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  • Letter
  • Open Access

Spin dynamics and possible topological magnons in the nonstoichiometric pyrochlore iridate Tb2Ir2O7 studied by RIXS

Q. Faure1,2,3,*, A. Toschi1,4, J. R. Soh5,4, E. Lhotel6, B. Detlefs1, D. Prabhakaran7, D. F. McMorrow3, and Ch. J. Sahle1

  • *Contact author: quentin.faure@cea.fr
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Phys. Rev. B 110, L140401 – Published 1 October, 2024

DOI: https://doi.org/10.1103/PhysRevB.110.L140401

Abstract

We report on a resonant inelastic x-ray scattering study on a single crystal of a nonstoichiometric pyrochlore iridate Tb2+xIr2−xO7−y (x≃0.25) that magnetically orders at TN≃50 K. We observe a propagating gapped magnon mode at low energy and model it using a Hamiltonian consisting of a Heisenberg exchange [J=16.2(9)meV] and Dzyaloshinskii-Moriya interactions [D=5.2(3)meV], which shows the robustness of interactions despite Tb stuffing at the Ir site. Strikingly, the ratio D/J=0.32(3) supports possible nontrivial topological magnon band crossing. This material may thus host coexisting fermionic and bosonic topology, with potential for manipulating electronic and magnonic topological bands thanks to the d−f interaction.

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References (55)

