Charge density wave (CDW) order appears throughout the underdoped high-temperature cuprate superconductors, but the underlying symmetry breaking and the origin of the CDW remain unclear. We use X-ray diffraction to determine the microscopic structure of the CDWs in an archetypical cuprate YBa2Cu3O6.54 at its superconducting transition temperature ∼60 K. We find that the CDWs in this material break the mirror symmetry of the CuO2 bilayers. The ionic displacements in the CDWs have two components, which are perpendicular and parallel to the CuO2 planes, and are out of phase with each other. The planar oxygen atoms have the largest displacements, perpendicular to the CuO2 planes. Our results allow many electronic properties of the underdoped cuprates to be understood. For instance, the CDWs will lead to local variations in the electronic structure, giving an explicit explanation of density-wave states with broken symmetry observed in scanning tunnelling microscopy and soft X-ray measurements.

We report on a detailed x-ray resonant scattering study of the bilayer iridate compound Sr 3 Ir 2 O 7 at the Ir L 2 and L 3 edges. Resonant scattering at the Ir L 3 edge has been used to determine that Sr 3 Ir 2 O 7 is a long-range ordered antiferromagnet below T N ≈ 230 K with an ordering wave vector q = ( 1 2 , 1 2 ,0). The energy resonance at the L 3 edge was found to be a factor of ∼30 times larger than that at the L 2 edge. This remarkable effect has been seen in the single-layer compound Sr 2 IrO 4 and has been linked to the observation of a J eff = 1 2 spin-orbit insulator. Our result shows that despite the modified electronic structure of the bilayer compound, caused by the larger bandwidth, the effect of strong spin-orbit coupling on the resonant magnetic scattering persists. Using the program SARAh, we have determined that the magnetic order consists of two domains with propagation vectors k 1 = ( 1 2 , 1 2 ,0) and k 2 = ( 1 2 , − 1 2 ,0), respectively. A raster measurement of a focused x-ray beam across the surface of the sample yielded images of domains of the order of 100 μm, with odd and even L components, respectively. Fully relativistic, monoelectronic calculations using the Green's function technique for a muffin-tin potential have been employed to calculate the relative intensities of the L 2,3 edge resonances, comparing the effects of including spin-orbit coupling and the Hubbard U term. A large L 3 to L 2 edge intensity ratio (∼5) was found for calculations including spin-orbit coupling. Adding the Hubbard U term had no significant effect on the calculated spectra.

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