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

Magnetic ground state of NdB4: Interplay between anisotropic exchange interactions and hidden order on a Shastry-Sutherland lattice

D. D. Khalyavin1, D. Brunt2,3, N. Qureshi4, A. R. Wildes4, B. Ouladdiaf4, R. D. Johnson5, G. Balakrishnan3, and O. A. Petrenko3

Phys. Rev. B 109, L220411 – Published 24 June, 2024

DOI: https://doi.org/10.1103/PhysRevB.109.L220411

Abstract

The neodymium tetraboride NdB4, crystalizing into a tetragonal crystal structure, has the magnetic ions located on a Shastry-Sutherland lattice. The compound undergoes several magnetic phase transitions and exhibits a complex multi-k ground state that has so far been elusive. Here we report the solution and quantitative refinement of the magnetic ground state of NdB4 based on neutron diffraction data. The magnetic structure consists of two separate components; one of them is confined within the ab plane and makes an orthogonal all-in-all-out spin configuration maintaining translation symmetry of the crystal. Another is pointing along the c axis, and this component forms an anharmonic spin density wave consisting of three-up-two-down sequences with fivefold periodicity. The in-plane and out of plane spin structures represent distinct magnetic instabilities which normally would not coexist. Their simultaneous presence in the same phase is an interesting phenomenon associated with anisotropic exchange interactions and coupling to a symmetry breaking nonmagnetic order parameter undetectable by the available diffraction data.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (40)