  1. W. Witczak-Krempa, G. Chen, Y. B. Kim, and L. Balents, Correlated quantum phenomena in the strong spin-orbit regime, Annu. Rev. Condens. Matter Phys. 5, 57 (2014).
  2. R. Schaffer, E. K.-H. Lee, B.-J. Yang, and Y. B. Kim, Recent progress on correlated electron systems with strong spin-orbit coupling, Rep. Prog. Phys. 79, 094504 (2016).
  3. J. G. Rau, E. K.-H. Lee, and H.-Y. Kee, Spin-orbit physics giving rise to novel phases in correlated systems: Iridates and related materials, Annu. Rev. Condens. Matter Phys. 7, 195 (2016).
  4. B. Yan and C. Felser, Topological materials: Weyl semimetals, Annu. Rev. Condens. Matter Phys. 8, 337 (2017).
  5. D. Pesin and L. Balents, Mott physics and band topology in materials with strong spin-orbit interaction, Nat. Phys. 6, 376 (2010).
  6. B.-J. Yang and Y. B. Kim, Topological insulators and metal-insulator transition in the pyrochlore iridates, Phys. Rev. B 82, 085111 (2010).
  7. X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates, Phys. Rev. B 83, 205101 (2011).
  8. W. Witczak-Krempa and Y. B. Kim, Topological and magnetic phases of interacting electrons in the pyrochlore iridates, Phys. Rev. B 85, 045124 (2012).
  9. A. Go, W. Witczak-Krempa, G. S. Jeon, K. Park, and Y. B. Kim, Correlation effects on 3D topological phases: From bulk to boundary, Phys. Rev. Lett. 109, 066401 (2012).
  10. H. Shinaoka, S. Hoshino, M. Troyer, and P. Werner, Phase diagram of pyrochlore iridates: All-in–all-out magnetic ordering and non-Fermi-liquid properties, Phys. Rev. Lett. 115, 156401 (2015).
  11. G. Chen and M. Hermele, Magnetic orders and topological phases from f−d exchange in pyrochlore iridates, Phys. Rev. B 86, 235129 (2012).
  12. K. Matsuhira, M. Wakeshima, Y. Hinatsu, and S. Takagi, Metal-insulator transitions in pyrochlore oxides Ln2Ir2O7, J. Phys. Soc. Jpn. 80, 094701 (2011).
  13. S. Zhao, J. M. Mackie, D. E. MacLaughlin, O. O. Bernal, J. J. Ishikawa, Y. Ohta, and S. Nakatsuji, Magnetic transition, long-range order, and moment fluctuations in the pyrochlore iridate Eu2Ir2O7, Phys. Rev. B 83, 180402(R) (2011).
  14. K. Tomiyasu, K. Matsuhira, K. Iwasa, M. Watahiki, S. Takagi, M. Wakeshima, Y. Hinatsu, M. Yokoyama, K. Ohoyama, and K. Yamada, Emergence of magnetic long-range order in frustrated pyrochlore Nd2Ir2O7 with metal-insulator transition, J. Phys. Soc. Jpn. 81, 034709 (2012).
  15. H. Sagayama, D. Uematsu, T. Arima, K. Sugimoto, J. J. Ishikawa, E. O'Farrell, and S. Nakatsuji, Determination of long-range all-in-all-out ordering of Ir4+ moments in a pyrochlore iridate Eu2Ir2O7 by resonant x-ray diffraction, Phys. Rev. B 87, 100403(R) (2013).
  16. S. M. Disseler, Direct evidence for the all-in/all-out magnetic structure in the pyrochlore iridates from muon spin relaxation, Phys. Rev. B 89, 140413(R) (2014).
  17. E. Lefrançois, V. Simonet, R. Ballou, E. Lhotel, A. Hadj-Azzem, S. Kodjikian, P. Lejay, P. Manuel, D. Khalyavin, and L. C. Chapon, Anisotropy-tuned magnetic order in pyrochlore iridates, Phys. Rev. Lett. 114, 247202 (2015).
  18. J. P. Clancy, H. Gretarsson, E. K. H. Lee, D. Tian, J. Kim, M. H. Upton, D. Casa, T. Gog, Z. Islam, B.-G. Jeon et al., X-ray scattering study of pyrochlore iridates: Crystal structure, electronic, and magnetic excitations, Phys. Rev. B 94, 024408 (2016).
  19. H. Guo, C. Ritter, and A. C. Komarek, Direct determination of the spin structure of Nd2Ir2O7 by means of neutron diffraction, Phys. Rev. B 94, 161102(R) (2016).
  20. R. Wang, A. Go, and A. J. Millis, Electron interactions, spin-orbit coupling, and intersite correlations in pyrochlore iridates, Phys. Rev. B 95, 045133 (2017).
  21. R. Wang, A. Go, and A. Millis, Weyl rings and enhanced susceptibilities in pyrochlore iridates: k·p analysis of cluster dynamical mean-field theory results, Phys. Rev. B 96, 195158 (2017).
