The magnetic structure and electronic ground state of the layered perovskite Ba(2)IrO(4) have been investigated using x-ray resonant magnetic scattering. Our results are compared with those for Sr(2)IrO(4), for which we provide supplementary data on its magnetic structure. We find that the dominant, long-range antiferromagnetic order is remarkably similar in the two compounds and that the electronic ground state in Ba(2)IrO(4), deduced from an investigation of the x-ray resonant magnetic scattering L(3)/L(2) intensity ratio, is consistent with a J(eff)=1/2 description. The robustness of these two key electronic properties to the considerable structural differences between the Ba and Sr analogues is discussed in terms of the enhanced role of the spin-orbit interaction in 5d transition metal oxides.

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.

Sr2IrO4 is a prototype of the class of Mott insulators in the strong spin-orbit interaction (SOI) limit described by a Jeff = 1/2 ground state. In Sr2IrO4, the strong SOI is predicted to manifest itself in the locking of the canting of the magnetic moments to the correlated rotation by 11.8(1)° of the oxygen octahedra that characterizes its distorted layered perovskite structure. Using x-ray resonant scattering at the Ir L3 edge we have measured accurately the intensities of Bragg peaks arising from different components of the magnetic structure. From a careful comparison of integrated intensities of peaks due to basal-plane antiferromagnetism, with those due to b-axis ferromagnetism, we deduce a canting of the magnetic moments of 12.2(8)°. We thus confirm that in Sr2IrO4 the magnetic moments rigidly follow the rotation of the oxygen octahedra, indicating that, even in the presence of significant non-cubic structural distortions, it is a close realization of the Jeff = 1/2 state.

Magnetism-the spontaneous alignment of atomic moments in a material-is driven by quantum mechanical exchange interactions that operate over interatomic distances. Some magnetic interactions cause 1,2 , or are caused by 3,4 , a twisting of arrangements of atoms. This can lead to the magnetoelectric e ect, predicted to play a prominent role in future technology, and to the phenomenon of weak ferromagnetism, governed by the so-called Dzyaloshinskii-Moriya interaction 5-8 . Here we determine the sign of the latter interaction in iron borate (FeBO 3 ) by using synchrotron radiation. We present a novel experimental technique based on the interference between two X-ray scattering processes, where one acts as a reference wave. Our experimental results are validated by state-ofthe-art ab initio calculations. Together, our experimental and theoretical approaches are expected to open up new possibilities for exploring, modelling and exploiting novel magnetic and magnetoelectric materials.There is considerable mystery behind the origins of complicated structures. Although the dominant short-range interactions that allow the building blocks to grow are well understood, the much more subtle forces that lead to a particular twisting at larger lengthscales, such as chiral biological molecules and liquid crystals 9 , and canted magnetic systems 3 , remain subjects of topical debate. In this Letter we seek to address this question for the case of magnetism. Our main findings are twofold: first, we demonstrate a novel and elegant experimental method for exploring magnetic materials with weak relativistic spin-orbit interactions, and second, we present a state-of-the-art quantum-mechanical many-body approach to the detailed description of such interactions in crystals. As a touchstone example we selected crystalline iron borate (FeBO 3 ), which is a strongly correlated electron system with a relatively simple crystal structure, nonetheless allowing a nontrivial canted and locally twisted magnetic ordering pattern. Taken together, these two strands demonstrate that modern condensed matter theory is capable of determining the elusive sign of the Dzyaloshinskii-Moriya interaction, and is thus able to elucidate the mechanism for coupling electric and magnetic degrees of freedom in magnetoelectric multiferroics, and to begin to predict the properties of this important class of materials.The interactions between atomic magnetic moments (or spins) are not direct, but mediated by the intervening matter. Coupling can be diminished through screening 10 , or enhanced, for example, by superexchange via oxygen atoms 11 . Moreover, the coupling is a property of the material and, according to Neumann's principle, must therefore possess all of its symmetries. The most general form of the bilinear coupling energy between two spins contains a scalar (isotropic) exchange term, exchange anisotropy (which we will neglect for the present discussion) and an antisymmetric term that reverses with permutation of the spin indices. The latter is the Dzyaloshi...

