Probing Excitations in Pyrochlore Iridates with Resonant Inelastic X-ray Scattering J.P. Clancy1, H. Gretarsson1, J. Kim2, M.H. Upton2, D. Casa2, T. Gog2, A.H. Said2, B.-G. Jeon3, B. Lee3, K.H. Kim3, and Y.J. Kim1 1University of Toronto, 2Argonne National Laboratory, 3Seoul National University Novel Physics in Pyrochlore Iridates • The pyrochlore iridates A2Ir2O7 (A = Y or lanthanide) have attracted considerable attention due to the potential for exotic physics driven by the interplay between electronic correlations, band topology, geometric frustration, and strong 5d spin-orbit coupling . • Proposed ground states for these materials include: fractional topological insulators/topological Mott insulators [2,3], topological (or Weyl) semi-metals [4-6], axion insulators [6,7], and chiral spin liquids . • Previous experimental work has shown that the electronic and magnetic properties of these materials are very sensitive to A-site cation size. [9-11] Physical behaviour can be tuned via chemical composition. Resonant Inelastic X-ray Scattering • Resonant Inelastic X-ray Scattering (RIXS) is a second-order scattering process which can be used to probe elementary excitations involving spin, orbital, charge, and lattice degrees of freedom . • RIXS is particularly well-suited to the study of iridates [17-20]: - Element specific probe of magnetic and electronic properties. - Small sample volumes required (<10 mg). - Large resonant enhancement at Ir L3 absorption edge (2p3/2 → 5d3/2,5/2 at Ei = 11.215 keV). - These materials are not amenable to conventional inelastic neutron scattering due to strong neutron absorption cross section and difficulty of synthesizing large single crystal samples. • Ir L3-edge RIXS measurements carried out using the Advanced Photon Source at Argonne National Lab. Elastic Scattering A Eu2Ir2O7 Electrical resistivity data courtesy of  Magnons, Phonons d-d Excitations (jeff=1/2→3/2) Magnetic susceptibility data courtesy of  “All-in, all-out” magnetic structure courtesy of  Pyrochlore iridate phase diagram courtesy of  • The majority of pyrochlore iridates (A = Dy to Nd) display simultaneous magnetic and metal-to-insulator phase transitions at TMI ~ Tc. The chief exceptions are A = Pr, which remains metallic and paramagnetic down to T < 30 mK, and A = Lu to Y, which order at TC but remain non-metallic up to room temperature. • The magnetic ground state below TMI has been predicted to display “all-in, all-out” (Q = 0) magnetic order [5,6]. Although such a state is difficult to experimentally verify, recent resonant magnetic x-ray scattering  and μSR  results are consistent with commensurate Q = 0 antiferromagnetic order. • By measuring the characteristic excitation spectra of the pyrochlore iridates, we hope to: 1. Identify the relevant energy scales associated with magnetic interactions (J), crystal field splitting (CEF, Δ), and spin-orbit coupling (SOC, λ). 2. Shed further light on the nature of the low temperature magnetic ground state. d-d Excitations in A2Ir2O7 (A = Y, Eu, Pr) eg MERIX Spectrometer at Advanced Photon Source Representative RIXS Spectrum (Pr2Ir2O7, T=300K, Q=7.5,7.5,7.5) • High resolution setup: Beamline 30-ID-B (MERIX) – Diamond-(111) primary mono, Si-(844) secondary mono, and spherical (2m) diced Si-(844) analyzer. Overall energy resolution of ΔE ~ 35 meV. • Low resolution setup: Beamline 9-ID-B – Si-(111) primary mono, Si-(444) secondary mono, spherical (1m) diced Si-(844) analyzer. Overall energy resolution of ΔE ~ 175 meV. • Sample Synthesis: Single crystal samples of Pr2Ir2O7 and Eu2Ir2O7 (~ 0.5 × 0.5 × 0.5 mm3) grown using KF flux methods as described in  Powder sample of Y2Ir2O7 synthesized as described in . • Electronic and magnetic properties of these systems appear to quite sensitive to sample stoichiometry . Electron Probe Microanalysis (EPMA) used to determine single crystal sample of Eu2Ir2O7 has actual stoichiometry of Eu2(1+x)Ir2(1-x)O7+d, with x = 0.09(2) and d = 0.06(2) Compound a (Å) x Electronic Magnetic Y2Ir2O7 10.18 0.333 Always Non-Metallic Tc ~ 150 K Eu2Ir2O7 10.28 0.331 TMI ~ 120 K Tc ~ 120 K Pr2Ir2O7 10.40 0.329 Always Metallic Tc < 30 mK Ir4+ (5d5) E3 Magnetic Excitations in A2Ir2O7 (A = Eu) Jeff = 1/2 E1 t2g E2 Jeff = 3/2 • Investigate low-lying inelastic scattering in single crystal Eu2Ir2O7 using high-resolution experimental set-up (ΔE ~ 35 meV). Observe broad, dispersive feature at ~ 45 meV. • Temperature dependence, incident energy dependence, and Q-dependence indicate that this feature is magnetic in