  22. H. Zhang, K. Haule, and D. Vanderbilt, Metal-insulator transition and topological properties of pyrochlore iridates, Phys. Rev. Lett. 118, 026404 (2017).
  23. A. B. Sushkov, J. B. Hofmann, G. S. Jenkins, J. Ishikawa, S. Nakatsuji, S. Das Sarma, and H. D. Drew, Optical evidence for a Weyl semimetal state in pyrochlore Eu2Ir2O7, Phys. Rev. B 92, 241108(R) (2015).
  24. K. Ueda, J. Fujioka, B.-J. Yang, J. Shiogai, A. Tsukazaki, S. Nakamura, S. Awaji, N. Nagaosa, and Y. Tokura, Magnetic field-induced insulator-semimetal transition in a pyrochlore Nd2Ir2O7, Phys. Rev. Lett. 115, 056402 (2015).
  25. Z. Tian, Y. Kohama, T. Tomita, H. Ishizuka, T. H. Hsieh, J. J. Ishikawa, K. Kindo, L. Balents, and S. Nakatsuji, Field-induced quantum metal-insulator transition in the pyrochlore iridate Nd2Ir2O7, Nat. Phys. 12, 134 (2016).
  26. K. Ueda, T. Oh, B.-J. Yang, R. Kaneko, J. Fujioka, N. Nagaosa, and Y. Tokura, Magnetic-field induced multiple topological phases in pyrochlore iridates with Mott criticality, Nat. Commun. 8, 15515 (2017).
  27. B.-J. Yang and N. Nagaosa, Emergent topological phenomena in thin films of pyrochlore iridates, Phys. Rev. Lett. 112, 246402 (2014).
  28. X. Liu, S. Fang, Y. Fu, W. Ge, M. Kareev, J.-W. Kim, Y. Choi, E. Karapetrova, Q. Zhang, L. Gu et al., Magnetic Weyl semimetallic phase in thin films of Eu2Ir2O7, Phys. Rev. Lett. 127, 277204 (2021).
  29. M. Ghosh, D. Samal, and P. S. Anil Kumar, Spin chirality induced large topological Hall effect in magnetic Weyl semimetallic Eu2Ir2O7 (111) thin films, Phys. Rev. B 106, 085139 (2022).
  30. Y. Onose, T. Ideue, H. Katsura, Y. Shiomi, N. Nagaosa, and Y. Tokura, Observation of the magnon Hall effect, Science 329, 297 (2010).
  31. M. Mena, R. S. Perry, T. G. Perring, M. D. Le, S. Guerrero, M. Storni, D. T. Adroja, C. Rüegg, and D. F. McMorrow, Spin-wave spectrum of the quantum ferromagnet on the pyrochlore lattice Lu2V2O7, Phys. Rev. Lett. 113, 047202 (2014).
  32. P. Laurell and G. A. Fiete, Topological magnon bands and unconventional superconductivity in pyrochlore iridate thin films, Phys. Rev. Lett. 118, 177201 (2017).
  33. K. Hwang, N. Trivedi, and M. Randeria, Topological magnons with nodal-line and triple-point degeneracies: Implications for thermal Hall effect in pyrochlore iridates, Phys. Rev. Lett. 125, 047203 (2020).
  34. P. A. McClarty, Topological magnons: A review, Annu. Rev. Condens. Matter Phys. 13, 171 (2022).
  35. L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, Resonant inelastic x-ray scattering studies of elementary excitations, Rev. Mod. Phys. 83, 705 (2011).
  36. C. Donnerer, M. C. Rahn, M. M. Sala, J. G. Vale, D. Pincini, J. Strempfer, M. Krisch, D. Prabhakaran, A. T. Boothroyd, and D. F. McMorrow, All-in–all-out magnetic order and propagating spin waves in Sm2Ir2O7, Phys. Rev. Lett. 117, 037201 (2016).
  37. S. H. Chun, B. Yuan, D. Casa, J. Kim, C.-Y. Kim, Z. Tian, Y. Qiu, S. Nakatsuji, and Y.-J. Kim, Magnetic excitations across the metal-insulator transition in the pyrochlore iridate Eu2Ir2O7, Phys. Rev. Lett. 120, 177203 (2018).
  38. T. H. Nguyen, J. Son, S. Kim, H. Cho, C. H. Kim, Y. P. Wang, K. S. Burch, I.-S. Yang, J. Jeong, J.-G. Park et al., Topological magnon band crossing in Y2Ir2O7, Phys. Rev. Lett. 127, 267203 (2021).
  39. H. Jacobsen, C. D. Dashwood, E. Lhotel, D. Khalyavin, P. Manuel, R. Stewart, D. Prabhakaran, D. F. McMorrow, and A. T. Boothroyd, Strong quantum fluctuations from competition between magnetic phases in a pyrochlore iridate, Phys. Rev. B 101, 104404 (2020).
