Magnetic excitations and phonons simultaneously studied by resonant inelastic x-ray scattering in optimally doped Bi${}_{1.5}$Pb${}_{0.55}$Sr${}_{1.6}$La${}_{0.4}$CuO${}_{6+\hat{I}´}$

Abstract

Magnetic excitations in the optimally doped high-$T_{\mathrm{c}}$ superconductor Bi${}_{1.5}$Pb${}_{0.55}$Sr${}_{1.6}$La${}_{0.4}$CuO${}_{6+\hat{I}´}$ (OP-Bi2201, $T_{\mathrm{c}}\simeq 34$ K) are investigated by Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS), below and above the pseudogap opening temperature. At both temperatures the broad spectral distribution disperses along the (1,0) direction up to $\sim$350~meV at zone boundary, similarly to other hole-doped cuprates. However, above $\sim$0.22 reciprocal lattice units, we observe a concurrent intensity decrease for magnetic excitations and quasi-elastic signals with weak temperature dependence. This anomaly seems to indicate a coupling between magnetic, lattice and charge modes in this compound. We also compare the magnetic excitation spectra near the anti-nodal zone boundary in the single layer OP-Bi2201 and in the bi-layer optimally doped Bi${}_{1.5}$Pb${}_{0.6}$Sr${}_{1.54}$CaCu${}_2$O${}_{8+\hat{I}´}$ (OP-Bi2212, $T_{\mathrm{c}}\simeq 96$ K). The strong similarities in the paramagnon dispersion and in their energy at zone boundary indicate that the strength of the super-exchange interaction and the short-range magnetic correlation cannot be directly related to $T_{\mathrm{c}}$, not even within the same family of cuprates.