Research ArticlePHYSICS

Resonant inelastic x-ray incarnation of Young’s double-slit experiment

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Science Advances  18 Jan 2019:
Vol. 5, no. 1, eaav4020
DOI: 10.1126/sciadv.aav4020
  • Fig. 1 Double-slit-type RIXS interferometry for an Ir2O9 bioctahedron.

    The incident plane wave (blue) resonantly excites a core electron on one of two equivalent Ir sites at r1 and r2. This intermediate state decays to a quasi-molecular final state, which is delocalized over both sites, i.e., without which-path information. The emitted x-rays interfere with each other, giving rise to a double-slit-type sinusoidal interference pattern as a function of the transferred momentum q, which points along r1r2.

  • Fig. 2 Crystal structure and quasi-molecular orbitals of Ba3CeIr2O9.

    (A) Layers of Ir2O9 bioctahedra (light green) are sandwiched between Ce layers. The two Ir ions are displaced by 2.5 Å along c. (B) All sketches refer to the hole representation. For a single Ir4+ site, the t2g level is split by a trigonal crystal field ΔCF into a1g and Embedded Image orbitals or by spin-orbit coupling λ (SOC) into j = 1/2 and 3/2 states. Real materials show both λ and ΔCF, which yields three distinct orbitals (right), where the two excited states are called spin-orbit exciton. (C and D) Sketches of quasi-molecular orbitals for two Ir4+ sites with dominant hopping and small ΔCF. Bonding and antibonding levels (27, 29) are depicted in red and blue, respectively. In (C), λ = 0, as on the left-hand side in (B). The ground state is the Embedded Image spin singlet with total S = 0 (green arrows). In (D), both spin-orbit coupling and hopping are large, as on the right-hand side in (B). Bonding and antibonding states are formed from local j states. The ground state is a total jdim = 0 singlet built from two j = 1/2 states (orange arrows). Vertical dashed arrows indicate the three lowest excitations, which correspond to peaks α, β, and γ in the RIXS spectra. Rigorous calculations of the eigenstates (see Materials and Methods and Supplementary Text) support that the simple picture plotted in (D) contains the essential character of the low-energy excitations.

  • Fig. 3 RIXS data of intra-t2g excitations in BCIO.

    (A) High-resolution RIXS spectra at T = 20 K for different transferred momenta q = (0 0 mQ) with integer m and Q = π/d = 2.914 ⋅ 2π/c, where d and c denote the intradimer Ir-Ir distance and the lattice constant, respectively. The spectra show a pronounced even/odd behavior with respect to m, reflecting the sinusoidal q dependence. Note that the elastic peak is suppressed in π polarization for a scattering angle of 2θ = 90° and that the data for 4Q to 7Q were measured at 2θ = 52°, 67°, 83°, and 101°, respectively. Accordingly, the elastic peak is strongest for 4Q. (B and C) Interference patterns in the RIXS intensity as a function of q. The data cover about 3.5 periods in Q, equivalent to more than 20 Brillouin zones (top axis). The intensity was integrated over the energy loss ranges indicated in the figure and normalized by the width ΔE of the respective energy range. Data in (B) were measured at 10 K with lower energy resolution of 0.36 eV, integrating over features α and β, to enhance the signal-to-noise ratio. The high-resolution data in (C) discriminate between the three peaks α (dark blue), β (light blue), and γ (brown). Solid lines depict fits using Embedded Image with the parameters Q, a0, a1, b0, and b1, as well as ϕ = 0 or π/2.

  • Fig. 4 Calculated RIXS data of BCIO.

    (A) Calculated RIXS spectra are plotted for the same q values as the experimental data in Fig. 3, reproducing peaks α, β, and γ, as well as their pronounced even/odd behavior with respect to Q (see Supplementary Text for more details). (B) Interference patterns as a function of q for peaks α, β, and γ, which have to be compared with the experimental result depicted in Fig. 3C. Parameters are Embedded Image = 1.1 eV, Embedded Image = 0.5 eV, U = 1.0 eV, JH = 0.3 eV, ΔCF = −0.2 eV, and λ = 0.45 eV (see Supplementary Text).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/1/eaav4020/DC1

    Supplementary Text

    Fig. S1. Sample of Ba3CeIr2O9 used for single-crystal x-ray diffraction (left) and sketch of an Ir2O9 bioctahedron with face-sharing octahedra (right).

    Fig. S2. RIXS spectra of Ba3Ti2.7Ir0.3O9.

    Fig. S3. Absence of dispersion in the RIXS spectra.

    Fig. S4. RIXS spectra calculated with reduced width.

    Table S1. Structural parameters determined by x-ray diffractometry.

    References (3035)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • Fig. S1. Sample of Ba3CeIr2O9 used for single-crystal x-ray diffraction (left) and sketch of an Ir2O9 bioctahedron with face-sharing octahedra (right).
    • Fig. S2. RIXS spectra of Ba3Ti2.7Ir0.3O9.
    • Fig. S3. Absence of dispersion in the RIXS spectra.
    • Fig. S4. RIXS spectra calculated with reduced width.
    • Table S1. Structural parameters determined by x-ray diffractometry.
    • References (3035)

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