Spin correlations in La$_3$Ni$_2$O$_7$ superconducting thin films

The discovery of ambient-pressure superconductivity with $T_{c,\text{onset}} > 40$ K in {\LNO} (LNO) thin films grown on the SrLaAlO$_4$ (SLAO) substrate with compressive ($\varepsilon\approx-2\%$) epitaxial strain provides a unique platform for investigating the superconducting mechanisms in nickelate superconductors. Here, we use resonant inelastic X-ray scattering (RIXS) to unveil the dispersive spin excitations in the LNO/SLAO superconducting thin film and establish the strain dependence of the electronic and spin excitations in LNO thin films with strain ranging from $\varepsilon\approx-2\%$ to $+1.9\%$. Compared with the bulk crystal, the LNO/SLAO thin film (with $\varepsilon\approx-2\%$) exhibits similar $dd$ excitations and spin dynamics with larger bandwidth. By contrast, tensile-strained LNO/SrTiO$_3$ ($\varepsilon \approx +1.9\%$) exhibits a marked suppression of both the spin excitations and the Ni 3{\dz}-derived $dd$ excitations. The strain dependence of the spin excitations reflects significant changes in the interlayer exchange coupling $J_z$, and the diminishing $dd$ excitations in tensile-strained samples indicate weaker Ni 3{\dz}-O 2$p_{z}$ hybridization. This strain evolution of the spin excitations and $J_z$ is attributed to the strain-tuned $c$-axis Ni-O-Ni bond angle $\varphi$, which controls the Ni 3{\dz}-O 2$p_{z}$ hybridization. Since superconductivity is observed only in films grown on SLAO, and spin correlations are enhanced along with the emergence of superconductivity, our results identify $\varphi$ as a key structural lever controlling $J_z$ and provide direct spectroscopic support for interlayer spin-fluctuation-mediated pairing scenarios in bilayer nickelates.