  The striking discovery of high-temperature superconductivity (HTSC) of 80 K
in a bilayer nickelate La$_3$Ni$_2$O$_7$ under a moderately high pressure of
about 14 GPa ignited a new wave of studying HTSC in nickelates. The properties
of the parental phase at ambient pressure may contain key information on basic
interactions therein and bosons that may mediate pairing giving birth to
superconductivity. Moreover, the bilayer structure of La$_3$Ni$_2$O$_7$ may
suggest a distinct minimal model in comparison to cuprate superconductors. Here
using X-ray absorption spectroscopy and resonant inelastic X-ray scattering, we
studied La$_3$Ni$_2$O$_7$ at ambient pressure, and found that Ni
3$d_{x^2-y^2}$, Ni 3$d_{z^2}$, and ligand oxygen 2$p$ orbitals dominate the
low-energy physics with a small charge-transfer energy. Remarkably,
well-defined optical-like magnetic excitations were found to soften into a
quasi-static spin-density-wave ordering, evidencing the strong electronic
correlations and rich magnetic properties. Based on a Heisenberg spin model, we
found that the inter-layer effective magnetic superexchange interaction is much
larger than the intra-layer ones, and proposed two viable magnetic structures.
Our results set the foundation for further exploration of La$_3$Ni$_2$O$_7$
superconductor.
