Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate

Abstract

Evidence of an odd-parity hidden order in a strongly spin-orbit coupled correlated iridate Contents: S1. RA-SHG data for Sin-Pout and Sin-Sout geometries above and below TΩ show that the crystal structure of Sr2IrO4 belongs to the centrosymmetric tetragonal 4/m point group as opposed to the previously accepted 4/mmm point group 4,5 . Given the presence of inversion symmetry, the leading order contribution to SHG is the non-local term of electricquadrupole type, which can be expressed as an effective nonlinear polarization aswhere is the electric-quadrupole susceptibility tensor. By enforcing 4/m point group symmetry, is reduced to having 21 non-zero independent elements 6 :With the four additional constraints from degenerate SHG { = , = , = , = }, the number of non-zero independent tensor elements is further reduced to 17. The rotation of the crystal by an angle φ about the c-axis is carried out mathematically by applying a basis transformation on the reduced tensor from the original (primed) to rotated (unprimed) reference frame usingwhere ( ) is the rotation matrix about the c-axis. Finally, the expression that is used to fit theA is a constant determined by the experimental geometry, ( ) is the intensity of the incident 4 beam and ̂ is the polarization of the incoming or outgoing light, which we select to be either linearly P or S polarized. We note that previous work has already shown that there is no evidence of a surface electric-dipole contribution SHG 3 and that the crystallographic symmetry of the surface remains unchanged across TΩ 7 .ii) Fitting RA-SHG data for T < TThe low temperature RA-SHG data are fit to a coherent sum of the electric-quadrupole term described above and a hidden order induced electric-dipole term. The electric-dipole contribution is expressed as a nonlinear polarization (2 ) ∝ ( ) ( ). By enforcing 2/m magnetic point group symmetry, is reduced to having 14 non-zero independent elements:We only discuss the results using a 2/m magnetic point group here although the same procedure was applied to all of the magnetic point groups we surveyed. The additional constraints from degenerate SHG { = , = , = , = } leaves 10 non-zero independent tensor elements remaining. A basis transformation was then carried out on using ( ) = ′ ′ ′ ′ ′ ′ and the expression used to fit the RA-SHG data at Invariance of the magnetic structure under the elements of 2/m1 is explicitly shown in Figs S2 b-e. We note that the 2/m1 magnetic point group assignment does not rely on the magnitude of the magnetic moments on the two structural sub-lattices being equal, even though experimentally they are found to be so. S4. Loop-current order in cuprates versus iridatesLoop-current ordered phases were initially proposed in a three-band CuO2 model of the copperoxide planes where the charge currents are emergent complex hopping terms between oxygen and copper sites 8,9 . In this section, we examine how this model would be modified for Sr2IrO4.Our intention is not to elaborate on any of the details of loop-curr...

Magnetic ground state ofSr2IrO4and implications for second-harmonic generation

“…The existence of an SHG signal [5] points to a reduction of the magnetic space group symmetry 2/m1 previously indicated by neutrons and resonant x-ray measurements. Whether this reduction is due to orbital currents or another mechanism remains to be seen.…”

“…5. We argue that any such pattern breaking should in general lead to an SHG signal because of the resulting symmetry reduction.…”

“…5, looking for alternative explanations of the SHG signal, and as a byproduct address some important issues on the suppression of the resonant x-ray scattering (RXS) intensity at the Ir L 2 edge. To reach our goals, the present article is organized as follows: in Section II, we review the details of the crystal and mag-netic symmetries of Sr 2 IrO 4 , and show how RXS data on Rh-doped samples below T N might be explained in terms of the − + −+ state as well as the previously suggested + + ++ state [10][11][12].…”

Towards properties on demand in quantum materials

“…At present, state-of-the-art ultrafast methods offer a near-complete characterization of the transient state 152 . Indeed, tr-ARPES provides a direct probe of the transient electronic structure 66,67,120,153 , tabletop and accelerator-based X-ray free-electron lasers readily capture momentary crystal arrangements 118,154 , nonlinear optical methods can directly interrogate the symmetries of quantum phases and their host lattices 30,[155][156][157][158] , while optical and soft X-ray techniques document electronic excitations, in some cases with elemental and orbital specificity 159 . Importantly, mesoscopic phenomena that are prevalent in quantum materials lead to new time and energy scales, as documented in various ultrafast studies 110,160 .…”

Iridium's impact

“…As a heavy transition metal with partially filled 5d orbitals, the oxides would be expected to display metallic conductivity, yet relativistic effects (spin-orbit coupling to be precise) on the electronic structure, drive a number of the oxides into an insulating state. It is these insulators that have been predicted to display exotic magnetic and electronic physics 4 .…”