
• zhang rice singlet
• density wave transition

Highlights

• First quantitative bulk measurement of the Ni e_g hole orbital distribution in a bilayer nickelate using bulk-sensitive s-NIXS at the Ni M₁ edge, free from multiplet effects and La-edge overlap.
• The measured ratio exceeds the filled-bonding-band value by 4.4 statistical standard deviations, and constraining it to 2/3 strongly worsens the fit.
• The method provides a model-free description of orbital physics in bulk correlated systems and could be extended across the rare-earth series, to low temperature, or under applied pressure.

Conclusions

• The Ni 3d hole occupation ratio h_z/h_x = 0.94 ± 0.06 in La₂SmNi₂O₇, significantly above the 2/3 expected for a filled d_z² bonding band and close to the Hund's-coupling picture.
• The result is consistent with DMFT charge-transfer calculations for the high-pressure phase and suggests a Ni configuration close to d⁸ with remaining holes on oxygen ligands.
• Hund's coupling rather than the bonding-antibonding splitting of d_z² governs the orbital occupations.
• Superconductivity scenarios in which both e_g orbitals contribute to electron pairing are supported.

Main claims

• The Ni e_g hole occupation ratio in La₂SmNi₂O₇ is h_z/h_x = 0.94 +/- 0.06, significantly above the value 2/3 expected for a filled d_z² bonding band.
  • Evidence: s-NIXS angular dependence of Ni M₁ edge intensity,fitted intensity contrast larger than 0.73,constraining ratio to 2/3 deteriorates fit chi-squared from 1.09 to 2.53,measured value exceeds 2/3 by 4.4 statistical standard deviations
• The hole distribution is close to the Hund's-coupling picture with approximately one hole per e_g orbital, implying a Ni configuration near d⁸ with remaining holes on oxygen ligands.
  • Evidence: measured ratio close to 1,consistency with DMFT prediction from Wannier occupations of 0.60 and 0.54 per spin orbital,consistency with O K-edge linear dichroism and weak orbital polarization in bulk x-ray absorption
• Superconductivity scenarios in La₂SmNi₂O₇ should allow both e_g orbitals to participate in electron pairing rather than being dominated solely by d_z².
  • Evidence: near-equal e_g hole occupations,electron-occupation ratio close to the equal-occupation picture,consistency with DMFT charge-transfer calculations

Workflow

• sample_preparation — A bulk single crystal of La₂SmNi₂O₇ suitable for bulk-sensitive orbital measurements was prepared and oriented.
  • Materials: single crystal of La₂SmNi₂O₇ (m3) grown at ambient pressure from a K₂CO₃ flux; Ni-free cuprate La_2−xSr_xCuO₄ reference for La edge line shape
  • Methods: flux growth at ambient pressure; x-ray diffraction orientation within average tetragonal space group (139)
  • Observations: crystal oriented by x-ray diffraction with a and c lattice parameters reported; azimuthal orientation known to within a small angle
• measurement — The angular distribution of Ni 3d holes was measured in a bulk-sensitive, multiplet-free manner.
  • Materials: La₂SmNi₂O₇ single crystal
  • Methods: s-core-level non-resonant inelastic x-ray scattering (s-NIXS) at the Ni M₁ edge; GALAXIES beamline at SOLEIL with MATRIXS spectrometer, 40 Si(110) spherically bent analyzers, fixed Johann geometry, Bragg angle 87 degrees; crystal rotation about the axis to sweep momentum transfer direction
  • Observations: spectra contain La edges between 98 and 107 eV and Ni M₁ edge centered near 105 eV; La contribution is isotropic and used for normalization; Ni integrated intensity shows pronounced angular dependence with similar values along the two in-plane directions and a minimum near the intermediate angle
• analysis — The measured e_g hole occupancy ratio is 0.94 +/- 0.06, significantly above 2/3.
  • Materials: s-NIXS spectra at multiple azimuthal angles
  • Methods: fitting full spectrum per angle with quadratic background, single Gaussian for Ni peak, and scaled La edge line shape; fitting angular intensity model based on spherical Bessel function and orbital angular density with three free parameters (scaling, hole ratio, angular offset); symmetry averaging and systematic variation of analysis choices
  • Observations: fitted intensity contrast substantially larger than 0.73 expected for hole ratio 2/3; no evidence of d holes; off-diagonal terms cancel for equal twin fractions; hole occupation ratio h_z/h_x = 0.94 +/- 0.06; constraining ratio to 2/3 worsens fit from 1.09 to 2.53; lowest alternative analysis value remains above 2/3
• interpretation — The results support superconductivity scenarios in which both e_g orbitals contribute to electron pairing in La₂SmNi₂O₇.
  • Materials: measured hole ratio compared with model predictions and DMFT calculations
  • Methods: comparison with electron-counting models, Hund's-coupling picture, and DMFT charge-transfer calculations; derivation of electron-occupation ratio from hole ratio
  • Observations: ratio close to 1 consistent with Hund's-coupled high-spin Ni configuration with ligand holes; consistent with DMFT prediction and with O K-edge linear dichroism and x-ray absorption results; electron-occupation ratio between about 0.73 and 0.95 depending on total hole count