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In this study, the magnetic ground state of iridium perovskites(Sr$_{n+1}$Ir$_{n}$O$_{3n+1}$, where $n=1$, 2, and $\infty$) was consideredusing muon spin spectroscopy ($\mu$SR). When probed by muons in Sr$_2$IrO$_4$and Sr$_3$Ir$_2$O$_7$ ($n=1,2$), the internal field ($B_{\rm loc}$) showedclear sign of a magnetic order in two stages at transition temperatures $T_{\rmN}\simeq 230$ K and $T_{\rm m}\simeq 90$ K in Sr$_2$IrO$_4$ and $T_{\rmN}\simeq 280$ K and $T_{\rm m}\simeq 70$ K in Sr$_3$Ir$_2$O$_7$, respectively.In contrast, no long-range magnetic order was observed in orthorhombicSrIrO$_3$ ($n=\infty$). Based on the known magnetic structure in Sr$_2$IrO$_4$and Sr$_3$Ir$_2$O$_7$, we successfully identified muon sites in these compoundsfrom the magnitude of $B_{\rm loc}$ in the first stage ($T_{\rm m}\le T\leT_{\rm N}$). Below $T_{\rm m}$, $B_{\rm loc}$ probed by a fraction of muonsoccupying sites near the apical oxygen of IrO$_6$ octahedra exhibited a furtherincrease but remained mostly unchanged for sites close to the in-plane oxygen.While such behavior cannot be explained by the alteration of the Ir spinstructure, it is consistent with the selective appearance of ordered magneticmoments on the apical oxygen. The oxygen polarization was also in line with thereported magnetization anomalies in these compounds below $\sim T_{\rm m}$. Apossible link between the oxygen polarization and ferroelectric (multiferroic)behavior in Sr$_2$IrO$_4$ was considered.

Evidence for ordered magnetic moments at oxygen sites in antiferromagnetic Sr$_2$IrO$_4$ and Sr$_3$Ir$_2$O$_7$