Emergent spin-charge-orbital order in superconductor La$_3$Ni$_2$O$_7$

Abstract

The bilayer nickelate La$_3$Ni$_2$O$_7$ (LNO) exhibits a remarkably high-temperature superconductivity of approximately 80 K under pressure, sparking considerable attentions. However, the nature of the spin, charge, and orbital order in LNO remains unknown, hindering the exploration of the mechanism of superconductivity. Here, supported by symmetry analysis and density functional theory calculations, we unravel a double strip ground state of LNO with alternating magnetic moments arrangements. Interestingly, a charge density wave emerges under this determined magnetic order. Such CDW phase exhibits a Pmnm space group with breathing deformation of the NiO$_6$ octahedra, where the stretching and shrinking of the octahedra correspond to the formation of \emph{d}$_{z^2}^1$\emph{d}$_{x^2-y^2}^1$ and \emph{d}$_{z^2}^1$ orbital order. Moreover, we build a first-principles-based Hamiltonian for LNO, which provides deeper insight into its peculiar magnetic order. Our work thus reveals a systematic spin-charge-orbital picture for LNO, which can be extended to other nickelate-based superconductors, paving the way for determining the mechanism of superconductivity.