  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 considered
using 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 ($B_{\rm loc}$) showed
clear sign of a magnetic order in two stages at transition temperatures $T_{\rm
N}\simeq 230$ K and $T_{\rm m}\simeq 90$ K in Sr$_2$IrO$_4$ and $T_{\rm
N}\simeq 280$ 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 orthorhombic
SrIrO$_3$ ($n=\infty$). 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 compounds
from the magnitude of $B_{\rm loc}$ in the first stage ($T_{\rm m}\le T\le
T_{\rm N}$). Below $T_{\rm m}$, $B_{\rm loc}$ probed by a fraction of muons
occupying sites near the apical oxygen of IrO$_6$ octahedra exhibited a further
increase but remained mostly unchanged for sites close to the in-plane oxygen.
While such behavior cannot be explained by the alteration of the Ir spin
structure, it is consistent with the selective appearance of ordered magnetic
moments on the apical oxygen. The oxygen polarization was also in line with the
reported magnetization anomalies in these compounds below $\sim T_{\rm m}$. A
possible link between the oxygen polarization and ferroelectric (multiferroic)
behavior in Sr$_2$IrO$_4$ was considered.
