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Microscopic Origin of Reduced Magnetic Order in a Frustrated Metal

X. Boraley1, O. Stockert2,*, J. Lass1, R. Sibille1, Ø. S. Fjellvåg1,3, S. H. Moody1, A. M. Läuchli4,5, V. Fritsch6, and D. G. Mazzone1,†

  • *Contact author: oliver.stockert@cpfs.mpg.de
  • †Contact author: daniel.mazzone@psi.ch
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Phys. Rev. Lett. 135, 046702 – Published 23 July, 2025

DOI: https://doi.org/10.1103/38ds-xjl3

Abstract

Although magnetic frustration in metals provides a promising avenue for novel quantum phenomena, their microscopic interpretation is often challenging. Here, we use the face-centered cubic intermetallic HoInCu4 as model material to show that Hamiltonians neglecting the charge degree of freedom are appropriate for frustrated metals possessing low density of states at the Fermi surface. Through neutron scattering techniques we determine matching magnetic exchange interactions in the paramagnetic and field-polarized states using an effective spin-1 Heisenberg Hamiltonian, for which we identify antiferromagnetic nearest and next-nearest-neighbor interactions J1 and J2 that are close to the critical ratio J2/J1=1/2. The study further provides evidence that spin-wave theory fails to predict the low-energy spin dynamics in the antiferromagnetic zero-field state, which is dominated by overdamped magnetic excitations. We conclude that the low-energy fluctuations arise from quantum fluctuations, accounting for the missing moment of the strongly renormalized magnetic long-range order.

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References (41)

