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This paper develops a unified itinerant electron description for the nature of spin-density wave (SDW) order and magnetic excitations in Ruddlesden-Popper nickelates. The central element is the mirror symmetry of the NiO₂ multilayer blocks, which organizes the low-energy electronic states into mirror-even and mirror-odd sectors. It is shown that the dominant interband nesting between mirror-opposite sectors drives a mirror-selective itinerant SDW instability, whose collective modes naturally reproduce the spin-wave-like spectra observed experimentally. In La₄Ni₃O₁₀, the SDW further induces a secondary mirror-even charge density wave, giving rise to intertwined spin and charge textures. These results demonstrate that magnetism in multilayer nickelates is intrinsically itinerant rather than of local-moment origin, and establish mirror-selective interband SDW order as a unifying organizational principle for magnetic correlations in these systems.

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This study systematically analyzed the electronic structure of strained La₃Ni₂O₇ thin films using density functional theory calculations, revealing that biaxial compressive strain primarily elongates the outer apical Ni–O bonds while leaving the inner apical Ni–O bonds nearly unchanged, thereby significantly enhancing the Jahn–Teller splitting energy Δ_JT, yet the interlayer d_z² orbital hopping parameter t_⊥^z exhibits only a weak variation. Given that superconductivity emerges only when the in-plane lattice constant falls below a critical value, these results identify strain-enhanced Δ_JT as a key microscopic tuning parameter. The calculated Fermi surface topology and Hall response agree well with angle-resolved photoemission spectroscopy (ARPES) and Hall measurements on LaAlO₃ and SrLaAlO₄ substrates, confirming that Jahn–Teller distortion plays a central role in optimizing superconductivity in bilayer nickelates.

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