- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Electric field induced thermal Hall effect of triplons in the quantum dimer magnets XCuCl3 (X=Tl,K)

Nanse Esaki* and Yutaka Akagi

Hosho Katsura

  • *Contact author: esaki-nanse0428@g.ecc.u-tokyo.ac.jp
PDF

Phys. Rev. Research 6, L032050 – Published 3 September, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L032050

Abstract

We theoretically propose the electric field induced thermal Hall effect of triplons in the quantum dimer magnets XCuCl3 (X=Tl,K), which exhibit ferroelectricity in the Bose-Einstein condensation phase of triplons. The interplay between ferroelectricity and magnetism in these materials leads to the magnetoelectric effect, i.e., an electric-field induced Dzyaloshinskii-Moriya (DM) interaction between spins on the same dimer. We argue that this intradimer DM interaction breaks the symmetry of the system in the absence of an electric field and gives rise to the thermal Hall effect, which can be detected in experimentally accessible electric and magnetic fields. We also show that the thermal Hall effect can be controlled by changing the strength or direction of the electric field.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (108)

  1. T. Nikuni, M. Oshikawa, A. Oosawa, and H. Tanaka, Bose-Einstein condensation of dilute magnons in TlCuCl3, Phys. Rev. Lett. 84, 5868 (2000).
  2. H. Tanaka, A. Oosawa, T. Kato, H. Uekusa, Y. Ohashi, K. Kakurai, and A. Hoser, Observation of field-induced transverse Néel ordering in the spin gap system TlCuCl3, J. Phys. Soc. Jpn. 70, 939 (2001).
  3. M. Matsumoto, B. Normand, T. M. Rice, and M. Sigrist, Magnon dispersion in the field-induced magnetically ordered phase of TlCuCl3, Phys. Rev. Lett. 89, 077203 (2002).
  4. A. Oosawa, T. Takamasu, K. Tatani, H. Abe, N. Tsujii, O. Suzuki, H. Tanaka, G. Kido, and K. Kindo, Field-induced magnetic ordering in the quantum spin system KCuCl3, Phys. Rev. B 66, 104405 (2002).
  5. M. Matsumoto, B. Normand, T. M. Rice, and M. Sigrist, Field-and pressure-induced magnetic quantum phase transitions in TlCuCl3, Phys. Rev. B 69, 054423 (2004).
  6. F. Yamada, T. Ono, H. Tanaka, G. Misguich, M. Oshikawa, and T. Sakakibara, Magnetic-field induced Bose–Einstein condensation of magnons and critical behavior in interacting spin dimer system TlCuCl3, J. Phys. Soc. Jpn. 77, 013701 (2008).
  7. T. Giamarchi, C. Rüegg, and O. Tchernyshyov, Bose-Einstein condensation in magnetic insulators, Nat. Phys. 4, 198 (2008).
  8. N. Cavadini, G. Heigold, W. Henggeler, A. Furrer, H.-U. Güdel, K. Krämer, and H. Mutka, Magnetic excitations in the quantum spin system TlCuCl3, Phys. Rev. B 63, 172414 (2001).
  9. N. Cavadini, C. Rüegg, A. Furrer, H.-U. Güdel, K. Krämer, H. Mutka, and P. Vorderwisch, Triplet excitations in low-Hc spin-gap systems KCuCl3 and TlCuCl3: An inelastic neutron scattering study, Phys. Rev. B 65, 132415 (2002).
  10. C. Rüegg, N. Cavadini, A. Furrer, H. Güdel, K. Krämer, H. Mutka, A. Wildes, K. Habicht, and P. Vorderwisch, Bose–Einstein condensation of the triplet states in the magnetic insulator TlCuCl3, Nature (London) 423, 62 (2003).
  11. S. Kimura, K. Kakihata, Y. Sawada, K. Watanabe, M. Matsumoto, M. Hagiwara, and H. Tanaka, Ferroelectricity by Bose-Einstein condensation in a quantum magnet, Nat. Commun. 7, 12822 (2016).
