Magnetic Excitations across the Metal-Insulator Transition in the Pyrochlore Iridate ${\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$

We report a resonant inelastic x-ray scattering study of the magnetic excitation spectrum in a highly insulating ${\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ single crystal that exhibits a metal-insulator transition at $T_{\mathrm{MI}}=111(7)\mathrm{K}$. A propagating magnon mode with a 20 meV bandwidth and a 28 meV magnon gap is found in the excitation spectrum at 7 K, which is expected in the all-in–all-out magnetically ordered state. This magnetic excitation exhibits substantial softening as the temperature is raised towards $T_{\mathrm{MI}}$ and turns into a highly damped excitation in the paramagnetic phase. Remarkably, the softening occurs throughout the whole Brillouin zone including the zone boundary. This observation is inconsistent with the magnon renormalization expected in a local moment system and indicates that the strength of the electron correlation in ${\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ is only moderate, so that electron itinerancy should be taken into account in describing its magnetism.

Figure 1

The RIXS spectra at $T=7\mathrm{K}$. The spectrum at (7, 7, 7), the center of the structural and magnetic Brillouin zone, displays the elastic line profile fitted by a Gaussian line profile with $\mathrm{FWHM}=28\mathrm{meV}$ (top). The intensity is reduced by a factor of $10^4$ for comparison with the other spectra. The fitting curves for the spectra at $\mathit{q}=(0.1,0.1,0.1)$ and (0.5, 0.5, 0.5) ($\mathit{q}\equiv \mathit{Q}-\mathit{G}$) comprise the elastic background (solid black line), inelastic peak from the magnetic excitation (red line), and inelastic background continuum (dashed black line) (middle and bottom). The spectra are shifted vertically for clarity.

Figure 2

The RIXS spectra at $T=7\mathrm{K}$ along the high symmetric directions: the $\mathrm{\Gamma }\to L$ (a), $\mathrm{\Gamma }\to K$ (b), and $\mathrm{\Gamma }\to X$ (c) lines in the Brillouin zone centered at $\mathit{G}=(7,7,7)$. (d) Intensity map of the RIXS spectra. The open circles denote the ${\omega }_{\mathit{q}}$ positions of the magnetic excitations. The inset shows the Brillouin zone and notations for high symmetry positions.

Figure 3

(a) Intensity maps of the RIXS spectra along the $\mathrm{\Gamma }\to L$ line at $T=7$ (left) and 95 K (right). Magnetic excitation monitored at $\mathit{Q}=(7.1,7.1,7.1)$ near the $\mathrm{\Gamma }$ point (b) and at (7.5, 7.5, 7.5), the $L$ point (c) for selected temperatures. The shaded peaks represent the damped harmonic oscillator model fitting of the magnetic excitations. The elastic peak and the temperature-independent (except for the Bose factor) continuum background are denoted as solid and dashed black lines, respectively. The ${\omega }_{\mathit{q}}$ (open arrow) starts to be lower than the apparent position at high temperatures due to the Bose thermal factor. (d) Dispersive magnetic excitations along the $\mathrm{\Gamma }\to L$ line at 7 (square), 95 (circle), and 125 K (rhombus). The solid lines are spin-wave fitting as described in the text. The gray and green dashed lines simulate magnon dispersion with $(\mathrm{\Delta },J)=(17\mathrm{meV},40\mathrm{meV})$ and (0 meV, 22 meV), respectively. (e) The temperature dependence of the imaginary part of spin susceptibility ${\chi }^{\prime \prime }$ determined at (7.1, 7.1, 7.1) (square, left scale) and the integrated magnetic Bragg reflection intensity at (8, 6, 8) (circle, right scale). The solid line is a power law fit with $T_N=111(7)\mathrm{K}$ and $\beta =0.20(1)$ deviating from 0.325 known for the 3D Heisenberg magnet [26]. (f) Scaling of $J$ (circle) and $\mathrm{\Delta }$ (square) with the magnetic order parameter $|M|$. The dashed line is a guide to the eye.