Weak antiferromagnetism of $J_{\mathrm{eff}}=\frac{1}{2}$ band in bilayer iridate Sr${}_3$Ir${}_2$O${}_7$

The antiferromagnetic structure of Sr${}_3$Ir${}_2$O${}_7$, the bilayer analog of a spin-orbital Mott insulator Sr${}_2$IrO${}_4$, was revealed by resonant magnetic x-ray diffraction. Contrasting intensities of the magnetic diffraction at the Ir $L_{\mathrm{III}}$ and $L_{\mathrm{II}}$ edges show a $J_{\mathrm{eff}}=1/2$ character of the magnetic moment as is argued in Sr${}_2$IrO${}_4$. The magnitude of moment, however, was found to be smaller than that of Sr${}_2$IrO${}_4$ by a factor of 5 to 6, implying that Sr${}_3$Ir${}_2$O${}_7$ is no longer a Mott insulator but a weak antiferromagnet. An evident change of the temperature dependence of the resistivity at $T_{\mathrm{N}}$, from almost temperature-independent resistivity to insulating, strongly suggests that the emergent weak magnetism controls the charge gap. The magnetic structure was found to be an out-of-plane collinear antiferromagnetic ordering in contrast to the in-plane canted antiferromagnetism in Sr${}_2$IrO${}_4$, originating from the strong bilayer antiferromagnetic coupling.

Figure 1

(a) The crystal and magnetic structures of Sr${}_3$Ir${}_2$O${}_7$. The dashed line denotes the unit cell. Note that the volume of the magnetic unit cell agrees with that of the lattice. We label eight iridium sites (gray circles, Ir$j$, $j=0...7$) for the following analysis of the magnetic structure. (b) In-plane resistivities of Sr${}_3$Ir${}_2$O${}_7$ and Sr${}_2$IrO${}_4$. (c and d) Magnetizations of Sr${}_3$Ir${}_2$O${}_7$ at 260 K and Sr${}_2$IrO${}_4$ at 5 K.[15]

Figure 2

(a) The resonant magnetic diffraction normalized by the charge scattering of Sr${}_2$IrO${}_4$ [$I_m$(1 0 22)$/I_c$(0 0 24)] and Sr${}_3$Ir${}_2$O${}_7$ [$I_m$(0 1 13)/$I_c$(0 0 20)]. (b) Temperature evolution of the magnetic diffraction (0 1 13). (c) Strong enhancement of the diffraction at the $L_{\mathrm{III}}$ edge ($c\hslash /\lambda =11.2$ keV) observed while only a small diffraction is observed at the $L_{\mathrm{II}}$ edge ($c\hslash /\lambda =12.8$ keV).

Figure 3

(a) Intensities of the resonant magnetic x-ray diffraction at (0 1 $l$) (blue circle). We encountered a technical difficulty in measuring (0 1 8) reflection by the geometry of the diffractometer, and this is missing. The orange dashed line is the calculated intensity for the antiferromagnetic intra-bi-layer coupling with moment parallel to the $c$ axis assuming a mixture of 90${}^{\circ }$ rotated domains by a factor of 0.7 to 0.3. See the text for details. (b) Calculated $|F_{01l}{|}^2$ of four possible magnetic structures with intra-bi-layer magnetic couplings ($f_4=\pm f_2$) and inter-bi-layer antiparallel (AP) and parallel (P) relations ($f_0=\mp f_2$). (c) The $|\left({\mathbf{\epsilon }}_{{\mathbf{\pi }}^{\prime }}\times {\mathbf{\epsilon }}_{\mathbf{\sigma }}\right)·{\widehat{\mathbf{e}}}_{\mathbf{\alpha }}{|}^2$ for ${\widehat{\mathbf{e}}}_{\mathbf{\alpha }}\parallel a,b$, and $c$.