  12. S. Kimura, K. Kakihata, Y. Sawada, K. Watanabe, M. Matsumoto, M. Hagiwara, and H. Tanaka, Magnetoelectric effect in the quantum spin gap system TlCuCl3, Phys. Rev. B 95, 184420 (2017).
  13. S. Kimura, M. Matsumoto, M. Akaki, M. Hagiwara, K. Kindo, and H. Tanaka, Electric dipole spin resonance in a quantum spin dimer system driven by magnetoelectric coupling, Phys. Rev. B 97, 140406(R) (2018).
  14. S. Kimura, M. Matsumoto, and H. Tanaka, Electrical switching of the nonreciprocal directional microwave response in a triplon Bose-Einstein condensate, Phys. Rev. Lett. 124, 217401 (2020).
  15. R. Ramesh and N. A. Spaldin, Multiferroics: progress and prospects in thin films, Nat. Mater. 6, 21 (2007).
  16. S.-W. Cheong and M. Mostovoy, Multiferroics: a magnetic twist for ferroelectricity, Nat. Mater. 6, 13 (2007).
  17. M. Bibes and A. Barthélémy, Towards a magnetoelectric memory, Nat. Mater. 7, 425 (2008).
  18. T. Liu and G. Vignale, Electric control of spin currents and spin-wave logic, Phys. Rev. Lett. 106, 247203 (2011).
  19. Y. Tokura, S. Seki, and N. Nagaosa, Multiferroics of spin origin, Rep. Prog. Phys. 77, 076501 (2014).
  20. H. Yang, O. Boulle, V. Cros, A. Fert, and M. Chshiev, Controlling Dzyaloshinskii-Moriya interaction via chirality dependent atomic-layer stacking, insulator capping and electric field, Sci. Rep. 8, 12356 (2018).
  21. W. Zhang, H. Zhong, R. Zang, Y. Zhang, S. Yu, G. Han, G. L. Liu, S. S. Yan, S. Kang, and L. M. Mei, Electrical field enhanced interfacial Dzyaloshinskii-Moriya interaction in MgO/Fe/Pt system, Appl. Phys. Lett. 113, 122406 (2018).
  22. T. Srivastava, M. Schott, R. Juge, V. Krizakova, M. Belmeguenai, Y. Roussigné, A. Bernand-Mantel, L. Ranno, S. Pizzini, S.-M. Chérif et al., Large-voltage tuning of Dzyaloshinskii–Moriya interactions: A route toward dynamic control of skyrmion chirality, Nano Lett. 18, 4871 (2018).
  23. B. Rana and Y. Otani, Towards magnonic devices based on voltage-controlled magnetic anisotropy, Commun. Phys. 2, 90 (2019).
  24. C.-K. Li, X.-P. Yao, and G. Chen, Writing and deleting skyrmions with electric fields in a multiferroic heterostructure, Phys. Rev. Res. 3, L012026 (2021).
  25. S. Mankovsky, E. Simon, S. Polesya, A. Marmodoro, and H. Ebert, Electric-field control of exchange interactions, Phys. Rev. B 104, 174443 (2021).
  26. C. Huang, L. Z. Jiang, Y. Zhu, Y. F. Pan, J. Y. Fan, C. L. Ma, J. Hu, and D. N. Shi, Tuning Dzyaloshinskii–Moriya interaction via an electric field at the Co/h-BN interface, Phys. Chem. Chem. Phys. 23, 22246 (2021).
  27. J. Richter, V. Ohanyan, J. Schulenburg, and J. Schnack, Electric field driven flat bands: Enhanced magnetoelectric and electrocaloric effects in frustrated quantum magnets, Phys. Rev. B 105, 054420 (2022).
  28. H. Katsura, N. Nagaosa, and P. A. Lee, Theory of the thermal Hall effect in quantum magnets, Phys. Rev. Lett. 104, 066403 (2010).