  40. J. N. Millican, R. T. Macaluso, S. Nakatsuji, Y. Machida, Y. Maeno, and J. Y. Chan, Crystal growth and structure of R2Ir2O7 (R = Pr, Eu) using molten KF, Mater. Res. Bull. 42, 928 (2007).
  41. See Supplemental Material at https://link.aps.org/supplemental/10.1103/PhysRevB.110.L140401 for detailed information about EDX measurements and spin-wave calculations as well as additional resonant x-ray scattering data, which includes Refs. [12, 33, 36, 37, 38, 42, 43, 44, 45, 46, 47, 48].
  42. M. M. Sala, K. Martel, C. Henriquet, A. Al Zein, L. Simonelli, C. Sahle, H. Gonzalez et al., A high-energy-resolution resonant inelastic X-ray scattering spectrometer at ID20 of the European Synchrotron Radiation Facility, J. Synchrotron Radiat. 25, 580 (2018).
  43. P. J. E. M. van der Linden, M. M. Sala, C. Henriquet, M. Rossi, K. Ohgushi, F. Fauth, L. Simonelli, C. Marini, E. Fraga, C. Murray et al., A compact and versatile dynamic flow cryostat for photon science, Rev. Sci. Instrum. 87, 115103 (2016).
  44. X. Liu, V. M. Katukuri, L. Hozoi, W.-G. Yin, M. P. M. Dean, M. H. Upton, J. Kim, D. Casa, A. Said, T. Gog et al., Testing the validity of the strong spin-orbit-coupling limit for octahedrally coordinated iridate compounds in a model system Sr3CuIrO6, Phys. Rev. Lett. 109, 157401 (2012).
  45. M. M. Sala, K. Ohgushi, A. Al-Zein, Y. Hirata, G. Monaco, and M. Krisch, CaIrO3: A spin-orbit Mott insulator beyond the jeff=1/2 ground state, Phys. Rev. Lett. 112, 176402 (2014).
  46. M. Elhajal, B. Canals, R. Sunyer, and C. Lacroix, Ordering in the pyrochlore antiferromagnet due to Dzyaloshinsky-Moriya interactions, Phys. Rev. B 71, 094420 (2005).
  47. R. Yadav, M. Pereiro, N. A. Bogdanov, S. Nishimoto, A. Bergman, O. Eriksson, J. van den Brink, and L. Hozoi, Heavy-mass magnetic modes in pyrochlore iridates due to dominant Dzyaloshinskii-Moriya interaction, Phys. Rev. Mater. 2, 074408 (2018).
  48. S. Toth and B. Lake, Linear spin wave theory for single-Q incommensurate magnetic structures, J. Phys.: Condens. Matter 27, 166002 (2015).
  49. C. Donnerer, M. C. Rahn, E. Schierle, R. S. Perry, L. S. I. Veiga, G. Nisbet, S. P. Collins, D. Prabhakaran, A. T. Boothroyd, and D. F. McMorrow, Selective probing of magnetic order on Tb and Ir sites in stuffed Tb2Ir2O7 using resonant x-ray scattering, J. Phys.: Condens. Matter 31, 344001 (2019).
  50. J. J. Ishikawa, E. C. T. O'Farrell, and S. Nakatsuji, Continuous transition between antiferromagnetic insulator and paramagnetic metal in the pyrochlore iridate Eu2Ir2O7, Phys. Rev. B 85, 245109 (2012).
  51. P. Telang, K. Mishra, A. K. Sood, and S. Singh, Dilute stuffing in the pyrochlore iridate Eu2Ir2O7, Phys. Rev. B 97, 235118 (2018).
  52. L. Hozoi, H. Gretarsson, J. P. Clancy, B.-G. Jeon, B. Lee, K. H. Kim, V. Yushankhai, P. Fulde, D. Casa, T. Gog et al., Longer-range lattice anisotropy strongly competing with spin-orbit interactions in pyrochlore iridates, Phys. Rev. B 89, 115111 (2014).
  53. E. K.-H. Lee, S. Bhattacharjee, and Y. B. Kim, Magnetic excitation spectra in pyrochlore iridates, Phys. Rev. B 87, 214416 (2013).
  54. J. Son, B. C. Park, C. H. Kim, H. Cho, S. Y. Kim, L. J. Sandilands, C. Sohn, J.-G. Park, S. J. Moon, and T. W. Noh, Unconventional spin-phonon coupling via the Dzyaloshinskii-Moriya interaction, npj Quantum Mater. 4, 17 (2019).
  55. M. Léger, F. Vayer, M. C. Hatnean, F. Damay, C. Decorse, D. Berardan, B. Fåk, J.-M. Zanotti, Q. Berrod, J. Ollivier et al., Impact of disorder in Nd-based pyrochlore magnets, Phys. Rev. B 109, 224416 (2024).

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Phys. Rev. B 110, L140401– Published 1 October, 2024
  • Received 9 April 2024
  • Accepted 18 September 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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