Structural Distortion-Induced Magnetoelastic Locking in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ Revealed through Nonlinear Optical Harmonic Generation

We report a global structural distortion in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ using spatially resolved optical second and third harmonic generation rotational anisotropy measurements. A symmetry lowering from an $I{4}_1/acd$ to $I{4}_1/a$ space group is observed both above and below the Néel temperature that arises from a staggered tetragonal distortion of the oxygen octahedra. By studying an effective superexchange Hamiltonian that accounts for this lowered symmetry, we find that perfect locking between the octahedral rotation and magnetic moment canting angles can persist even in the presence of large noncubic local distortions. Our results explain the origin of the forbidden Bragg peaks recently observed in neutron diffraction experiments and reconcile the observations of strong tetragonal distortion and perfect magnetoelastic locking in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$.

Figure 1

(a) Typical optical image of the (001) surface of a ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ single crystal. (b) Schematic of the RA experimental geometry. $P(S)$ polarization denotes an electric field lying parallel (perpendicular) to the scattering plane. (c) Layout of the scanning RA setup showing how the rotating scattering plane is created inside the reflective objective lens [25]. (d) Select THG-RA patterns taken in PS geometry obtained from regions 1–4 in panel (a).

Figure 2

SHG-RA patterns (open circles) taken under (a) $SS$, (b) $PS$, (c) $SP$, and (d) $PP$ geometries. The data were collected using 800 nm incident and 400 nm reflected light at $T=295\mathrm{K}$. The magnitudes of all patterns are normalized to the PP trace. Red and cyan lines are best fits to bulk electric quadrupole induced SHG-RA calculated using centrosymmetric $4/m$ and $4/mmm$ point groups, respectively. (e)–(h) Best fit results to bulk electric dipole induced SHG calculated using the three proposed noncentrosymmetric point groups $mm2$, 222, and 422 as well as the monoclinic point group $m$ for comparison. Responses that are absent in the plots are symmetry forbidden.

Figure 3

THG-RA patterns taken under (a) $SS$, (b) $PS$, (c) $SP$, and (d) $PP$ geometries. The data were collected using 1200 nm incident and 400 nm reflected light at both $T=295\mathrm{K}$ (black circles) and $T=180\mathrm{K}$ (green circles). The magnitudes of all patterns are normalized to the $PP$ trace. Red lines are best fits to the 295 K data using bulk electric dipole induced THG-RA calculated using the centrosymmetric $4/m$ point group.

Figure 4

(a) Illustration of an ${\mathrm{IrO}}_2$ plane in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. The oxygen octahedra rotate about the $c$ axis by $\pm \alpha$ creating a two sublattice structure. The magnetic moments couple to the lattice and exhibit canting angles $\pm \varphi$. (b) An unequal tetragonal distortion (${\mathrm{\Delta }}_1$ and ${\mathrm{\Delta }}_2$) on the two sublattices as required by the $I{4}_1/a$ space group. (c) The ratio $\varphi /\alpha$ as a function of both $\lambda$ and $\mathrm{\Delta }$ calculated for the case of uniform and (d) staggered (${\mathrm{\Delta }}_1=-{\mathrm{\Delta }}_2$) tetragonal distortion using Eq. (1), assuming a Coulomb energy $U_1=2.4\mathrm{eV}$, a Hund’s coupling $J_H=0.3\mathrm{eV}$, hopping $t=0.13\mathrm{eV}$, and $\alpha =11.5°$.