  29. Y. Onose, T. Ideue, H. Katsura, Y. Shiomi, N. Nagaosa, and Y. Tokura, Observation of the magnon Hall effect, Science 329, 297 (2010).
  30. R. Matsumoto and S. Murakami, Theoretical prediction of a rotating magnon wave packet in ferromagnets, Phys. Rev. Lett. 106, 197202 (2011).
  31. T. Ideue, Y. Onose, H. Katsura, Y. Shiomi, S. Ishiwata, N. Nagaosa, and Y. Tokura, Effect of lattice geometry on magnon Hall effect in ferromagnetic insulators, Phys. Rev. B 85, 134411 (2012).
  32. R. Shindou, R. Matsumoto, S. Murakami, and J. I. Ohe, Topological chiral magnonic edge mode in a magnonic crystal, Phys. Rev. B 87, 174427 (2013).
  33. L. Zhang, J. Ren, J.-S. Wang, and B. Li, Topological magnon insulator in insulating ferromagnet, Phys. Rev. B 87, 144101 (2013).
  34. R. Matsumoto, R. Shindou, and S. Murakami, Thermal hall effect of magnons in magnets with dipolar interaction, Phys. Rev. B 89, 054420 (2014).
  35. A. Mook, J. Henk, and I. Mertig, Edge states in topological magnon insulators, Phys. Rev. B 90, 024412 (2014).
  36. A. Mook, J. Henk, and I. Mertig, Magnon Hall effect and topology in kagome lattices: A theoretical investigation, Phys. Rev. B 89, 134409 (2014).
  37. M. Hirschberger, R. Chisnell, Y. S. Lee, and N. P. Ong, Thermal Hall effect of spin excitations in a kagome magnet, Phys. Rev. Lett. 115, 106603 (2015).
  38. R. Chisnell, J. S. Helton, D. E. Freedman, D. K. Singh, R. I. Bewley, D. G. Nocera, and Y. S. Lee, Topological magnon bands in a kagome lattice ferromagnet, Phys. Rev. Lett. 115, 147201 (2015).
  39. B. Xu, T. Ohtsuki, and R. Shindou, Integer quantum magnon Hall plateau-plateau transition in a spin-ice model, Phys. Rev. B 94, 220403(R) (2016).
  40. R. Cheng, S. Okamoto, and D. Xiao, Spin Nernst effect of magnons in collinear antiferromagnets, Phys. Rev. Lett. 117, 217202 (2016).
  41. V. A. Zyuzin and A. A. Kovalev, Magnon spin Nernst effect in antiferromagnets, Phys. Rev. Lett. 117, 217203 (2016).
  42. S. K. Kim, H. Ochoa, R. Zarzuela, and Y. Tserkovnyak, Realization of the Haldane-Kane-Mele model in a system of localized spins, Phys. Rev. Lett. 117, 227201 (2016).
  43. Y. Shiomi, R. Takashima, and E. Saitoh, Experimental evidence consistent with a magnon Nernst effect in the antiferromagnetic insulator MnPS3, Phys. Rev. B 96, 134425 (2017).
  44. P. Laurell and G. A. Fiete, Topological magnon bands and unconventional superconductivity in pyrochlore iridate thin films, Phys. Rev. Lett. 118, 177201 (2017).
  45. K. Nakata, J. Klinovaja, and D. Loss, Magnonic quantum Hall effect and Wiedemann-Franz law, Phys. Rev. B 95, 125429 (2017).
  46. K. Nakata, S. K. Kim, J. Klinovaja, and D. Loss, Magnonic topological insulators in antiferromagnets, Phys. Rev. B 96, 224414 (2017).
  47. S. A. Owerre, Topological thermal Hall effect in frustrated kagome antiferromagnets, Phys. Rev. B 95, 014422 (2017).
  48. S. Murakami and A. Okamoto, Thermal Hall effect of magnons, J. Phys. Soc. Jpn. 86, 011010 (2017).
  49. P. Laurell and G. A. Fiete, Magnon thermal Hall effect in kagome antiferromagnets with Dzyaloshinskii-Moriya interactions, Phys. Rev. B 98, 094419 (2018).