  1. S. B. Shastry and B. Sutherland, Exact ground state of a quantum mechanical antiferromagnet, Physica B+C 108, 1069 (1981).
  2. Y. H. Matsuda, N. Abe, S. Takeyama, H. Kageyama, P. Corboz, A. Honecker, S. R. Manmana, G. R. Foltin, K. P. Schmidt, and F. Mila, Magnetization of SrCu2(BO3)2 in ultrahigh magnetic fields up to 118 T, Phys. Rev. Lett. 111, 137204 (2013).
  3. M. E. Zayed, C. Ruegg, J. J. Larrea, A. M. Laeuchli, C. Panagopoulos, S. S. Saxena, M. Ellerby, D. F. McMorrow, T. Strassle, S. Klotz, G. Hamel, R. A. Sadykov, V. Pomjakushin, M. Boehm, M. Jimenez-Ruiz, A. Schneidewind, E. Pomjakushina, M. Stingaciu, K. Conder, and H. M. Ronnow, 4-spin plaquette singlet state in the shastry-sutherland compound SrCu2(BO3)2, Nat. Phys. 13, 962 (2017).
  4. J. Guo, G. Sun, B. Zhao, L. Wang, W. Hong, V. A. Sidorov, N. Ma, Q. Wu, S. Li, Z. Y. Meng, A. W. Sandvik, and L. Sun, Quantum phases of SrCu2(BO3)2 from high-pressure thermodynamics, Phys. Rev. Lett. 124, 206602 (2020).
  5. J. Larrea Jiménez, S. P. G. Crone, E. Fogh, M. E. Zayed, R. Lortz, E. Pomjakushina, K. Conder, A. M. Laeuchli, L. Weber, S. Wessel, A. Honecker, B. Normand, C. Rueegg, P. Corboz, H. M. Ronnow, and F. Mila, A quantum magnetic analogue to the critical point of water, Nature (London) 592, 370 (2021).
  6. Y. Cui, L. Liu, H. Lin, K.-H. Wu, W. Hong, X. Liu, C. Li, Z. Hu, N. Xi, S. Li, R. Yu, A. W. Sandvik, and W. Yu, Proximate deconfined quantum critical point in SrCu2(BO3)2, Science 380, 1179 (2023).
  7. C. Castelnovo, R. Moessner, and S. L. Sondhi, Magnetic monopoles in spin ice, Nature (London) 451, 42 (2008).
  8. W. Miiller, L. S. Wu, M. S. Kim, T. Orvis, J. W. Simonson, M. Gamża, D. M. McNally, C. S. Nelson, G. Ehlers, A. Podlesnyak, J. S. Helton, Y. Zhao, Y. Qiu, J. R. D. Copley, J. W. Lynn, I. Zaliznyak, and M. C. Aronson, Magnetic structure of Yb2Pt2Pb: Ising moments on the shastry-sutherland lattice, Phys. Rev. B 93, 104419 (2016).
  9. K. Siemensmeyer, E. Wulf, H.-J. Mikeska, K. Flachbart, S. Gabáni, S. Mat'aš, P. Priputen, A. Efdokimova, and N. Shitsevalova, Fractional magnetization plateaus and magnetic order in the shastry-sutherland magnet TmB4, Phys. Rev. Lett. 101, 177201 (2008).
  10. K. Wierschem and P. Sengupta, Columnar antiferromagnetic order and spin supersolid phase on the extended shastry-sutherland lattice, Phys. Rev. Lett. 110, 207207 (2013).
  11. D. Brunt, G. Balakrishnan, A. R. Wildes, B. Ouladdiaf, N. Qureshi, and O. A. Petrenko, Field-induced magnetic states in holmium tetraboride, Phys. Rev. B 95, 024410 (2017).
  12. J. Trinh, S. Mitra, C. Panagopoulos, T. Kong, P. C. Canfield, and A. P. Ramirez, Degeneracy of the 1/8 plateau and antiferromagnetic phases in the shastry-sutherland magnet TmB4, Phys. Rev. Lett. 121, 167203 (2018).
  13. D. Lançon, V. Scagnoli, U. Staub, O. A. Petrenko, M. Ciomaga Hatnean, E. Canevet, R. Sibille, S. Francoual, J. R. L. Mardegan, K. Beauvois, G. Balakrishnan, L. J. Heyderman, C. Rüegg, and T. Fennell, Evolution of field-induced metastable phases in the shastry-sutherland lattice magnet TmB4, Phys. Rev. B 102, 060407(R) (2020).
  14. H. Yamauchi, N. Metoki, R. Watanuki, K. Suzuki, H. Fukazawa, S. Chi, and J. A. Fernandez-Baca, Magnetic structure and quadrupolar order parameter driven by geometrical frustration effect in NdB4, J. Phys. Soc. Jpn. 86, 044705 (2017).
  15. N. Metoki, H. Yamauchi, M. Matsuda, J. A. Fernandez-Baca, R. Watanuki, and M. Hagihala, Polarized neutron scattering study of the multiple order parameter system NdB4, Phys. Rev. B 97, 174416 (2018).
  16. J. A. Blanco, P. J. Brown, A. Stunault, K. Katsumata, F. Iga, and S. Michimura, Magnetic structure of GdB4 from spherical neutron polarimetry, Phys. Rev. B 73, 212411 (2006).
  17. D. Okuyama, T. Matsumura, T. Mouri, N. Ishikawa, K. Ohoyama, H. Hiraka, H. Nakao, K. Iwasa, and Y. Murakami, Competition of magnetic and quadrupolar order parameters in HoB4, J. Phys. Soc. Jpn. 77, 044709 (2008).
  18. T. Matsumura, D. Okuyama, T. Mouri, and Y. Murakami, Successive magnetic phase transitions of component orderings in DyB4, J. Phys. Soc. Jpn. 80, 074701 (2011).
  19. G. Will and W. Schafer, Neutron diffraction and the magnetic structures of some rare earth diborides and tetraborides, J. Less-Common Met. 67, 31 (1979).
  20. S. Michimura, A. Shigekawa, F. Iga, T. Takabatake, and K. Ohoyama, Complex magnetic structures of a shastry-sutherland lattice TmB4 studied by powder neutron diffraction analysis, J. Phys. Soc. Jpn. 78, 024707 (2009).