  1. L. Balents, Spin liquids in frustrated magnets, Nature (London) 464, 199 (2010).
  2. C. Broholm, R. J. Cava, S. A. Kivelson, D. G. Nocera, M. R. Norman, and T. Senthil, Quantum spin liquids, Science 367, eaay0668 (2020).
  3. Y. Zhou, K. Kanoda, and T.-K. Ng, Quantum spin liquid states, Rev. Mod. Phys. 89, 025003 (2017).
  4. M. Vojta, Frustration and quantum criticality, Rep. Prog. Phys. 81, 064501 (2018).
  5. K. W. Plumb, H. J. Changlani, A. Scheie, S. Zhang, J. W. Kriza, J. A. Rodriguez Rivera, Y. Qiu, B. Winn, R. J. Cava, and C. L. Broholm, Continuum of quantum fluctuations in a three-dimensional S=1 Heisenberg magnet, Nat. Phys. 15, 54 (2019).
  6. C. Lacroix, Frustrated metallic systems: A review of some peculiar behavior, J. Phys. Soc. Jpn. 79, 011008 (2010).
  7. S. Gao, O. Zaharko, V. Tsurkan, Y. Su, J. S. White, G. S. Tucker, B. Roessli, F. Bourdarot, R. Sibille, D. Chernyshov, T. Fennell, A. Loidl, and C. Rüegg, Spiral spin-liquid and the emergence of a vortex-like state in MnSc2S4, Nat. Phys. 13, 157 (2017).
  8. O. A. Starykh, Unusual ordered phases of highly frustrated magnets: A review, Rep. Prog. Phys. 78, 052502 (2015).
  9. S. Hayami and Y. Motome, Topological spin crystals by itinerant frustration, J. Phys. Condens. Matter 33, 443001 (2021).
  10. M. A. Ruderman and C. Kittel, Indirect exchange coupling of nuclear magnetic moments by conduction electrons, Phys. Rev. 96, 99 (1954).
  11. T. Kasuya, A theory of metallic ferro- and antiferromagnetism on Zener’s model, Prog. Theor. Phys. 16, 45 (1956).
  12. K. Yosida, Magnetic properties of Cu-Mn alloys, Phys. Rev. 106, 893 (1957).
  13. T. Kurumaji, T. Nakajima, M. Hirschberger, A. Kikkawa, Y. Yamasaki, H. Sagayama, H. Nakao, Y. Taguchi, T.-H. Arima, and Y. Tokura, Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet, Science 365, 914 (2019).
  14. J. Kondo, Resistance minimum in dilute magnetic alloys, Prog. Theor. Phys. 32, 37 (1964).
  15. O. Stockert, J.-U. Hoffmann, M. Mühlbauer, A. Senyshyn, M. M. Koza, A. A. Tsirlin, F. M. Wolf, S. Bachus, P. Gegenwart, R. Movshovich, S. Bobev, and V. Fritsch, Magnetic frustration in a metallic fcc lattice, Phys. Rev. Res. 2, 013183 (2020).
  16. T. Chatterji, L. P. Regnault, S. Ghosh, and A. Singh, Magnetic excitations in frustrated fcc type-III antiferromagnet MnS2, J. Phys. Condens. Matter 31, 125802 (2019).
  17. M. Matsuura, Y. Endoh, H. Hiraka, K. Yamada, A. S. Mishchenko, N. Nagaosa, and I. V. Solovyev, Classical and quantum spin dynamics in the fcc antiferromagnet NiS2 with frustration, Phys. Rev. B 68, 094409 (2003).
  18. D. C. Joshi, P. Pramanik, S. Nayak, K. Dasari, R. J. Choudhary, and S. Thota, Magnetic exchange interactions and dielectric studies of Zn1−xNixO−NiO composites, J. Phys. D 50, 325002 (2017).
  19. H. Nakamura, N. Kim, M. Shiga, R. Kmiec, K. Tomala, E. Ressouche, J. P. Sanchez, and B. Malaman, The partially disordered state of the frustrated face-centred cubic antiferromagnet GdInCu4, J. Phys. Condens. Matter 11, 1095 (1999).
  20. J. Oitmaa, Ordered phases in the frustrated fcc lattice antiferromagnet, Phys. Rev. B 108, 014414 (2023).
  21. N.-N. Sun and H.-Y. Wang, The J1-J2 model on the face-centered-cubic lattices, J. Magn. Magn. Mater. 454, 176 (2018).
  22. T. Yildirim, A. B. Harris, and E. F. Shender, Frustration and quantum fluctuations in Heisenberg fcc antiferromagnets, Phys. Rev. B 58, 3144 (1998).
  23. R. Schick, O. Götze, T. Ziman, R. Zinke, J. Richter, and M. E. Zhitomirsky, Ground-state selection by magnon interactions in a fcc antiferromagnet, Phys. Rev. B 106, 094431 (2022).
  24. R. Schick, T. Ziman, and M. E. Zhitomirsky, Quantum versus thermal fluctuations in the fcc antiferromagnet: Alternative routes to order by disorder, Phys. Rev. B 102, 220405 (2020).
  25. L. A. Batalov and A. V. Syromyatnikov, Order-by-disorder effects in antiferromagnets on face-centered cubic lattice, J. Magn. Magn. Mater. 414, 180 (2016).
  26. D. Kiese, T. Müller, Y. Iqbal, R. Thomale, and S. Trebst, Multiloop functional renormalization group approach to quantum spin systems, Phys. Rev. Res. 4, 023185 (2022).
  27. A. Singh, S. Mohapatra, T. Ziman, and T. Chatterji, Spin waves in the fcc lattice antiferromagnet: Competing interactions, frustration, and instabilities in the Hubbard model, J. Appl. Phys. 121, 073903 (2017).
  28. J. A. M. Paddison, spinteract: A program to refine magnetic interactions to diffuse scattering data, J. Phys. Condens. Matter 35, 495802 (2023).
  29. J. Lass, S. H. Moody, and Ø. S. Fjellvåg, DMCpy: A powder and single crystal neutron diffraction software for DMC, SoftwareX 31, 102237 (2025).
  30. J. Lass et al., Commissioning of the novel continuous angle multi-energy analysis spectrometer at the Paul Scherrer Institut, Rev. Sci. Instrum. 94, 023302 (2023).
  31. J. Lass, H. Jacobsen, D. G. Mazzone, and K. Lefmann, Mjolnir: A software package for multiplexing neutron spectrometers, SoftwareX 12, 100600 (2020).
  32. D. Dahlbom, H. Zhang, C. Miles, S. Quinn, A. Niraula, B. Thipe, M. Wilson, S. Matin, H. Mankad, S. Hahn, D. Pajerowski, S. Johnston, Z. Wang, H. Lane, Y. W. Li, X. Bai, M. Mourigal, C. D. Batista, and K. Barros, Sunny.jl: A Julia package for spin dynamics, arXiv:2501.13095.
  33. S. Toth and B. Lake, Linear spin wave theory for single-q incommensurate magnetic structures, J. Phys. Condens. Matter 27, 166002 (2015).
  34. A. Scheie, pycrystalfield: Software for calculation, analysis and fitting of crystal electric field Hamiltonians, J. Appl. Crystallogr. 54, 356 (2021).
  35. See Supplemental Material at http://link.aps.org/supplemental/10.1103/38ds-xjl3 for more detailed results and additional information on the data analysis.
  36. Q. Li, H. Li, J. Zhao, H.-G. Luo, and Z. Y. Xie, Magnetization of the spin-12 Heisenberg antiferromagnet on the triangular lattice, Phys. Rev. B 105, 184418 (2022).
  37. F. Ferrari and F. Becca, Spectral signatures of fractionalization in the frustrated Heisenberg model on the square lattice, Phys. Rev. B 98, 100405 (2018).
  38. Q. Wang, A. de la Torre, J. A. Rodriguez-Rivera, A. A. Podlesnyak, W. Tian, A. A. Aczel, M. Matsuda, P. J. Ryan, J.-W. Kim, J. G. Rau, and K. W. Plumb, Pulling order back from the brink of disorder: Observation of a nodal-line spin liquid and fluctuation stabilized order in K2IrCl6, Phys. Rev. X 15, 021021 (2025).
  39. P. W. Anderson, Generalizations of the Weiss molecular field theory of antiferromagnetism, Phys. Rev. 79, 705 (1950).
  40. J. Villain, La structure des substances magnetiques, J. Phys. Chem. Solids 11, 303 (1959).
  41. X. Boraley, O. Stockert, J. Lass, R. Sibille, Ø. S. Fjellvåg, S. H. Moody, A. M. Läuchli, V. Fritsch, and D. G. Mazzone, Version v1 (2025), 10.5281/zenodo.14864167

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Phys. Rev. Lett. 135, 046702– Published 23 July, 2025
  • Received 13 February 2025
  • Accepted 20 June 2025
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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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