  50. T. Cookmeyer and J. E. Moore, Spin-wave analysis of the low-temperature thermal Hall effect in the candidate Kitaev spin liquid α−RuCl3, Phys. Rev. B 98, 060412(R) (2018).
  51. H. Doki, M. Akazawa, H.-Y. Lee, J. H. Han, K. Sugii, M. Shimozawa, N. Kawashima, M. Oda, H. Yoshida, and M. Yamashita, Spin thermal Hall conductivity of a kagome antiferromagnet, Phys. Rev. Lett. 121, 097203 (2018).
  52. P. A. McClarty, X.-Y. Dong, M. Gohlke, J. G. Rau, F. Pollmann, R. Moessner, and K. Penc, Topological magnons in Kitaev magnets at high fields, Phys. Rev. B 98, 060404(R) (2018).
  53. D. G. Joshi, Topological excitations in the ferromagnetic Kitaev-Heisenberg model, Phys. Rev. B 98, 060405(R) (2018).
  54. V. A. Zyuzin and A. A. Kovalev, Spin Hall and Nernst effects of Weyl magnons, Phys. Rev. B 97, 174407 (2018).
  55. A. Mook, J. Henk, and I. Mertig, Thermal Hall effect in noncollinear coplanar insulating antiferromagnets, Phys. Rev. B 99, 014427 (2019).
  56. H. Kondo, Y. Akagi, and H. Katsura, Z2 topological invariant for magnon spin Hall systems, Phys. Rev. B 99, 041110(R) (2019).
  57. M. Kawano and C. Hotta, Thermal Hall effect and topological edge states in a square-lattice antiferromagnet, Phys. Rev. B 99, 054422 (2019).
  58. H. Kondo, Y. Akagi, and H. Katsura, Three-dimensional topological magnon systems, Phys. Rev. B 100, 144401 (2019).
  59. S. K. Kim, K. Nakata, D. Loss, and Y. Tserkovnyak, Tunable magnonic thermal Hall effect in skyrmion crystal phases of ferrimagnets, Phys. Rev. Lett. 122, 057204 (2019).
  60. 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).
  61. Y. Akagi, Topological invariant for bosonic Bogoliubov–de Gennes systems with disorder, J. Phys. Soc. Jpn. 89, 123601 (2020).
  62. H. Kondo, Y. Akagi, and H. Katsura, Non-Hermiticity and topological invariants of magnon Bogoliubov–de Gennes systems, Prog. Theor. Exp. Phys. 2020, 12A104 (2020).
  63. K. Nakata and S. K. Kim, Topological Hall effects of magnons in ferrimagnets, J. Phys. Soc. Jpn. 90, 081004 (2021).
  64. H. Kondo and Y. Akagi, Dirac surface states in magnonic analogs of topological crystalline insulators, Phys. Rev. Lett. 127, 177201 (2021).
  65. K. Fujiwara, S. Kitamura, and T. Morimoto, Thermal Hall responses in frustrated honeycomb spin systems, Phys. Rev. B 106, 035113 (2022).
  66. H. Kim and S. K. Kim, Topological phase transition in magnon bands in a honeycomb ferromagnet driven by sublattice symmetry breaking, Phys. Rev. B 106, 104430 (2022).
  67. P. A. McClarty, Topological magnons: A review, Annu. Rev. Condens. Matter Phys. 13, 171 (2022).
  68. R. R. Neumann, A. Mook, J. Henk, and I. Mertig, Thermal Hall effect of magnons in collinear antiferromagnetic insulators: Signatures of magnetic and topological phase transitions, Phys. Rev. Lett. 128, 117201 (2022).
  69. G. Go, D. An, H.-W. Lee, and S. K. Kim, Magnon orbital Nernst effect in honeycomb antiferromagnets without spin–orbit coupling, Nano Lett. 24, 5968 (2024).