  21. R. Watanuki, G. Sato, K. Suzuki, M. Ishihara, T. Yanagisawa, Y. Nemoto, and T. Goto, Geometrical quadrupolar frustration in DyB4, J. Phys. Soc. Jpn. 74, 2169 (2005).
  22. S. Ji, C. Song, J. Koo, J. Park, Y. J. Park, K.-B. Lee, S. Lee, J.-G. Park, J. Y. Kim, B. K. Cho, K.-P. Hong, C.-H. Lee, and F. Iga, Resonant x-ray scattering study of quadrupole-strain coupling in DyB4, Phys. Rev. Lett. 99, 076401 (2007).
  23. H. Sim, S. Lee, K.-P. Hong, J. Jeong, J. R. Zhang, T. Kamiyama, D. T. Adroja, C. A. Murray, S. P. Thompson, F. Iga, S. Ji, D. Khomskii, and J.-G. Park, Spontaneous structural distortion of the metallic shastry-sutherland system DyB4 by quadrupole-spin-lattice coupling, Phys. Rev. B 94, 195128 (2016).
  24. D. Brunt, M. C. Hatnean, O. A. Petrenko, M. R. Lees, and G. Balakrishnan, Single-crystal growth of metallic rare-earth tetraborides by the floating-zone technique, Crystals 9, 211 (2019).
  25. J. R. Stewart, P. P. Deen, K. H. Andersen, H. Schober, J.-F. Barthélémy, J. M. Hillier, A. P. Murani, T. Hayes, and B. Lindenau, Disordered materials studied using neutron polarization analysis on the multi-detector spectrometer, D7, J. Appl. Crystallogr. 42, 69 (2009).
  26. L. C. Chapon, M. Pascal, P. G. Radaelli, C. Benson, L. Perrott, S. Ansell, N. J. Rhodes, D. Raspino, D. Duxbury, E. Spill, and J. Norris, Wish: The new powder and single crystal magnetic diffractometer on the second target station, Neutron News 22, 22 (2011).
  27. J. Rodríguez-Carvajal, Recent advances in magnetic structure determination by neutron powder diffraction, Phys. B: Condens. Matter 192, 55 (1993).
  28. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.109.L220411 for details of the crystal/magnetic structure refinement and the mean field approach to the ordered states, which includes Refs. [34, 35, 36, 39].
  29. D. Brunt, G. Balakrishnan, D. Mayoh, M. R. Lees, D. I. Gorbunov, N. Qureshi, and O. A. Petrenko, Magnetisation process in the rare earth tetraborides, NdB4 and HoB4, Sci. Rep. 8, 232 (2018).
  30. R. Ohlendorf, S. Spachmann, L. Fischer, K. Dey, D. Brunt, G. Balakrishnan, O. A. Petrenko, and R. Klingeler, Magnetoelastic coupling and grüneisen scaling in NdB4, Phys. Rev. B 103, 104424 (2021).
  31. A. Amorese, D. Khalyavin, K. Kummer, N. B. Brookes, C. Ritter, O. Zaharko, C. B. Larsen, O. Pavlosiuk, A. P. Pikul, D. Kaczorowski, M. Gutmann, A. T. Boothroyd, A. Severing, and D. T. Adroja, Metamagnetism and crystal-field splitting in pseudohexagonal CeRh3Si2, Phys. Rev. B 105, 125119 (2022).
  32. D. D. Khalyavin, P. Manuel, M. C. Hatnean, and O. A. Petrenko, Fragile ground state and rigid field-induced structures in the zigzag ladder compound BaDy2O4, Phys. Rev. B 103, 134434 (2021).
  33. N. Qureshi, Mag2Pol: a program for the analysis of spherical neutron polarimetry, flipping ratio and integrated intensity data, J. Appl. Cryst. 52, 175 (2019).
  34. M. J. Freiser, Thermal variation of the pitch of helical spin configurations, Phys. Rev. 123, 2003 (1961).
  35. J. N. Reimers, A. J. Berlinsky, and A. C. Shi, Mean-field approach to magnetic ordering in highly frustrated pyrochlores, Phys. Rev. B 43, 865 (1991).
  36. D. D. Khalyavin, P. Manuel, J. F. Mitchell, and L. C. Chapon, Spin correlations in the geometrically frustrated RBaCo4O7 antiferromagnets: Mean-field approach and monte carlo simulations, Phys. Rev. B 82, 094401 (2010).
  37. H. T. Stokes, D. M. Hatch, and B. J. Campbell, ISOTROPY Software Suite, iso.byu.edu.
  38. B. J. Campbell, H. T. Stokes, D. E. Tanner, and D. M. Hatch, Isodisplace: A web-based tool for exploring structural distortions, J. Appl. Crystallogr. 39, 607 (2006).
  39. L. Elcoro, B. Bradlyn, Z. Wang, M. G. Vergniory, J. Cano, C. Felser, B. A. Bernevig, D. Orobengoa, G. de la Flor, and M. I. Aroyo, Double crystallographic groups and their representations on the bilbao crystallographic server, J. Appl. Crystallogr. 50, 1457 (2017).
  40. D. Khalyavin, D. Brunt, N. Qureshi, A. Wildes, B. Ouladdiaf, R. Johnson, G. Balakrishnan, and O. Petrenko, Data set “Neutron diffraction data for magnetic ground state of NdB4: Interplay between anisotropic exchange interactions and hidden order on a Shastry-Sutherland lattice”, Zenodo (2024), doi:10.5281/zenodo.11297311; The data collected at Institut Laue-Langevin can be downloaded from https://doi.ill.fr/10.5291/ILL-DATA.5-41-825 and https://doi.ill.fr/10.5291/ILL-DATA.5-41-871.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation