  We use resonant inelastic x-ray scattering (RIXS) at the Ir L3 edge to study
the effect of hole doping upon the Jeff=1/2 Mott-insulating state in Sr2IrO4,
via Rh replacement of the Ir site. The spin-wave gap, associated with XY-type
spin-exchange anisotropy, collapses with increasing Rh content, prior to the
suppression of the Mott-insulating state and in contrast to electron doping via
La substitution of the Sr site. At the same time, despite heavy damping, the
d-d excitation spectra retain their overall amplitude and dispersion character.
A careful study of the spin-wave spectrum reveals that deviations from the
J1-J2-J3 Heisenberg used to model the pristine system disappear at intermediate
doping levels. These findings are interpreted in terms of a modulation of Ir-Ir
correlations due to the influence of Rh impurities upon nearby Ir wave
functions, even as the single-band Jeff=1/2 model remains valid up to full
carrier delocalization. They underline the importance of the transition metal
site symmetry when doping pseudospin systems such as Sr2IrO4.
