Anisotropic softening of magnetic excitations in lightly electron doped Sr$_2$IrO$_4$

The magnetic excitations in electron doped (Sr$_{1-x}$La$_x$)$_2$IrO$_4$ with $x = 0.03$ were measured using resonant inelastic X-ray scattering at the Ir $L_3$-edge. Although much broadened, well defined dispersive magnetic excitations were observed. Comparing with the magnetic dispersion from the parent compound, the evolution of the magnetic excitations upon doping is highly anisotropic. Along the anti-nodal direction, the dispersion is almost intact. On the other hand, the magnetic excitations along the nodal direction show significant softening. These results establish the presence of strong magnetic correlations in electron doped Sr$_{1-x}$La$_x$)$_2$IrO$_4$ with close analogies to the hole doped cuprates, further motivating the search for high temperature superconductivity in this system.