  We studied the magnetic excitations in the quasi-one-dimensional (q-1D)
ladder subsystem of Sr_(14-x) Ca_x Cu_24 O_41(SCCO) using Cu L_3-edge resonant
inelastic X-ray scattering (RIXS). By comparing momentum-resolved RIXS spectra
with (x=12.2) and without (x=0) high Ca content, we track the evolution of the
magnetic excitations from collective two-triplon (2T) excitations (x=0) to
weakly-dispersive gapped modes at an energy of 280 meV (x=12.2). Density matrix
renormalization group (DMRG) calculations of the RIXS response in the doped
ladders suggest that the flat magnetic dispersion and damped excitation profile
observed at x=12.2 originates from enhanced hole localization. This
interpretation is supported by polarization-dependent RIXS measurements, where
we disentangle the spin-conserving {\Delta}S=0 scattering from the predominant
{\Delta}S=1 spin-flip signal in the RIXS spectra. The results show that the
low-energy weight in the {\Delta}S=0 channel is depleted when Sr is replaced by
Ca, consistent with a reduced carrier mobility. Our results demonstrate that
off-ladder impurities can affect both the low-energy magnetic excitations and
superconducting correlations in the CuO_4 plaquettes. Finally, our study
characterizes the magnetic and charge fluctuations in the phase from which
superconductivity emerges in SCCO at elevated pressures.
