Doping Evolution of Magnetic Order and Magnetic Excitations in $({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{)}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$

We use resonant elastic and inelastic x-ray scattering at the Ir-$L_3$ edge to study the doping-dependent magnetic order, magnetic excitations, and spin-orbit excitons in the electron-doped bilayer iridate $({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{)}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ ($0\le x\le 0.065$). With increasing doping $x$, the three-dimensional long range antiferromagnetic order is gradually suppressed and evolves into a three-dimensional short range order across the insulator-to-metal transition from $x=0$ to 0.05, followed by a transition to two-dimensional short range order between $x=0.05$ and 0.065. Because of the interactions between the $J_{\mathrm{eff}}=\frac{1}{2}$ pseudospins and the emergent itinerant electrons, magnetic excitations undergo damping, anisotropic softening, and gap collapse, accompanied by weakly doping-dependent spin-orbit excitons. Therefore, we conclude that electron doping suppresses the magnetic anisotropy and interlayer couplings and drives $({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{)}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ into a correlated metallic state with two-dimensional short range antiferromagnetic order. Strong antiferromagnetic fluctuations of the $J_{\mathrm{eff}}=\frac{1}{2}$ moments persist deep in this correlated metallic state, with the magnon gap strongly suppressed.

Figure 1

(a) In-plane crystal structure and the rotation of the ${\mathrm{IrO}}_6$ octahedra ($\sim 12°$) around the $c$ axis. (b) $G$-type collinear antiferromagnetic order with moment along the $c$ axis. $J$, $J_2$, and $J_3$ are first, second, and third nearest superexchange couplings within the $ab$ plane, respectively. $J_c$ and $J_{2c}$ are first and second nearest couplings along the $c$ axis. (c) Schematic phase diagram of $({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{)}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$, adapted from Refs. [31, 32]. LAF and SAF are long range and short range antiferromagnetic order, respectively. The insulator-to-metal transition (IMT) occurs at $x\sim 0.04$. The dopings used in the present study are marked by red dots. (d) $L$ scan of the $c$-axis $G$-type antiferromagnetic order for $x=0$ and 0.03. (e),(f) Doping dependent $H$ and $L$ scans across the magnetic Bragg peak ($\frac{1}{2},\frac{1}{2},28$). The green solid curve in (e) is a fit of the $L$ scan for $x=0.05$. All the measurements were performed at 30 K unless otherwise indicated.

Figure 2

(a)–(c) In-plane momentum dependence of RIXS spectra of $({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{)}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ for $x=0,0.02$, and 0.065. (d),(e) Comparison of the elementary excitations between $x=0$, 0.02, 0.05, and 0.065 collected at $\mathbf{Q}=(\frac{1}{4},\frac{1}{4})$ and $(\frac{1}{2},0)$. For $x=0$, only magnetic excitations are shown. (f),(g) Doping-dependent magnetic excitations at $\mathbf{Q}=(\frac{1}{2},\frac{1}{2})$ and (0, 0). The insets in (d)–(g) illustrate the reciprocal space where the green dashed square and the pink solid square are the tetragonal Brillouin zone and the antiferromagnetic Brillouin zone, respectively. The pink filled circles mark the vector positions for (d)–(g). The vertical red dashed lines mark the peak position of the magnons for $x=0$. The blue and green arrows in (e) show the peak positions of the spin-orbit excitons and $\mathrm{\Delta }{E}_s$ marks the energy difference of the peak positions.

Figure 3

Doping-dependent magnon dispersions for $({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{)}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. To show the data clearly, the dispersions are split into two panels (a) $x=0$, 0.02, and 0.03 and (b) $x=0.05$ and 0.065. The dispersions for $x\le 0.05$ and the blue solid squares of $x=0.065$ are obtained by selecting the peak positions of the magnetic excitations. The blue open squares of $x=0.065$ are extracted from fitting of the magnetic excitations [39]. The solid curves are fits to the dispersions for $x=0.02$, 0.05, and 0.065 using the bilayer model, which includes an acoustic and an optical branch [29]. The pink dashed curve is the fitting of the dispersion for 0.065 using the $J-J_2-J_3$ model [23].