Determination of Hund's coupling in $5d$ oxides using resonant inelastic x-ray scattering

Determination of Hund's coupling in $5 d$ oxides using resonant inelastic x-ray scattering

Bo Yuan, J. P. Clancy, A. M. Cook, C. M. Thompson, J. Greedan, G. Cao, B. C. Jeon, T. W. Noh, M. H. Upton, D. Casa, T. Gog, A. Paramekanti, and Young-June Kim

Phys. Rev. B 95, 235114 – Published 8 June 2017

Abstract

We report resonant inelastic x-ray scattering (RIXS) measurements on ordered double-perovskite samples containing ${Re}^{5 +}$ and ${Ir}^{5 +}$ with $5 d^{2}$ and $5 d^{4}$ electronic configurations, respectively. In particular, the observed RIXS spectra of ${Ba}_{2} {YReO}_{6}$ and ${Sr}_{2} M {IrO}_{6}$ ( $M$ = Y, Gd) show sharp intra- $t_{2 g}$ transitions, which can be quantitatively understood using a minimal “atomic” Hamiltonian incorporating spin-orbit coupling $λ$ and Hund's coupling $J_{H}$ . Our analysis yields $λ = 0.38 (2) eV$ with $J_{H} = 0.26 (2) eV$ for ${Re}^{5 +}$ and $λ = 0.42 (2) eV$ with $J_{H} = 0.25 (4) eV$ for ${Ir}^{5 +}$ . Our results provide sharp estimates for Hund's coupling in $5 d$ oxides and suggest that it should be treated on equal footing with spin-orbit interaction in multiorbital $5 d$ transition-metal compounds.

Received 23 January 2017

DOI:https://doi.org/10.1103/PhysRevB.95.235114

Physics Subject Headings (PhySH)

Spin-orbit coupling

Iridates

Electron-correlation calculations Resonant inelastic x-ray scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Bo Yuan¹, J. P. Clancy¹, A. M. Cook^1,2, C. M. Thompson^3,*, J. Greedan^3,4, G. Cao⁵, B. C. Jeon^6,7, T. W. Noh^6,7, M. H. Upton⁸, D. Casa⁸, T. Gog⁸, A. Paramekanti¹, and Young-June Kim^1,†

¹Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7
²Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
³Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario, Canada L8S 4L8
⁴Brockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario, Canada L8S 4L8
⁵Department of Physics, University of Colorado Boulder, Boulder, Colorado 80309, USA
⁶Center for Correlated Electron Systems, Institute for Basic Science, Seoul 08826, Republic of Korea
⁷Department of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of Korea
⁸XSD, Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA

^*Present address: Department of Chemistry, Purdue University, 560 Oval Drive, West Lafayette, Indiana 47907-2084, USA.
^†yjkim@physics.utoronto.ca

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Vol. 95, Iss. 23 — 15 June 2017

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Images

Figure 1
Incident energy $E_{i}$ dependence of ${Ba}_{2} {YReO}_{6}$ RIXS spectra. The RIXS intensity is plotted as a function of incident energy $E_{i}$ (vertical axis) and energy transfer $ℏ ω$ (horizontal axis). An arbitrary intensity scale is used, where blue (red) denotes higher (lower) intensity.
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Figure 2
RIXS spectra of (a) Ir double perovskites and (b) Re double perovskites. Main panels show details of intra- $t_{2 g}$ excitations in the energy range $ℏ ω < 2.5 eV$ , while full RIXS spectra covering a wide range of energy transfer $ℏ ω < 10 eV$ are shown in the insets. Incident energies $E_{i} = 11.215$ keV and $E_{i} = 11.961$ keV with fixed $Q$ near $2 θ = 90^{\circ}$ were used to obtain spectra in (a) and (b), respectively. The scans are vertically offset for visual clarity, and the intensity scale is arbitrary. The arrow in (a) indicates the weak $\sim 2$ eV feature (see text). The thick blue line in (b) is a fit to the ${Ba}_{2} {YReO}_{6}$ spectrum as described in the text. Contributions from individual peaks are shown as black solid lines. The dashed line indicates the sloping quartic background.
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Figure 3
Calculated excitation energies as a function of $J_{H} / λ$ are plotted as solid black lines for (a)–(c) Ir and (d) Re double perovskites for indicated $λ$ values. Experimentally determined excitation energies [Ir DP: 0.39(2), 0.66(2), and 1.30(6) eV; Re DP: 0.49(3), 0.83(4), 1.85(5) eV] are plotted as horizontal colored bands (pink), whose widths reflect the experimental uncertainty. States involved in these transitions are labeled using nomenclature in the $J_{H} ≫ λ$ limit as ${}^{2 S + 1}L_{J}$ . (a) and (c) Incorrect and (b) and (d) correct choices of $λ$ as described in the text, which are indicated by $\times$ and $\sqrt$ , respectively. Green shaded regions in (b) and (d) illustrate $J_{H} / λ$ values for which all the observed modes intersect the calculated curves. The red arrow in (b) denotes the position of the weak feature $\sim 2$ eV in the Ir-DPs, which would correspond to the highest computed excitation energy.
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Figure 4
RIXS spectrum computed for $d^{4}$ iridates with $λ = 0.42 eV, J_{H} = 0.25 eV$ .
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Figure 5
RIXS spectrum of ${Ba}_{2} {YReO}_{6}$ at resonant ( $E_{i} = 11.961$ keV) and nonresonant incident energies (summed from $E_{i} = 11.969$ keV to $E_{i} = 11.971$ keV). The spectra have been scaled to have the same intensity at zero-energy transfer. The blue dashed line is fit to the spectrum at nonresonant energy and is used as the background. Inset: Inelastic features obtained by subtracting the background from the resonant spectrum. Clear spectral weight is observed for energy transfer $ℏ ω < 0.3 eV$ .
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Figure 6
RIXS spectra of ${Sr}_{2} {YIrO}_{6}$ at $Q = (7.40, 0, 0)$ and $Q = (7.40, 0.26, 0)$ . $E_{i} = 11.215$ keV was used in obtaining both spectra. An arbitrary intensity scale is used, and the spectra are shifted for visual clarity.
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