Dispersive magnetic and electronic excitations in iridate perovskites probed by oxygen $K$-edge resonant inelastic x-ray scattering

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Dispersive magnetic and electronic excitations in iridate perovskites probed by oxygen $K$ -edge resonant inelastic x-ray scattering

Xingye Lu, Paul Olalde-Velasco, Yaobo Huang, Valentina Bisogni, Jonathan Pelliciari, Sara Fatale, Marcus Dantz, James G. Vale, E. C. Hunter, Johan Chang, Vladimir N. Strocov, R. S. Perry, Marco Grioni, D. F. McMorrow, Henrik M. Rønnow, and Thorsten Schmitt

Phys. Rev. B 97, 041102(R) – Published 3 January 2018

Abstract

Resonant inelastic x-ray scattering (RIXS) experiments performed at the oxygen $K$ edge on the iridate perovskites ${Sr}_{2} {IrO}_{4}$ and ${Sr}_{3} {Ir}_{2} O_{7}$ reveal a sequence of well-defined dispersive modes over the energy range up to $\sim 0.8 eV$ . The momentum dependence of these modes and their variation with the experimental geometry allows us to assign each of them to specific collective magnetic and/or electronic excitation processes, including single and bimagnons, and spin-orbit and electron-hole excitons. We thus demonstrate that dispersive magnetic and electronic excitations are observable at the O $K$ edge in the presence of the strong spin-orbit coupling in the $5 d$ shell of iridium and strong hybridization between Ir $5 d$ and O $2 p$ orbitals, which confirm and expand theoretical expectations. More generally, our results establish the utility of O $K$ -edge RIXS for studying the collective excitations in a range of $5 d$ materials that are attracting increasing attention due to their novel magnetic and electronic properties. Especially, the strong RIXS response at O $K$ edge opens up the opportunity for investigating collective excitations in thin films and heterostructures fabricated from these materials.

Received 4 August 2017
Corrected 2 February 2018

DOI:https://doi.org/10.1103/PhysRevB.97.041102

Physics Subject Headings (PhySH)

Antiferromagnetism Excitons Magnons Spin-orbit coupling

Iridates Perovskites Strongly correlated systems

Resonant inelastic x-ray scattering

Condensed Matter, Materials & Applied Physics

Corrections

2 February 2018

Correction: A present address footnote was inserted for the tenth author.

Authors & Affiliations

Xingye Lu^1,*, Paul Olalde-Velasco^1,†, Yaobo Huang¹, Valentina Bisogni^1,‡, Jonathan Pelliciari^1,§, Sara Fatale², Marcus Dantz¹, James G. Vale³, E. C. Hunter⁴, Johan Chang^5,∥, Vladimir N. Strocov¹, R. S. Perry^6,7, Marco Grioni², D. F. McMorrow³, Henrik M. Rønnow⁵, and Thorsten Schmitt^1,¶

¹Research Department Synchrotron Radiation and Nanotechnology, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
²Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
³London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
⁴School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Mayfield Road, Edinburgh EH9 2TT, United Kingdom
⁵Laboratory for Quantum Magnetism, Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
⁶ISIS Neutron Spallation Source, Rutherford Appleton Laboratory (RAL), Harwell Campus, Didcot OX11 0QX, United Kingdom
⁷London Centre for Nanotechnology and UCL Centre for Materials Discovery, University College London, 17-19 Gordon Street, London WC1H 0AH, United Kingdom

^*Present address: Department of Physics, Beijing Normal University, Beijing 100875, China; xingye.lu@psi.ch
^†Present address: Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apdo. Postal J-48, Puebla, Puebla 72570, México.
^‡Present address: National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA.
^§Present address: Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
^∥Present address: Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland.
^¶thorsten.schmitt@psi.ch

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Vol. 97, Iss. 4 — 15 January 2018