Abstract. This report presents azimuthal dependent and polarisation dependent xray resonant magnetic scattering at the Ir L 3 edge for the bilayered iridate compound, Sr 3 Ir 2 O 7 . Two magnetic wave vectors, k 1 =( 1 2 , 1 2 ,0) and k 2 =( 1 2 ,-1 2 ,0), result in domains of two symmetry-related G-type antiferromagnetic structures, noted A and B, respectively. These domains are approximately 0.02 mm 2 and are independent of the thermal history. An understanding of this key aspect of the magnetism is necessary for an overall picture of the magnetic behaviour in this compound. Azimuthal and polarisation dependence of magnetic reflections, relating to both magnetic wave vectors, show that the Ir magnetic moments in the bilayer compound are oriented along the c axis. This contrasts with single layer Sr 2 IrO 4 where the moments are confined to the ab plane.

The chemical and magnetic structures of the series of compounds Ca 2−x La x RuO 4 [x = 0, 0.05(1), 0.07(1), 0.12(1)] have been investigated using neutron diffraction and resonant elastic x-ray scattering. Upon La doping, the low-temperature S-P bca space group of the parent compound is retained in all insulating samples [x 0.07(1)], but with significant changes to the atomic positions within the unit cell. These changes can be characterized in terms of the local RuO 6 octahedral coordination: with increasing doping, the structure, crudely speaking, evolves from an orthorhombic unit cell with compressed octahedra to a quasitetragonal unit cell with elongated ones. The magnetic structure on the other hand, is found to be robust, with the basic k = (0,0,0), b-axis antiferromagnetic order of the parent compound preserved below the critical La doping concentration of x ≈ 0.11. The only effects of La doping on the magnetic structure are to suppress the A-centred mode, favoring the B mode instead, and to reduce the Néel temperature somewhat. Our results are discussed with reference to previous experimental reports on the effects of cation substitution on the d 4 Mott insulator Ca 2 RuO 4 , as well as with regard to theoretical studies on the evolution of its electronic and magnetic structure. In particular, our results rule out the presence of a proposed ferromagnetic phase, and suggest that the structural effects associated with La substitution play an important role in the physics of the system.

We observe and explain theoretically a dramatic evolution of the Dzyaloshinskii-Moriya interaction (DMI) in the series of isostructural weak ferromagnets, MnCO_{3}, FeBO_{3}, CoCO_{3}, and NiCO_{3}. The sign of the interaction is encoded in the phase of the x-ray magnetic diffraction amplitude, observed through interference with resonant quadrupole scattering. We find very good quantitative agreement with first-principles electronic structure calculations, reproducing both sign and magnitude through the series, and propose a simplified "toy model" to explain the change in sign with 3d shell filling. The model gives insight into the evolution of the DMI in Mott and charge transfer insulators.

Nonlinear interactions between X-rays and long wavelength radiation can be used as a powerful atomic-scale probe for light-matter interactions and for properties of valence electrons. However, reported X-ray nonlinear effects were small and their observations required tremendous efforts. Here we report the observation of strong nonlinearities in parametric down-conversion (PDC) of X-rays to long wavelength radiation in gallium arsenide and lithium niobate crystals, with efficiencies about 4 orders of magnitude stronger than the efficiencies measured in any material studied before. Furthermore, we show that the efficiency in the ferroelectric phase of strontium barium niobite is two orders of magnitude stronger than in its paraelectric phase. This observation suggests that the lack of inversion symmetry is the origin for the strong observed nonlinearity. Additionally, we demonstrate the ability to use the effect for the investigation of the spectral response of non-centrosymmetric materials at wavelengths ranging from infrared to soft X-rays.