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Magnetic excitations in the optimally doped high-$T_\mathrm{c}$superconductor Bi$_{1.5}$Pb$_{0.55}$Sr$_{1.6}$La$_{0.4}$CuO$_{6+\delta}$(OP-Bi2201, $T_\mathrm{c}\simeq 34$ K) are investigated by Cu $L_3$ edgeresonant inelastic x-ray scattering (RIXS), below and above the pseudogapopening temperature. At both temperatures the broad spectral distributiondisperses along the (1,0) direction up to $\sim$350~meV at zone boundary,similarly to other hole-doped cuprates. However, above $\sim$0.22 reciprocallattice units, we observe a concurrent intensity decrease for magneticexcitations and quasi-elastic signals with weak temperature dependence. Thisanomaly seems to indicate a coupling between magnetic, lattice and charge modesin this compound. We also compare the magnetic excitation spectra near theanti-nodal zone boundary in the single layer OP-Bi2201 and in the bi-layeroptimally doped Bi$_{1.5}$Pb$_{0.6}$Sr$_{1.54}$CaCu$_2$O$_{8+\delta}$(OP-Bi2212, $T_\mathrm{c}\simeq96$ K). The strong similarities in theparamagnon dispersion and in their energy at zone boundary indicate that thestrength of the super-exchange interaction and the short-range magneticcorrelation cannot be directly related to $T_\mathrm{c}$, not even within thesame family of cuprates.

physical review. b, condensed matter and materials physics

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$_{6+\delta}$