  X-ray absorption spectroscopy (XAS) and magnetic circular dichroism (XMCD)
measurements at the oxygen (O) $K$-edge were performed to investigate the
magnetic polarization of ligand O atoms in the weak ferromagnetic (WFM) phase
of the Ir perovskite compound Sr$_2$IrO$_4$. With the onset of the WFM phase
below $T_{\rm N}\simeq240$ K, XMCD signals corresponding to XAS peaks
respectively identified as originating from the magnetic moments of apical and
planar oxygen (O$_{\rm A}$ and O$_{\rm P}$) in the IrO$_6$ octahedra were
observed. The observation of magnetic moments at O$_{\rm A}$ sites is
consistent (except for the relative orientation) with that suggested by prior
muon spin rotation ($\mu$SR) experiment in the non-collinear antiferromagnetic
(NC-AFM) phase below $T_{\rm M}\approx100$ K. Assuming that the O$_{\rm A}$
magnetic moment observed by $\mu$SR is also responsible for the corresponding
XMCD signal, the magnetic moment of O$_{\rm P}$ is estimated to be consistent
with the previous $\mu$SR result. Since the O$_{\rm A}$ XMCD signal is mainly
contributed by Ir 5$d$ $zx$ and $yz$ orbitals which also hybridize with O$_{\rm
P}$, it is inferred that the relatively large O$_{\rm P}$ magnetic moment is
induced by Ir 5$d$ $xy$ orbitals. Moreover, the inversion of O$_{\rm A}$
moments relative to Ir moments between the two magnetic phases revealed by XMCD
suggests the presence of competing magnetic interactions for O$_{\rm A}$, with
which the ordering of O$_{\rm A}$ moments in the NC-AFM phase may be suppressed
to $T_{\rm M}$.