  70. F. Zhuo, J. Kang, A. Manchon, and Z. Cheng, Topological phases in magnonics, Adv. Phys. Res., 2300054 (2023).
  71. X.-T. Zhang, Y. H. Gao, and G. Chen, Thermal Hall effects in quantum magnets, Phys. Rep. 1070, 1 (2024).
  72. S. Raghu and F. D. M. Haldane, Analogs of quantum-Hall-effect edge states in photonic crystals, Phys. Rev. A 78, 033834 (2008).
  73. A. Petrescu, A. A. Houck, and K. Le Hur, Anomalous Hall effects of light and chiral edge modes on the Kagomé lattice, Phys. Rev. A 86, 053804 (2012).
  74. M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Photonic Floquet topological insulators, Nature (London) 496, 196 (2013).
  75. M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, Imaging topological edge states in silicon photonics, Nat. Photon. 7, 1001 (2013).
  76. P. Ben-Abdallah, Photon thermal Hall effect, Phys. Rev. Lett. 116, 084301 (2016).
  77. C. Strohm, G. L. J. A. Rikken, and P. Wyder, Phenomenological evidence for the phonon Hall effect, Phys. Rev. Lett. 95, 155901 (2005).
  78. L. Sheng, D. N. Sheng, and C. S. Ting, Theory of the phonon Hall effect in paramagnetic dielectrics, Phys. Rev. Lett. 96, 155901 (2006).
  79. Y. Kagan and L. A. Maksimov, Anomalous Hall effect for the phonon heat conductivity in paramagnetic dielectrics, Phys. Rev. Lett. 100, 145902 (2008).
  80. L. Zhang, J. Ren, J.-S. Wang, and Baowen Li, Topological nature of the phonon Hall effect, Phys. Rev. Lett. 105, 225901 (2010).
  81. L. Zhang, J. Ren, J.-S. Wang, and B. Li, The phonon Hall effect: theory and application, J. Phys.: Condens. Matter 23, 305402 (2011).
  82. T. Qin, J. Zhou, and J. Shi, Berry curvature and the phonon Hall effect, Phys. Rev. B 86, 104305 (2012).
  83. J. Romhányi, K. Penc, and R. Ganesh, Hall effect of triplons in a dimerized quantum magnet, Nat. Commun. 6, 6805 (2015).
  84. M. Malki and K. P. Schmidt, Magnetic Chern bands and triplon Hall effect in an extended Shastry-Sutherland model, Phys. Rev. B 95, 195137 (2017).
  85. P. A. McClarty, F. Krüger, T. Guidi, S. F. Parker, K. Refson, A. W. Parker, D. Prabhakaran, and R. Coldea, Topological triplon modes and bound states in a Shastry–Sutherland magnet, Nat. Phys. 13, 736. (2017).
  86. D. G. Joshi and A. P. Schnyder, Z2 topological quantum paramagnet on a honeycomb bilayer, Phys. Rev. B 100, 020407(R) (2019).
  87. H. Sun, P. Sengupta, D. Nam, and B. Yang, Negative thermal Hall conductance in a two-dimer Shastry-Sutherland model with a π-flux Dirac triplon, Phys. Rev. B 103, L140404 (2021).
  88. D. Bhowmick and P. Sengupta, Weyl triplons in SrCu2(BO3)2, Phys. Rev. B 104, 085121 (2021).
  89. S. Suetsugu, T. Yokoi, K. Totsuka, T. Ono, I. Tanaka, S. Kasahara, Y. Kasahara, Z. Chengchao, H. Kageyama, and Y. Matsuda, Intrinsic suppression of the topological thermal Hall effect in an exactly solvable quantum magnet, Phys. Rev. B 105, 024415 (2022).
  90. A. Thomasen, K. Penc, N. Shannon, and J. Romhányi, Fragility of Z2 topological invariant characterizing triplet excitations in a bilayer kagome magnet, Phys. Rev. B 104, 104412 (2021).
