Contrasting Spin Excitations in Octahedral and Square-Planar n=8 Ruddlesden-Popper Nickelates

The discovery of superconductivity in reduced square-planar nickelates marked a major advance in identifying structural and electronic analogs to the high-$T_c$ cuprates. The more recent observation of superconductivity in parent Ruddlesden-Popper (RP) octahedral nickelates with a clear difference in electron count with respect to cuprates raises new questions about the nature of superconductivity across these related but distinct nickelate families. Here, we use Ni $L_3$-edge resonant inelastic x-ray scattering (RIXS) to probe the low-energy excitations in a representative compound of both families: the parent octahedral $n=8$ RP phase Nd$_9$Ni$_8$O$_{25}$ (p-RP), which is non-superconducting, and its reduced square-planar counterpart Nd$_9$Ni$_8$O$_{18}$ (r-RP), which exhibits superconducting correlations with a $T_c \approx 5$ K. The $n=8$ p-RP develops a spin-density-wave (SDW) ground state with ordering wave vector $q_{\mathrm{SDW}} = (1/4,\, 1/4)$, analogous to the bilayer RP, while the $n=8$ r-RP shows an elastic peak at $q^\star = (1/3,\, 0)$. Polarimetric RIXS shows that the p-RP exhibits low-energy spectra dominated by weakly dispersive paramagnons along the 0$\rightarrow\pi$ and $\pi \!\rightarrow\! \pi$ directions, whereas the r-RP with superconducting correlations displays dispersionless magnetic excitations. Our results comprehensively map out the spin excitations and reveal fundamental differences in the ground state between these two distinct structural families.