Doping-driven structural distortion in the bilayer iridate ${\left({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x\right)}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$

Neutron single-crystal diffraction and rotational anisotropy optical second harmonic generation data are presented resolving the nature of the structural distortion realized in electron-doped (${\mathrm{Sr}}_{1-x}{\mathrm{La}}_x$)${}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ with $x=0.035$ and $x=0.071$. Once electrons are introduced into the bilayer spin-orbit assisted Mott insulator ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$, previous studies have identified the appearance of a low-temperature structural distortion and have suggested the presence of a competing electronic instability in the phase diagram of this material. Our measurements resolve a lowering of the structural symmetry from monoclinic $C2/c$ to monoclinic $P{2}_1/c$ and the creation of two unique Ir sites within the chemical unit cell as the lattice distorts below a critical temperature $T_S$. Details regarding the modifications to oxygen octahedral rotations and tilting through the transition are discussed as well as the evolution of the low-temperature distorted lattice as a function of carrier substitution.

Figure 1

Rotational anisotropy second harmonic generation (RA-SHG) patterns of $x=0.033$ (${\mathrm{Sr}}_{1-x}{\mathrm{La}}_x$)${}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ acquired under (a) ${\mathrm{P}}_{\text{in}}-{\mathrm{P}}_{\text{out}}$ and (b) ${\mathrm{S}}_{\text{in}}-{\mathrm{P}}_{\text{out}}$ polarization geometries below (black circles) and above (red circles) the structural phase transition temperature $T_S$. P and S indicate the photon polarization parallel and perpendicular to the scattering plane, respectively, and “in” and “out” designate the incident and scattered light, respectively. All intensities are normalized to the maximum value of the ${\mathrm{P}}_{\text{in}}-{\mathrm{P}}_{\text{out}}$ pattern at $T=120$ K. Black and red lines are best fits to the low and high temperature data, respectively, using an expression for bulk electric quadrupole SHG radiation from a centrosymmetric $4/m$ or $2/m$ crystallographic point group. The ${\mathrm{P}}_{\text{in}}-{\mathrm{S}}_{\text{out}}$ and ${\mathrm{S}}_{\text{in}}-{\mathrm{S}}_{\text{out}}$ data [24] yield the same conclusions.

Figure 2

Maps of reciprocal space in the [H, 0, L] plane and indexed in using the $C2/c$ space group for the $x=0.035$ sample at both 295 K ($T>T_S$) and at 100 K ($T<T_S$). Representative violations of the high temperature $C2/c$ space group that appear at 100 K are highlighted by pink circles within the maps. Peaks of the form $(odd,0,even)$ violate the twinned scattering conditions for the $C2/c$ cell.

Figure 3

Schematic showing the evolution of the crystal structure as the sample is cooled below $T_S$. Adjacent ${\mathrm{IrO}}_6$ octahedra connected to form a bilayer are shown for (a) $T>T_S$ in the $C2/c$ structure and (b) for $T<T_S$ in the $P{2}_1/c$ structure. Ir-O1-Ir bonds denote the coupling between the planes of a bilayer. Below $T_S$ basal plane oxygen positions as well as the outer apical O2 oxygen sites split into unique oxygen sites. Additionally, two chemically distinct Ir-sites appear within a single plane as illustrated by the checkerboard pattern of Ir1 and Ir2 oxygen octahedra illustrated in panel (c). Green spheres indicate Sr/La positions and red spheres indicate O positions.

Figure 4

Rotational pattern of ${\mathrm{IrO}}_6$ octahedral tilting within a bilayer of the $x=0.035$ crystal activated below $T_S$. The sense of correlated titling is illustrated looking down the $[0,1,1]$ and $[0,\overline{1},1]$ axes of the $C2/c$ unit cell where nearest neighbor ${\mathrm{IrO}}_6$ octahedra tilt with an opposite sense relative to one another.