origin. (7.8,7.8,7.8) Electronic level scheme for A2Ir2O7, constructed from the 3 branches of d-d excitations (E1, E2, E3) observed in the RIXS spectra (7.5,7.5,7.5) • Compare experimental data with ab initio calculations by L. Hozoi et al : Compound E1 (Exp) E1 (Calc) E2 (Exp) E2 (Calc) E3 (Exp) E3 (Calc) λ (SOC) Δ (CEF) Y2Ir2O7 0.53 eV 0.58 eV 0.98 eV 0.94 eV 3.87 eV 3.48-4.84 eV 0.43 eV 0.56 eV Eu2Ir2O7 0.59 eV 0.60 eV 0.95 eV 0.91 eV 3.68 eV 3.39-4.72 eV 0.46 eV 0.46 eV Pr2Ir2O7 0.52 eV --- 0.98 eV 3.40 eV 0.42 eV 0.57 eV --- --- • Multiconfiguration self-consistent field (MCSCF) and multireference configuration interaction (MRCI) calculations performed on finite cluster (6 adjacent IrO6 octahedra and neighbouring A-site cations). • Good agreement between experimental and theoretical values. • Model E1 and E2 with simple single-ion Hamiltonian: H0 = ll∙s – Dlz2 • Obtain reasonable values for spin-orbit coupling (λ), but surprisingly large trigonal crystal field splitting (Δ). • Δ remains large, even for calculations with idealized crystal structure/no distortion of IrO6 octahedra. • Δ must originate from long-range anisotropy – trigonal field produced by neighbouring A-site ions and IrO6. (7.2,7.2,7.2) Temperature dependence of low-lying magnetic excitations in Eu2Ir2O7, Q = (7.5,7.5,7.5) Momentum dependence of low-lying magnetic excitations in Eu2Ir2O7, T=25K U=6.5 U=6.0 U=6.5 U=6.0 U=6.0 U=5.5 U=6.0 U=5.5 U=5.0 U=5.5 U=5.0 U=4.5 U=5.0 U=4.5 U=5.5 w U=5.0 Mean Field Phase Diagram courtesy of  Incident energy dependence of RIXS spectra for Eu2Ir2O7 Dispersion of low-lying magnetic excitations in Eu2Ir2O7. Peak positions obtained from multi-Lorentzian/Gaussian fits to the data. • Dispersion of magnetic excitation along [HHH] is consistent with Q = 0 or all-in, all out ordering. • Width of excitation is much broader than experimental resolution (FWHM ~ 150-200 meV). Are finite lifetimes intrinsic or due to deviation from ideal stoichiometry? • Compare observed magnetic excitation spectrum with theoretical calculations by E.K.H. Lee et al : w Momentum dependence of d-d excitations in Eu2Ir2O7 d-d Excitations (t2g→eg) A U=4.5 B U=4.0 A U=4.5 B U=4.0 Calculation of RPA dynamical structure factor Dynamical structure factor after convolution with for several representative choices of electron experimental resolution function (~15 meV FWHM) correlation (U) and hopping amplitude (θ)  • Underscores need for higher experimental resolution and further development of RIXS instrumentation. • d-d excitations in Eu2Ir2O7 display no obvious dispersion – very different from perovskite iridates [17,18]. • Incident energy dependence demonstrates that these features occur at fixed energy loss (i.e. not fluorescence), and that they resonate near the Ir L3 edge (Ei ~ 11.216 keV for t2g, Ei ~ 11.219 keV for eg).  W. Witczak-Krempa et al, arXiv:1305.2193 (2013).  D.A. Pesin and L. Balents, Nat. Phys. 6, 376 (2010).  M. Kargarian et al, Phys. Rev. B 83, 165112 (2011).  B.J. Yang et al, Phys. Rev. B 82, 085111 (2010).  W. Witczak-Krempa et al, Phys. Rev. B 85, 045124 (2012).  X. Wan et al, Phys. Rev. B 83, 205101 (2011).  A. Go et al, Phys. Rev. Lett. 109, 066401 (2012).  Y. Machida et al, Nature 463, 210 (2010).  D. Yanagishima et al, J. Phys. Soc. Jpn. 70, 2880 (2001).  N. Taira et al, J. Phys.: Condens. Matt. 13, 5527 (2001).  K. Matsuhira et al, J. Phys. Soc. Jpn. 76, 043706 (2005).  H. Sagayama et al, Phys. Rev. B 87, 100403(R) (2013).  S. Zhao et al, Phys. Rev. B 83, 180402(R) (2011).  J.J. Ishikawa et al, Phys. Rev. B 85, 245109 (2012).  J.N. Millican et al, Mater. Res. Bull. 42, 928 (2007).  L.J.P. Ament et al, Rev. Mod. Phys. 83, 705 (2011).  J. Kim et al, Phys. Rev. Lett. 108, 177003 (2012).  J. Kim et al, Phys. Rev. Lett. 109, 157402 (2012).  H. Gretarsson et al, Phys. Rev. B 87, 220407 (2013).  H. Gretarsson et al, Phys. Rev. Lett. 110, 076402 (2013).  L. Hozoi et al, arXiv:1212.4009 (2012).  E.K.H. Lee et al, Phys. Rev. B 87, 214416 (2013). Acknowledgements • The authors would like to acknowledge valuable collaborations with L. Hozoi and J. van den Brink (IFW Dresden), V. Yushankai and P. Fulde (MPI Dresden), and E.K.H. Lee, S. Bhattacharjee, and Y.B. Kim (University of Toronto) • Funding for this work was provided by NSERC of Canada, the Banting Postdoctoral Fellowship Program, the Ontario Postdoctoral Fellowship Program, and the Canada Research Chair Program. • Use of the Advanced Photon Source is supported by the U.S. Dept. of Energy, Office of Basic Energy Sciences under Contract No. DE-AC02-06CH11357.