Density waves in low-pressure bilayer nickelates

摘要

本文利用无约束Hartree-Fock方法，基于多轨道Hubbard-Hund模型，研究了低压双层镍酸盐La₃Ni₂O₇的密度波相图。计算表明，在正交相中，电子体系首先在约150 K形成波矢为QY=(0,π)的双条纹自旋密度波序；随后在约130 K，纯双条纹自旋态对共度电荷密度波不稳定，出现自旋调制的双条纹有序态，表现为面内Ni₁和Ni₂位点的磁矩与电荷密度发生调制，形成低自旋位点。该电荷序参数比磁序参数小一个数量级，并在能带中诱导额外的能隙和折叠费米面。研究确立了La₃Ni₂O₇中自旋密度波和电荷密度波的层级关系，为理解常压有序相与高压超导相之间的关联提供了重要线索，并提出了进一步实验检验的建议。

材料

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方法

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关键词

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亮点

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结论

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主要论断

• The low-pressure phase diagram of La₃Ni₂O₇ is dominated by a double-stripe spin-density wave at T_SDW ≈ 150 K.
  • 证据: 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.
  • 证据: 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.
  • 证据: 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.
  • 证据: 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.
  • 证据: 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.
  • 证据: providing an important link between its ambient-pressure and superconducting high-pressure phases

研究流程

• Model Construction — The 8-orbital tight-binding model reproduces the electronic structure of orthorhombic La₃Ni₂O₇, consistent with ARPES data.
  • 材料: 8-orbital tight-binding model; Slater-Kanamori Hubbard-Hund Hamiltonian; crystal-field splitting data from DFT; orthorhombic crystal structure (Amam)
  • 方法: DFT-based Wannier construction; fitting tight-binding parameters to DFT band structure
  • 观察: 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.
  • 材料: 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)
  • 方法: 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
  • 观察: 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.
  • 材料: computed spin and charge densities; Fermi surfaces, band structures, density of states
  • 方法: temperature evolution analysis; pressure dependence via crystal-field splitting tuning; characterization of orbital and site dependence
  • 观察: 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.
  • 材料: experimental literature (neutron scattering, ARPES, NMR, Raman, etc.)
  • 方法: qualitative comparison of calculated order parameters with experimental gaps and transition temperatures; proposal of experimental tests (kink observation, band splittings)
  • 观察: 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