Determination of long-range all-in-all-out ordering of Ir${}^{4+}$ moments in a pyrochlore iridate Eu${}_2$Ir${}_2$O${}_7$ by resonant x-ray diffraction

The pyrochlore-type iridium oxide Eu${}_2$Ir${}_2$O${}_7$ exhibits a metal-insulator transition at 120 K, accompanied by magnetic ordering. We used x-ray diffraction measurements with photon energies near the iridium $L_3$ absorption edge to analyze a single crystal to investigate the arrangement of Ir${}^{4+}$ magnetic moments. Resonant magnetic scattering at $\left(4n+200\right)$ was observed in the insulating phase, providing direct evidence of long-range ordering of Ir${}^{4+}$ magnetic moments with a propagation vector of $\mathit{q}=\left(000\right)$. Our single-crystal structure analysis revealed that the lattice retains its face-centered-cubic structure across the metal-insulator transition, indicating all-in-all-out magnetic order, where all the magnetic moments on the four vertices of each Ir tetrahedron point inward or outward.

Figure 1

(a) All-in-all-out magnetic structure where all four magnetic moments on the vertices of each tetrahedron point inward or outward. Arrows indicate the Ir${}^{4+}$ magnetic moments. (b) Coplanar magnetic order where four magnetic moments on a tetrahedron lie in the $\left(001\right)$ plane and are either antiparallel or orthogonal.

Figure 2

(a) Schematic view of the experimental setup for the resonant magnetic x-ray diffraction measurements. (b) Photograph of the Eu${}_{\mathbf{2}}$Ir${}_2$O${}_7$ single crystal used for the RXD experiment. (c) Ir-O network in the pyrochlore structure. Each Ir is coordinated to six O atoms. The IrO${}_6$ octahedra are connected by shared vertices to form a tetrahedral Ir network. Each IrO${}_6$ is compressed along a trigonal axis.

Figure 3

(a), (b) Profiles of the $\left(1000\right)$ reflections of Eu${}_2$Ir${}_2$O${}_7$ scanned along $\left(h00\right)$ in reciprocal space with a photon energy of 11.230 keV at several temperatures through the (a) $\sigma -{\sigma }^{\prime }$ and (b) $\sigma -{\pi }^{\prime }$ channels. (c) Temperature dependence of the integrated intensities of the $\left(1000\right)$ reflection detected though the $\sigma -{\sigma }^{\prime }$ (solid circles) and $\sigma -{\pi }^{\prime }$ (open circles) channels. (d) Temperature dependence of the electrical resistivity (solid line) and magnetic susceptibility (circles). The magnetic susceptibilities were measured for zero-field-cooling (ZFC; solid circles) and field-cooling (FC; open circles) processes in a field of 1000 Oe.

Figure 4

X-ray oscillation photographs of Eu${}_2$Ir${}_2$O${}_7$. Closeup pictures of two areas at (a), (d) 150 K and (c), (e) 30 K. Comparisons of the observed ($I_{\mathrm{obs}}$) and calculated ($I_{\mathrm{cal}}$) intensities of the reflections at (f) 150 K and (g) 30 K, where $x$ is the coordinate of the oxygen occupying the 48$f$ site.

Figure 5

Spectra of the intensity of the $\left(1000\right)$ reflection around the Ir $L_3$ edge in the $\sigma -{\sigma }^{\prime }$ and $\sigma -{\pi }^{\prime }$ channels. The inset shows an energy level scheme of the Ir${}^{4+}$ 5$d$ orbital, which is raised by the occupied octahedral ligand field. The long arrows show the electron excitation processes for the $L_3$ absorption edge. “A” and “B” denote the excitation from 2$p_{3/2}$ to $t_{2g}$ and that from 2$p_{3/2}$ to $e_g$, respectively.