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We report a global structural distortion in Sr$_2$IrO$_4$ using spatially resolved optical second and third harmonic generation rotational anisotropy measurements. A symmetry lowering from an $I4_{1}/acd$ to $I4_{1}/a$ space group is observed both above and below the N{e}el temperature that arises from a staggered tetragonal distortion of the oxygen octahedra. By studying an effective super-exchange 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 non-cubic 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 magneto-elastic locking in Sr$_2$IrO$_4$.
An anomalous optical second-harmonic generation (SHG) signal was previously reported in Sr$_2$IrO$_4$ and attributed to a hidden odd-parity bulk magnetic state. Here we investigate the origin of this SHG signal using a combination of bulk magnetic su
We investigate the crystal structure and lattice vibrations of Sr$_2$IrO$_4$ by a combined phonon Raman scattering and x-ray powder diffraction experiment under pressures up to $66$ GPa and room temperature. Density functional theory (DFT) and $ab$-i
The effect of compression on the magnetic ground state of Sr$_2$IrO$_4$ is studied with x-ray resonant techniques in the diamond anvil cell. The weak interlayer exchange coupling between square-planar 2D IrO$_2$ layers is readily modified upon compre
We investigate the temporal evolution of electronic states in strontium iridate Sr$_2$IrO$_4$. The time resolved photoemission spectra of intrinsic, electron doped and the hole doped samples are monitored in identical experimental conditions. Our dat
The crystal lattice of Sr$_2$IrO$_4$ is investigated with synchrotron X-ray powder diffraction under hydrostatic pressures up to $P=43$ GPa and temperatures down to $20$ K. The tetragonal unit cell is maintained over the whole investigated pressure r