Anisotropic exchange and spin-wave damping in pure and electron-doped ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$

The collective magnetic excitations in the spin-orbit Mott insulator ${\left({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x\right)}_2{\mathrm{IrO}}_4$ ($x=0,0.01,0.04,0.1$) were investigated by means of resonant inelastic x-ray scattering. We report significant magnon energy gaps at both the crystallographic and antiferromagnetic zone centers at all doping levels, along with a remarkably pronounced momentum-dependent lifetime broadening. The spin-wave gap is accounted for by a significant anisotropy in the interactions between $J_{\text{eff}}=1/2$ isospins, thus marking the departure of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ from the essentially isotropic Heisenberg model appropriate for the superconducting cuprates.

Figure 1

RIXS spectra along high-symmetry directions of the $(0,0,33)$ first BZ [see inset in (a)] for (a) $x=0$, (b) $x=0.01$, (c) $x=0.04$, and (d) $x=0.1$. The solid lines represent the fit to the 2DAH model discussed in the text (see Fig. 4). The spectra marked by the vertical dashed lines are plotted in Fig. 2. The data from different samples were normalized to the spectral weight around $E_{\text{loss}}=1$ eV of the $(0,0)$ spectrum.

Figure 2

Fit detail of representative RIXS spectra for samples with different La contents. Open symbols and solid lines represent the measured intensity and the fit of the spectra, respectively. The Voigt functions used to fit the elastic line and the various inelastic contributions (discussed in the text) are displayed through the shaded regions. The horizontal lines in the $x=0$ (same as $x=0.01,0.04$) and $x=0.1$ panels represent the Gaussian width of the resolution function (fixed during the fit). The spectra from different samples were normalized to the spectral weight around $E_{\text{loss}}=1$ eV of the $(0,0)$ spectrum.

Figure 3

Doping level dependence of the low-energy region of the RIXS spectra at (a) $(0,0)$ and (b) $(\pi ,\pi )$. The shaded regions show the fitted single-magnon peak, highlighting the presence of a finite spin-wave gap. The vertical dashed lines mark the value of the magnon energy in the parent compound $(x=0)$. The fitted magnon energies (and the corresponding $Q$-resolution-corrected values [24]) are reported in Table 1.

Figure 4

$Q$-resolution-corrected [24] energy dispersion (top) and Lorentzian lifetime broadening (bottom) of the single magnon for samples with different La contents. The error bars represent $1\sigma$ confidence intervals [apart from the energy at $(0,0)$ and $(\pi ,\pi )$, where the $2\sigma$ interval is reported instead]. The thick solid lines in color (top) show the fit to the 2DAH model as described in the text (best-fit values reported in Table 1), while the thin solid and dashed black lines represent the two modes calculated for the best-fit parameters.