This article reports a detailed x-ray resonant scattering study of the bilayer iridate compound, Sr3Ir2O7, at the Ir L2 and L3 edges. Resonant scattering at the Ir L3 edge has been used to determine that Sr3Ir2O7 is a long-range ordered antiferromagnet below TN 230K with an ordering wavevector, q=(1/2,1/2,0). The energy resonance at the L3 edge was found to be a factor of ~30 times larger than that at the L2. This remarkable effect has been seen in the single layer compound Sr2IrO4 and has been linked to the observation of a Jeff=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 programme SARAh, we have determined that the magnetic order consists of two domains with propagation vectors k1=(1/2,1/2,0) and k2=(1/2,-1/2,0), respectively. A raster measurement of a focussed x-ray beam across the surface of the sample yielded images of domains of the order of 100 microns size, with odd and even L components, respectively. Fully relativistic, monoelectronic calculations (FDMNES), using the Greens function technique for a muffin-tin potential have been employed to calculate the relative intensities of the L2,3 edge resonances, comparing the effects of including spin-orbit coupling and the Hubbard, U, term. A large L3 to L2 edge intensity ratio (~5) was found for calculations including spin-orbit coupling. Adding the Hubbard, U, term resulted in changes to the intensity ratio <5%.
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