d-d Excitations in Bilayer Manganites Probed by Resonant Inelastic X-ray Scattering

We report a high resolution resonant inelastic x-ray scattering investigation of the bilayer manganites La${}_{2-2x}$Sr${}_{1+2x}$Mn${}_2$O${}_7$ with $x=0.36$ and $0.5$. The momentum dependence along the crystallographic $(110)$ direction for energy losses $1\mathrm{e}\mathrm{V}\le \mathrm{\Delta }E\le 15\mathrm{e}\mathrm{V}$ has been measured in detail with the data analysis focusing on the energy loss region $1,\rm{eV} \leq \Delta E \leq 5,\rm{eV}$,whichincludesastrongpeaklocatedat$\Delta E \approx 2,\rm{eV}$\mathrm{.}Weobserveacleardispersionofupto$0.5,\rm{eV}$ in the measured $\mathbf{\text{q}}$ range, which is direct evidence of the non-local character of this excitation. Further, we found that the intensity in this low energy region strongly depends on both the reduced wave vector $$\mathbf{\text{q}}$ = (h, h, 0)$,$h = 0.1 - 0.5$, and temperature, i.e. different ordered phases. Results can be explained via an intersite $d-d$ charge transfer excitation, proposed for pseudo-cubic manganites, where the hopping rate is strongly increased (decreased) by ferromagnetic (antiferromagnetic) alignment of neighboring in-plane Mn ion core spins.