  91. T. Saha-Dasgupta and R. Valenti, Comparative study between two quantum spin systems KCuCl3 and TlCuCl3, Europhys. Lett. 60, 309 (2002).
  92. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L032050 for details.
  93. T. A. Kaplan and S. D. Mahanti, Canted-spin-caused electric dipoles: A local symmetry theory, Phys. Rev. B 83, 174432 (2011).
  94. In the later analysis, we only focus on the lowest triplon mode. Since the z component of the electric field-induced intradimer DM interaction term barely affects the lowest mode, we can ignore the z component in the present analysis.
  95. The values in Table 2 are taken from [14]. Although the values in Table 2 look different from the values in [14], they are consistent if we use the same coordinate system as in [14].
  96. S. Sachdev and R. N. Bhatt, Bond-operator representation of quantum spins: Mean-field theory of frustrated quantum heisenberg antiferromagnets, Phys. Rev. B 41, 9323 (1990).
  97. We used the method of Ref. [108].
  98. T. Lottermoser, T. Lonkai, U. Amann, D. Hohlwein, J. Ihringer, and M. Fiebig, Magnetic phase control by an electric field, Nature (London) 430, 541 (2004).
  99. The BdG Hamiltonian does not exactly return to the original one if ϕ2−ϕ1≠±π. However, the difference from ±π is usually small enough to be neglected.
  100. The qualitative explanation is as follows. The swapping between the ground state of sublattice 1 and 2 effectively corresponds to the sign change of the symmetry-allowed interdimer DM interaction due to its antisymmetry. This leads to the reversal of fictitious fluxes induced by the interdimer DM interaction (see also the Supplemental Material for the explanation of fictitious fluxes), resulting in the time reversal operation.
  101. The ground state (9) drastically changes around |Ey|=0, where κzx shows a sharp change.
  102. As expected from Fig. 3, the Chern numbers for these two bands are zero. Nonetheless, the thermal Hall effect can manifest owing to the bosonic nature, i.e., thermally excited triplons contribute to the thermal Hall conductivity through the Bose distribution function ρ(En(k))=1/(eβEn(k)−1) as seen in Eq. (14).
  103. R. Samajdar, S. Chatterjee, S. Sachdev, and M. S. Scheurer, Thermal Hall effect in square-lattice spin liquids: A Schwinger boson mean-field study, Phys. Rev. B 99, 165126 (2019).
  104. O. M. Volkov, D. D. Sheka, Y. Gaididei, V. P. Kravchuk, U. K. Rößler, J. Fassbender, and D. Makarov, Mesoscale Dzyaloshinskii-Moriya interaction: geometrical tailoring of the magnetochirality, Sci. Rep. 8, 866 (2018).
  105. S. Qi, J. Jiang, and W. Mi, Tunable valley polarization, magnetic anisotropy and Dzyaloshinskii–Moriya interaction in two-dimensional intrinsic ferromagnetic Janus 2H-VSeX (X = S, Te) monolayers, Phys. Chem. Chem. Phys. 22, 23597 (2020).
  106. C. Xu, Q.-J. Wang, B. Xu, and J. Hu, Effect of biaxial strain and hydrostatic pressure on the magnetic properties of bilayer CrI3, Front. Phys. 16, 53502 (2021).
  107. Y. Xing, H. Chen, N. Xu, X. Li, and L. Zhang, Valley modulation and single-edge transport of magnons in breathing kagome ferromagnets, Phys. Rev. B 105, 104409 (2022).
  108. T. Fukui, Y. Hatsugai, and H. Suzuki, Chern numbers in discretized Brillouin zone: Efficient method of computing (spin) Hall conductances, J. Phys. Soc. Jpn. 74, 1674 (2005).

Outline

Information

Phys. Rev. Research 6, L032050– Published 3 September, 2024
  • Received 18 October 2023
  • Accepted 22 July 2024
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation