Strong anisotropy within a Heisenberg model in the $J_{\text{eff}}=\frac{1}{2}$ insulating state of ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.8}{\mathrm{Ru}}_{0.2}{\mathrm{O}}_4$

The dispersive magnetic excitations in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ have previously been well described within an isospin-1/2 Heisenberg model on a square lattice that revealed parallels with ${\mathrm{La}}_2{\mathrm{CuO}}_4$. Here we investigate the inelastic spectra of ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.8}{\mathrm{Ru}}_{0.2}{\mathrm{O}}_4$ with resonant inelastic x-ray scattering (RIXS) at the Ir $L_3$ edge. The results are well described using linear spin-wave theory within a similar Heisenberg model applicable to ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$; however, the disorder induced by the substitution of $20\%{\mathrm{Ir}}^{4+}$ ions for ${\mathrm{Ru}}^{4+}$ removes longer range exchange interactions. A large spin gap (40 meV) is measured indicating strong anisotropy from spin-orbit coupling that is manifest due to the altered magnetic structure in ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.8}{\mathrm{Ru}}_{0.2}{\mathrm{O}}_4$ with $c$-axis aligned moments compared to the basal plane moments in the parent. Collectively the results indicate the robustness of a Heisenberg model description even when the magnetic structure is altered and the $J_{\mathrm{eff}}=1/2$ moments are diluted.

Figure 1

(a) Structural (red circles) and magnetic (black circles) reciprocal space. High symmetry magnetic zone boundary points are indicated by the blue diamonds. $H$ and $K$ points are labeled along with the labeling in the square lattice notation used to describe the dispersions. The square lattice is rotated from the conventional lattice of ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.8}{\mathrm{Ru}}_{0.2}{\mathrm{O}}_4$. (b) Magnetic ground state of ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.8}{\mathrm{Ru}}_{0.2}{\mathrm{O}}_4$ has spins (red arrows) aligned along the $c$ axis. The nearest and next-nearest bonds are shown as thick and thin black lines, respectively. (c) RIXS measurements at the Ir $L$ edge along several high symmetry directions in the low resolution setup ($\mathrm{\Delta }E=90$ meV).

Figure 2

(a)–(e) High resolution RIXS ($\mathrm{\Delta }E=35$ meV) at the Ir $L_3$ edge following the low energy magnetic excitation along high symmetry directions. (f) FWHM of the magnetic excitation. (g) and (h) RIXS spectra around ($\pi ,\pi$) zone center. The elastic line (gray dashed line) and excitation (blue solid line) are shown. (i) RIXS map with the elastic line subtracted.

Figure 3

(a) Measured (circles) and calculated (solid line) dispersion along high symmetry directions and (b) measured (squares) and calculated (solid line) intensity. The dashed blue line is the dispersion for undoped ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ based on the Hamiltonian in Ref. [2]. (c) Calculated map of the dispersion and intensity.