Raman scattering study of vibrational and magnetic excitations in ${\mathbf{Sr}}_{2-x}{\mathbf{La}}_x{\mathbf{IrO}}_4$

We have measured the doping and temperature dependence of lattice vibrations and magnetic excitations in the prototypical doped spin-orbit Mott insulator ${\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{IrO}}_4$ $(x=0$, 0.015, and 0.10). Our findings show that the pseudospin-lattice coupling—responsible for the renormalization of several low energy phonon modes—is preserved even when long-range magnetic order is suppressed by doping. In our most highly doped sample, the single magnon $(\mathrm{\Gamma }$ point) excitation disappears while the two-magnon mode softens and becomes heavily damped. Doping-induced electron-phonon coupling is also observed in a higher energy phonon mode. We observe two different electron-phonon interaction channels, which provide evidence of the coexistence of fluctuating magnetic moments and mobile carriers in doped iridates.

Figure 1

(a) Temperature-dependent magnetization of ${\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{IrO}}_4$ in field cooled warming mode with applied field of $H=5$ kOe perpendicular to the c axis. (b) Schematic phase diagram for ${\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{IrO}}_4$. Data were extracted from Ref. [12]. Long-range antiferromagnetic order is found in samples with $x=0$ and 0.015 while only a short-range antiferromagnetic order and a sizable Fermi surface is seen in $x=0.10$. Inset shows the $ab$ plane of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$, arrows indicate magnetic order.

Figure 2

Raman spectra of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ taken at $T=50\mathrm{K}$ using four different in-plane polarization. The arrows in the insets indicate the electric field vectors of the incident and the scattered light with respect to the unit cell of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. XX-channel probes the $A_{1g}+B_{1g}$ modes, XY the $B_{2g},{\mathrm{X}}^{\prime }{\mathrm{X}}^{\prime }$ the $A_{1g}+B_{2g}$, and ${\mathrm{X}}^{\prime }{\mathrm{Y}}^{\prime }$ the $B_{1g}$.

Figure 3

Doping and temperature dependence of the $A_{1g}+B_{1g}$ [top: (a), (c), and (e)] and the $B_{2g}$ [bottom: (b), (d), and (f)] phonon modes in ${\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{IrO}}_4$.

Figure 4

Detailed view of the doping and temperature dependence of the $278{\mathrm{cm}}^{-1}{A}_{1g}$ mode, included are the two new modes at $337{\mathrm{cm}}^{-1}$ and $342{\mathrm{cm}}^{-1}$ (triangle). The filled Lorentzian function represents the contribution from the $278{\mathrm{cm}}^{-1}$ mode.

Figure 5

Doping dependence of the (a) 188-${\mathrm{cm}}^{-1}{A}_{1g}$ phonon mode taken at high- and low-temperatures. Spectrum have been shifted for clarity. The filled area is a result of a fit (see text). (b) Temperature dependence of the inverse Fano asymmetry parameter, $1/\left|q\right|$. The dashed vertical lines represent $T_N$ for $x=0$ and 0.015 samples. Solid lines are a guide to the eye. (c) Calculated eigenvector of the 188-${\mathrm{cm}}^{-1}{A}_{1g}$ twisting mode.

Figure 6

Doping dependence of the (a) $191{\mathrm{cm}}^{-1}$ and (d) 395 ${\mathrm{cm}}^{-1}{B}_{2g}$ phonon modes taken at high and low temperatures. Spectrum have been shifted and scaled in intensity (where indicated) for clarity. The filled area is a result of a fit (see text). [(b) and (e)] Temperature dependence of their inverse Fano asymmetry parameter, $1/\left|q\right|$. The dashed vertical lines represent $T_N$ for $x=0$ and 0.015 samples. Solid lines are a guide to the eye. [(c) and (f)] The calculated eigenvectors.

Figure 7

Low-energy Raman spectra of the $B_{2g}$ single-magnon scattering in ${\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{IrO}}_4$ at selected temperatures. Both the Stokes and anti-Stokes part are shown. Spectrum have been shifted and scaled in intensity (where indicated) for clarity. The filled Lorentzians are a results of a fit (see text).

Figure 8

High-energy Raman spectra of the $B_{2g}$ modes showing the two-magnon scattering in ${\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{IrO}}_4$ as a function of doping. Spectrum have been shifted for clarity. For each doping level the spectrum at $T=30\mathrm{K}$ and $T=310\mathrm{K}$ is shown. The filled area emphasizes the change in spectral weight on cooling.

Figure 9

(a) Temperature dependence of the integrated intensity of the (a) single magnon excitation in ${\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{IrO}}_4$ $(x=0$ and $x=0.015)$ and (b) two-magnon scattering $(x=0,x=0.015$, and $x=0.10)$. Solid lines are a guide to the eye. In (a) the background at high temperature has been subtracted, while in (b), where the two-magnon persists to high temperature, the change in the integrated intensity is plotted with respect to $T=310\mathrm{K}$. Dashed vertical lines represent Neel temperature, determined from susceptibility measurements on the $x=0$ and $x=0.015$ samples.