Evolution of effective magnetic exchange interaction under spin dilution in SrIr$_{1-x}$Sn$_x$O$_3$

Resonant inelastic X-ray scattering measurements reveal robust magnetic excitations in the perovskite iridates SrIr$_{1-x}$Sn$_x$O$_3$. We analyzed the dispersions of the magnetic excitation with spin-dilution ratio $x$ = 0, 0.03, 0.06, 0.1, and 0.2, crossing from semi-metal to spin-diluted while antiferromagnetically ordered insulators. The extracted effective magnetic exchange interactions decrease continuously upon increasing spin dilution, and their evolution follows a simple spin-dilution scaling law. These results not only verify the strong electron-correlation nature of the metallic parent SrIrO$_3$, but also reveal the entanglement of the charge and spin dynamics in this system.