Magnetic order and excitations in perovskite iridates studied with resonant X-ray scattering techniques

Transition metal oxides containing a 5d element are increasingly attracting attention as an arena in which to search for novel electronic states. These are proposed to derive from the interplay between the strong spin-orbit interaction (SOI) in the 5ds, the electronic correlations and crystal field effects. Iridium based compounds have featured predominantly in this quest, with considerable focus on the layered perovskites in which a novel “spin-orbit induced” Mott-like insulating state emerges. In this case, the SOI leads to the jeff = 1/2 ground state for the Ir4+ (5d5) ions observed in Sr2IrO4. In this thesis I demonstrate that resonant X-ray scattering techniques at the Ir L edges are a valuable tool to investigate the electronic and magnetic properties of iridium oxides. In particular the evolution of the jeff = 1/2 state as a function of structural distortions in the single layer iridates Sr2IrO4 and Ba2IrO4, and as a function of the dimensionality in the bilayer Sr3Ir2O7 is investigated. My findings show that the magnetic and electronic structures in the single layered perovskites are remarkably robust to structural distortions. Conversely, adding an extra IrO6 layer (Sr2IrO4 →Sr3Ir2O7) the ground and excited states change dramatically. Both these phenomena can be linked directly to the unique three-dimensional character of the jeff = 1/2 state. Furthermore, the X-ray resonant scattering cross-section of Ir4+ at the L2,3 edges, calculated in a single-ion model, shows a non-trivial dependence on the direction of the magnetic moment, μ. These results provide important insights into the interpretation of X-ray data from the iridates, including that a jeff = 1/2 ground state cannot be assigned on the basis of L2/L3 intensity ratio alone

Resonant X-Ray Scattering and the<i> j</i>_eff=1/2 Electronic Ground State in Iridate Perovskites

The resonant x-ray scattering (magnetic elastic, RXMS, and inelastic, RIXS) of Ir4+ at the L2,3 edges relevant to spin-orbit Mott insulators An+1IrnO3n+1 (A=Sr, Ba, etc.) are calculated using a single-ion model which treats the spin-orbit and tetragonal crystal-field terms on an equal footing. Both RXMS and RIXS in the spin-flip channel are found to display a nontrivial dependence on the direction of the magnetic moment, μ. Crucially, we show that for μ in the ab plane, RXMS in the cross-polarized channel at the L2 edge is zero irrespective of the tetragonal crystal field; spin-flip RIXS, relevant to measurements of magnons, behaves reciprocally, being zero at L2 when μ is perpendicular to the ab plane. Our results have important implications for the assignment of a jeff=1/2 ground state on the basis of resonant x-ray experiments

The J_{eff}=1/2 insulator Sr3Ir2O7 studied by means of angle-resolved photoemission spectroscopy

The low-energy electronic structure of the J_{eff}=1/2 spin-orbit insulator Sr3Ir2O7 has been studied by means of angle-resolved photoemission spectroscopy. A comparison of the results for bilayer Sr3Ir2O7 with available literature data for the related single-layer compound Sr2IrO4 reveals qualitative similarities and similar J_{eff}=1/2 bandwidths for the two materials, but also pronounced differences in the distribution of the spectral weight. In particuar, photoemission from the J_{eff}=1/2 states appears to be suppressed. Yet, it is found that the Sr3Ir2O7 data are in overall better agreement with band-structure calculations than the data for Sr2IrO4.Comment: 5 pages, 3 figure

Orbital occupancies and the putative jeff = 1/2 groundstate in Ba2IrO4: a combined oxygen K edge XAS and RIXS study

The nature of the electronic groundstate of Ba2IrO4 has been addressed using soft X-ray absorption and inelastic scattering techniques in the vicinity of the oxygen K edge. From the polarization and angular dependence of XAS we deduce an approximately equal superposition of xy, yz and zx Ir4+ 5d orbitals. By combining the measured orbital occupancies, with the value of the spin-orbit coupling provided by RIXS, we estimate the crystal field splitting associated with the tetragonal distortion of the IrO6 octahedra to be small, \Delta=50(50) meV. We thus conclude definitively that Ba2IrO4 is a close realization of a spin-orbit Mott insulator with a jeff = 1/2 groundstate, thereby overcoming ambiguities in this assignment associated with the interpretation of X-ray resonant scattering experiments.Comment: 5 pages, 5 figure

The importance of XY anisotropy in Sr2IrO4 revealed by magnetic critical scattering experiments

The magnetic critical scattering in Sr$_2$IrO$_4$ has been characterized using X-ray resonant magnetic scattering (XRMS) both below and above the 3D antiferromagnetic ordering temperature, T$_{\text{N}}$. The order parameter critical exponent below T$_{\text{N}}$ is found to be \beta=0.195(4), in the range of the 2D XYh$_4$ universality class. Over an extended temperature range above T$_{\text{N}}$, the amplitude and correlation length of the intrinsic critical fluctuations are well described by the 2D Heisenberg model with XY anisotropy. This contrasts with an earlier study of the critical scattering over a more limited range of temperature which found agreement with the theory of the isotropic 2D Heisenberg quantum antiferromagnet, developed to describe the critical fluctuations of the conventional Mott insulator La$_2$CuO$_4$ and related systems. Our study therefore establishes the importance of XY anisotropy in the low-energy effective Hamiltonian of Sr$_2$IrO$_4$, the prototypical spin-orbit Mott insulator.Comment: 6 pages, 4 figure

Antiferromagnetic order and domains in Sr3Ir2O7 probed by x-ray resonant scattering

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 Green's 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%.Comment: 9 pages, 9 figure

Critical fluctuations in the spin-orbit Mott Insulator Sr₃Ir₂O₇

X-ray magnetic critical scattering measurements and specific heat measurements were performed on the perovskite iridate Sr₃Ir₂O₇. We find that the magnetic interactions close to the N´eel temperature T_{N} = 283.4(2) K are threedimensional. This contrasts with previous studies which suggest two-dimensional behaviour like Sr₃IrO₄. Violation of the Harris criterion (dν > 2) means that weak disorder becomes relevant. This leads a rounding of the antiferromagnetic phase transition at T_{N}, and modifies the critical exponents relative to the clean system. Specifically, we determine that the critical behaviour of Sr₃Ir₂O₇ is representative of the diluted 3D Ising universality class

Persistence of antiferromagnetic order upon La substitution in the 4d44d^4 Mott insulator Ca2_2RuO4_4

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-Pbca space group of the parent compound is retained in all insulating samples [$x\leq0.07(1)$], but with significant changes to the atomic positions within the unit cell. These changes can be characterised 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 quasi-tetragonal 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 $x\approx0.11$. The only effects of La doping on the magnetic structure are to suppress the A-centred mode, favouring the B mode instead, and to reduce the N\'{e}el 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.Comment: 10 pages, 9 figure