Observation of a 500 meV Collective Mode in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ and ${\mathrm{Nd}}_2{\mathrm{CuO}}_4$ Using Resonant Inelastic X-Ray Scattering

Utilizing resonant inelastic x-ray scattering, we report a previously unobserved mode in the excitation spectrum of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ and ${\mathrm{Nd}}_2{\mathrm{CuO}}_4$ at 500 meV. The mode is peaked around the ($\pi$, 0) point in reciprocal space and is observed to soften, and broaden, away from this point. Samples with $x=0$, 0.01, 0.05, and 0.17 were studied. The new mode is found to be rapidly suppressed with increasing Sr content and is absent at $x=0.17$, where it is replaced by a continuum of excitations. This mode is only observed when the incident x-ray polarization is normal to the CuO planes.

Figure 1

(a) Inelastic x-ray scattering in ${\mathrm{La}}_2{\mathrm{CuO}}_4$ observed at the ($\pi$, 0) point, $\mathbf{Q}=(2.5,0,0)$, on and off resonance (closed and open symbols, respectively). A clear peak is observed at 500 meV on resonance.

Figure 2

Momentum dependence of the 500 meV feature in ${\mathrm{La}}_2{\mathrm{CuO}}_4$. The figure shows the inelastic data, with the elastic scattering subtracted off, for 5 different momenta in the 2D Brillouin zone.

Figure 3

Doping dependence of the 500 meV feature. Data are taken at ($\pi$, 0) and have the elastic scattering subtracted off.

Figure 4

Polarization dependence of the 500 meV peak in ${\mathrm{La}}_2{\mathrm{CuO}}_4$ (closed symbols). The peak is only observed with the incident polarization parallel to the $c$ axis. Data taken for ${\mathrm{Nd}}_2{\mathrm{CuO}}_4$ (open circles) show a weak peak at the same energy. Scans are shifted vertically for clarity.

Figure 5

Possible resonant scattering process resulting in the creation of two magnons. The Cu (hole) spin on site 1 is repelled onto a neighboring site, site 2, by the 1s core hole in the intermediate state. Following the decay of the core hole, the “other” spin hops back resulting in spin flips on both sites. Note the two sites could, in principle, be in neighboring layers.