Summary
Using the unrestricted Hartree-Fock method based on a multiorbital Hubbard-Hund model, we investigate the density-wave phase diagram of the low-pressure bilayer nickelate La3Ni2O7. Our calculations reveal that in the orthorhombic phase, the electron system first develops a double-stripe spin-density-wave order with wave vector QY = (0, π) at about 150 K; subsequently, at about 130 K, the pure double-stripe spin state becomes unstable against a commensurate charge density wave, resulting in a spin-modulated double-stripe ordered state where the magnetic moments and charge densities on the in-plane Ni1 and Ni2 sites are modulated, forming low-spin sites. This charge order parameter is an order of magnitude smaller than the magnetic order parameter and induces additional band gaps and folded Fermi surfaces in the electronic structure. The study establishes the hierarchical relationship between spin-density-wave and charge-density-wave orders in La3Ni2O7, provides important clues for understanding the connection between the ambient-pressure ordered phases and the high-pressure superconducting phase, and proposes suggestions for further experimental verification.
Materials
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Methods
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Keywords
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Highlights
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Conclusions
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Main claims
- The low-pressure phase diagram of La3Ni2O7 is dominated by a double-stripe spin-density wave at T_SDW ≈ 150 K.
- Evidence: Within the orthorhombic phase… the electronic system develops a double-stripe spin-density wave with ordering vector QY=(0,π).
- A commensurate charge-density wave emerges at T_DW ≈ 130 K, intertwined with the SDW, forming a spin-modulated double-stripe order.
- Evidence: We identify that the pure double stripe spin state is unstable… towards a commensurate charge-density wave instability…
- The charge order parameter is about an order of magnitude smaller than the magnetic order parameter.
- Evidence: This charge order parameter is an order of magnitude smaller than the magnetic order parameter
- The CDW produces low-spin sites and a kink in the temperature dependence of magnetic moments.
- Evidence: the CDW plays the main role of splitting the band degeneracies… generating low-spin sites… a kink in the temperature evolution of the magnetic moments per site
- Pressure evolution of the density waves is controlled by crystal-field splitting, with the CDW being suppressed as pressure increases.
- Evidence: as a function of crystal-field splitting, the SDW critical temperature is enhanced and the CDW critical temperature suppressed
- The intertwined SDW and CDW orders provide a crucial link to the high-pressure superconducting phase.
- Evidence: providing an important link between its ambient-pressure and superconducting high-pressure phases
Workflow
- Model Construction — The 8-orbital tight-binding model reproduces the electronic structure of orthorhombic La3Ni2O7, consistent with ARPES data.
- Materials: 8-orbital tight-binding model; Slater-Kanamori Hubbard-Hund Hamiltonian; crystal-field splitting data from DFT; orthorhombic crystal structure (Amam)
- Methods: DFT-based Wannier construction; fitting tight-binding parameters to DFT band structure
- Observations: normal-state Fermi surface with β pocket; band structure with double degeneracy at Y point; orbital-dependent spectral weights
- Mean-Field Calculation — Unrestricted Hartree-Fock calculations predict a metallic double-stripe SDW at ≈150 K, followed by a weak commensurate CDW at ≈130 K.
- Materials: unrestricted Hartree-Fock (UHF) method; Hubbard U = 1.8 eV, Hund's coupling J = 0.2U; spin and charge order parameters (n_i and m_i); ordering wavevector QY = (0,π)
- Methods: Hubbard-Stratonovich transformation; mean-field saddle-point approximation; numerical minimization of grand potential using BFGS algorithm; self-consistent solution for chemical potential to fix electron density
- Observations: SDW critical temperature T_SDW ≈ 150K; CDW onset temperature T_DW ≈ 130K; double-stripe antiferromagnetic pattern; magnetic order parameter up to ≈30 meV; charge order parameter ≈3 meV
- Analysis of Order Parameters — The CDW introduces a small charge modulation, low-spin sites, and a kink in the magnetic order parameter, while pressure suppresses the CDW by restoring in-plane site symmetry.
- Materials: computed spin and charge densities; Fermi surfaces, band structures, density of states
- Methods: temperature evolution analysis; pressure dependence via crystal-field splitting tuning; characterization of orbital and site dependence
- Observations: spin density splitting between Ni1 and Ni2 sites below T_DW; kink in magnetic moment temperature dependence at T_DW; orbital-selective SDW gap (larger for dx2-y2); CDW breaks in-plane site equivalence; folded β pocket from band folding; pressure: SDW T_c increases, CDW T_c suppressed
- Interpretation and Experimental Comparison — The theoretical results establish a hierarchy of intertwined SDW and CDW orders, providing a link between the ambient-pressure ordered phases and the high-pressure superconducting state.
- Materials: experimental literature (neutron scattering, ARPES, NMR, Raman, etc.)
- Methods: qualitative comparison of calculated order parameters with experimental gaps and transition temperatures; proposal of experimental tests (kink observation, band splittings)
- Observations: calculated SDW gap ≈30 meV matches experimental ≈50-100 meV; hierarchy of transitions T_SDW > T_DW observed in experiments; CDW explains DW features; pressure dependence of CDW consistent with experiments