Symmetry-Resolved Two-Magnon Excitations in a Strong Spin-Orbit-Coupled Bilayer Antiferromagnet

We used a combination of polarized Raman spectroscopy and spin wave calculations to study magnetic excitations in the strong spin-orbit-coupled bilayer perovskite antiferromagnet ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. We observed two broad Raman features at $\sim 800$ and $\sim 1400{\mathrm{cm}}^{-1}$ arising from magnetic excitations. Unconventionally, the $\sim 800{\mathrm{cm}}^{-1}$ feature is fully symmetric ($A_{1g}$) with respect to the underlying tetragonal ($D_{4h}$) crystal lattice which, together with its broad line shape, definitively rules out the possibility of a single magnon excitation as its origin. In contrast, the $\sim 1400{\mathrm{cm}}^{-1}$ feature shows up in both the $A_{1g}$ and $B_{2g}$ channels. From spin wave and two-magnon scattering cross-section calculations of a tetragonal bilayer antiferromagnet, we identified the $\sim 800{\mathrm{cm}}^{-1}$ ($1400{\mathrm{cm}}^{-1}$) feature as two-magnon excitations with pairs of magnons from the zone-center $\mathrm{\Gamma }$ point (zone-boundary van Hove singularity $X$ point). We further found that this zone-center two-magnon scattering is unique to bilayer perovskite magnets which host an optical branch in addition to the acoustic branch, as compared to their single layer counterparts. This zone-center two-magnon mode is distinct in symmetry from the time-reversal symmetry broken “spin wave gap” and “phase mode” proposed to explain the $\sim 92\mathrm{meV}$ ($742{\mathrm{cm}}^{-1}$) gap in resonant inelastic x-ray spectroscopy magnetic excitation spectra of ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$.

Figure 1

Crystalline and magnetic structures of ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. (a) The expanded unit cell for the bilayer AFM ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$, where gray octahedra are the oxygen octahedra, gray spheres are the Ir atoms, and orange and yellow arrows are $J_{\mathrm{eff}}=\pm 1/2$ magnetic moments. (b) Top view of a layer of IrO cages, where $J$ stands for the nearest-neighbor intralayer exchange coupling. (c) Side view of two layers of IrO cages within a bilayer, where $J_c$ stands for the nearest-neighbor interlayer exchange coupling. $a$, $b$, and $c$ are crystal axes. The yellow-red colored patterns in (b) and (c) are for the $J_{\mathrm{eff}}=\pm 1/2$ wave functions.

Figure 2

Temperature dependent magnetic Raman spectra of ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. (a) Raman spectra taken over a temperature range from 300 down to 8 K with linearly polarized incident (whose polarization is at about 45° from crystal axis (a) and unpolarized scattered light, where the spectra above 200 K are multiplied by a factor of 2. These spectra are offset vertically for clarity. $M_1$ and $M_2$ label the two broad continuums shaded in red and yellow, respectively. (b) Temperature dependence of the extracted peak intensities for $M_1$ and $M_2$. (c) Temperature dependence of the extracted central frequencies for $M_1$ and $M_2$. The error bars in (b) and (c) are defined by one standard error for the extracted parameters.

Figure 3

Symmetry selection rules for the magnetic excitations in ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. Raman spectra were taken at 80 K in four polarization channels: $aa$, $a^{\prime }{a}^{\prime }$, $ab$, and $a^{\prime }{b}^{\prime }$. The insets indicate the polarization channels and the selected symmetry modes under the $D_{4h}$ point group.

Figure 4

Theoretical calculations for magnetic excitations in ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. (a) Calculated magnon band dispersions along the high symmetry cut in the momentum space $\mathrm{\Gamma }\text{−}X\text{−}M$ (left), magnon DOS (middle), and two-magnon scattering cross section in the $A_{1g}$ and $B_{2g}$ channels (right) under the nearest-neighbor (inset) and the longer-range (main panels) exchange coupling approximation. The magnon dispersions and DOS share the same vertical axis (left side axis) while the two-magnon cross section has its own vertical axis (right side axis). (b) Schematics to illustrate the magnetic ground states and two-spin excitations as a function of $r=J_c/J$.