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

In this study, the magnetic ground state of iridium perovskites $({\text{Sr}}_{n+1}{\text{Ir}}_n{\text{O}}_{3n+1}$, where $n=1$, 2, and $\infty )$ was considered using muon spin spectroscopy $\left(\mu \text{SR}\right)$. When probed by muons in ${\text{Sr}}_2{\text{IrO}}_4$ and ${\text{Sr}}_3{\text{Ir}}_2{\text{O}}_7$ $(n=1,2)$, the internal field $\left(B_{\mathrm{loc}}\right)$ showed clear signs of a magnetic order in two stages at transition temperatures $T_{\mathrm{N}}\simeq 230\text{K}$ and $T_{\mathrm{m}}\simeq 90\text{K}$ in ${\text{Sr}}_2{\text{IrO}}_4$ and $T_{\mathrm{N}}\simeq 280\text{K}$ and $T_{\mathrm{m}}\simeq 70\text{K}$ in ${\text{Sr}}_3{\text{Ir}}_2{\text{O}}_7$. In contrast, no long-range magnetic order was observed in orthorhombic ${\text{SrIrO}}_3$ $(n=\infty )$. Based on the known magnetic structure in ${\text{Sr}}_2{\text{IrO}}_4$ and ${\text{Sr}}_3{\text{Ir}}_2{\text{O}}_7$, we successfully identified muon sites in these compounds from the magnitude of $B_{\mathrm{loc}}$ in the first stage $(T_{\mathrm{m}}\le T\le T_{\mathrm{N}})$. Below $T_{\mathrm{m}},B_{\mathrm{loc}}$ probed by a fraction of muons occupying sites near the apical oxygen of ${\text{IrO}}_6$ 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 $\sim T_{\mathrm{m}}$. A possible link between the oxygen polarization and ferroelectric (multiferroic) behavior in ${\text{Sr}}_2{\text{IrO}}_4$ was considered.

Figure 1

Magnetization $\left(M\right)$ of ${\text{Sr}}_2{\text{IrO}}_4$ and ${\text{Sr}}_3{\text{Ir}}_2{\text{O}}_7$ samples used for $\mu \mathrm{SR}$ measurements (quoted from Ref. [13]). (a) $M$ vs temperature, where measurements were made after zero-field cooling to 5 K with a sequence of (1) warming up to 350 K under a field $H=1$ T parallel to the $a$ axis and (2) then cooling down to 5 K. (b) $M$ vs external field measured at 5 K $\left(H\parallel a\right)$.

Figure 2

Typical $\mu \text{SR}$ time spectra under zero external field (ZF) in (a) ${\text{Sr}}_2{\text{IrO}}_4$, (b) ${\text{Sr}}_3{\text{Ir}}_2{\text{O}}_7$, and (c) ${\text{SrIrO}}_3$, with inset showing some spectra under longitudinal field (LF). Modulation of sinusoidal pattern due to overlap of signals with different frequencies $\mathrm{[}\sim 4.5$ MHz and $\sim 8$ MHz at 1.9 K in (a), $\sim 9$ MHz and $\sim 13$ MHz at 1.7 K in (b)] can be clearly observed in the earlier time range of the spectra up to $1\mu \mathrm{s}$. Fast Fourier transform of ZF-$\mu \text{SR}$ time spectra is shown for (d) ${\text{Sr}}_2{\text{IrO}}_4$ and (e) ${\text{Sr}}_3{\text{Ir}}_2{\text{O}}_7$. (f) LF-$\mu \text{SR}$ spectra in ${\text{Sr}}_3{\text{Ir}}_2{\text{O}}_7$.

Figure 3

Temperature dependence of (a) partial asymmetry $A_i,A_{\mathrm{para}}$, (b) muon precession frequency $f_i$, and (c) relaxation rate ${\lambda }_i,{\lambda }_L$ in ${\text{Sr}}_2{\text{IrO}}_4$. Solid curves are results of curve fitting by $f_0{(1-T/T_{\mathrm{N}})}^{\beta }$, and dashed curves are visual guides. For the correspondence between $f_i$ and muon sites, see Fig. 6.

Figure 4

Temperature dependence of (a), (b) partial asymmetry, (c) muon precession frequency, and (d) relaxation rate in ${\text{Sr}}_3{\text{Ir}}_2{\text{O}}_7$. Solid curve is fitting line, and dashed curves are visual guides. For the correspondence between $f_i$ and muon sites, see Fig. 7.

Figure 5

Temperature dependence of (a) partial asymmetry $A_i$ and (b) relaxation rate ${\Delta }_i,{\lambda }_2$ in ${\text{SrIrO}}_3$.

Figure 6

Presumed muon sites in ${\text{Sr}}_2{\text{IrO}}_4$. Site 1 and site $1^{\prime }$ are close to apical oxygen (O1), and site 2 and site $2^{\prime }$ are near the ${\text{IrO}}_2$ plane (O2).

Figure 7

Presumed muon sites in ${\text{Sr}}_3{\text{Ir}}_2{\text{O}}_7$. Site 1 is close to apical oxygen (O1), sites 2 and $2^{\prime }$ are near ${\text{IrO}}_2$ planes (O2, $\mathrm{O}{2}^{\prime })$, and site 3 is near the shared apical oxygen (O3).

Figure 8

Presumed muon sites in ${\text{SrIrO}}_3$. Site 1 is close to apical oxygen (O1), and site 2 is near ${\text{IrO}}_2$ planes (O2).

Figure 9

Presumed structure of oxygen magnetic moments associated with apical oxygen (O1) in (a) ${\text{Sr}}_2{\text{IrO}}_4$ and (b) ${\text{Sr}}_3{\text{Ir}}_2{\text{O}}_7$. Oxygen moments are antiparallel with those of iridium in each compound.