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Images

Figure 1
(a) Schematic of the distorted IrO plane of ${Sr}_{2} {IrO}_{4}$ and ${Sr}_{3} {Ir}_{2} O_{7}$ . (b) The corresponding reciprocal space in tetragonal notation. The solid pink circle around the $Γ がんま$ point is the momentum coverage of O $K$ RIXS with $2 {θ しーた}_{s} = 130^{\circ}$ . The solid green lines mark the two directions $[H, 0]$ and $[H, H]$ we measured. (c) Schematic of elementary excitations of iridates in a single-ion picture. A denotes the single magnon, B and C spin-orbit excitons, and E the electron-hole exciton. ${Δ でるた}_{BC}$ marks the energy difference between B and C. (d) Schematics of the backscattering RIXS experimental setup. The blue arrows $k_{i}$ and $k_{f}$ denote the incident and scattered photons, where the polarizations are shown as a red arrow ( $π ぱい$ ) and a green dotted circle ( $σ しぐま$ ). The scattering angle is $2 {θ しーた}_{s} = 130^{\circ}$ . The projections of $q$ onto two reciprocal axes ( $q_{∥}$ and $q_{⊥}$ ) can be tuned continuously by changing $δ でるた$ . (e) and (f) X-ray absorption spectra at a grazing-incidence angle ( $δ でるた = - 45^{\circ}$ ) along $[H, 0]$ . The probed Ir $t_{2 g}$ orbitals ( $x y$ , $y z$ , and $z x$ ) are marked, where the subscripts A and P indicate that orbitals are probed via their hybridization with apical or plane oxygens. (g) and (h) Incident-energy dependence of the elementary excitations of ${Sr}_{2} {IrO}_{4}$ and ${Sr}_{3} {Ir}_{2} O_{7}$ , measured near the O $K$ edge with $π ぱい$ polarization and $δ でるた = - 45^{\circ}$ along $[H, 0]$ .
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Figure 2
Multi-Gaussian fitting of the RIXS spectra for (a) ${Sr}_{2} {IrO}_{4}$ and (b) ${Sr}_{3} {Ir}_{2} O_{7}$ . The spectra at three different $δ でるた$ 's are shown as open colored circles. From low- to high-energy loss, the Gaussian peaks (solid curves) denote the elastic peak (centered at zero energy loss), single magnon ( $A / A^{'}$ ), bimagnon (BM), electron-hole exciton (E), excitonic quasiparticle ( $B / B^{'}$ ), and spin-orbit exciton ( $C / C^{'}$ ). The dashed curves are the residual weight of the fitting.
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Figure 3
Momentum-dependent RIXS spectra along $[H, 0]$ and $[H, H]$ directions for (a) ${Sr}_{2} {IrO}_{4}$ and (b) ${Sr}_{3} {Ir}_{2} O_{7}$ . The inset in (b) illustrates the reciprocal space, where the pink diamond is the magnetic Brillouin zone and the solid pink circle the momentum coverage by O $K$ RIXS. The green lines are the $[H, 0]$ and $[H, H]$ high-symmetry directions for RIXS measurements. The red vertical lines mark the zero energy loss positions. The red, green, and blue markers indicate the fitted peak energies of the single magnons ( $A / A^{'}$ ), the electron-hole excitons (E), and the excitonic quasiparticles ( $B / B^{'}$ ), respectively.
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Figure 4
Dispersions of the collective modes in (a) ${Sr}_{2} {IrO}_{4}$ and (b) ${Sr}_{3} {Ir}_{2} O_{7}$ probed by O $K$ RIXS. From low- to high-energy loss, the green diamonds, blue squares, cyan circles, orange circles, and pink hexagons denote the single magnons ( $A / A^{'}$ ), bimagnons (BM), electron-hole excitons (E), spin-orbit excitons creating magnons ( $B / B^{'}$ ), and spin-orbit excitons ( $C / C^{'}$ ), respectively. The solid and open symbols are extracted from the spectra with $δ でるた < 0$ and $δ でるた > 0$ , respectively (Figs. 1 and 2). The open red circles are the single-magnon energies extracted from previous Ir $L_{3}$ RIXS measurements [15, 18]. The open black diamonds denote the dispersions of the excitonic quasiparticles extracted from Refs. [16, 50]. The black curve in (a) is a theoretical fit of the magnon dispersion using a Heisenberg model reported in Refs. [45, 46]. The black and red curves in (b) are transverse and longitudinal magnon dispersions for ${Sr}_{3} {Ir}_{2} O_{7}$ using the quantum-dimer model reported in Ref. [18]. The blue dashed curves are the expected lower bound of the bimagnon continuum.
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