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Spin glass effects and nonexistence of a ferromagnetic quantum critical point in the compositionally tuned FeGa3−xGex metallic quantum ferromagnets (x=0.0−0.16)

Stanislav Vrtnik1,2, Primož Koželj1,2, Magdalena Wencka1,3, Kristian Bader4, Julia Petrović1, Jože Luzar1, Peter Mihor1, Andreja Jelen1, Peter Gille4 et al.

Janez Dolinšek1,2,*

  • *Contact author. jani.dolinsek@ijs.si

Phys. Rev. B 112, 104420 – Published 11 September, 2025

DOI: https://doi.org/10.1103/8dh8-91qh

Abstract

Searching for a ferromagnetic (FM) quantum critical point of a compositionally tuned system, we have investigated experimentally the quantum phase transition (QPT) in the FeGa3−xGex (x=0.0−0.16) metallic quantum ferromagnet, by using crystallographically oriented single-crystalline samples with the Ge contents x below and within the quantum critical regime. Performing the measurements of dc and ac magnetic susceptibility and M(H) curves down to the temperature of 0.4 K in low magnetic fields 0.01–25 mT, and the measurements of electrical resistivity and specific heat down to 0.35 K, we found that there is no direct, continuous transition from the paramagnetic to the FM state and consequently no FM quantum critical point in the compositional phase diagram, but the QPT involves an intermediate canonical spin glass (SG) state at x≈ 0.12–0.16. The compositional region of the SG state is narrow, it is formed at low temperatures (the spin freezing temperatures are in the range 1.1–1.8 K) and the coupling between the spins is weak, so that the SG ordering is fragile with respect to the external magnetic field. The analysis of the ac susceptibility via the Cole-Cole diagrams in the QPT region has revealed that the slowing-down spin dynamics of the SG state remains thermally activated down to the lowest investigated temperature of 0.4 K, so that the regime of quantum fluctuations is not yet entered. The employed experimental conditions have enabled us to follow the formation of fragile magnetic ordering in the FeGa3−xGex compositionally tuned system in its infancy state.

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References (57)

  1. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999).
  2. Understanding Quantum Phase Transitions, edited by L. D. Carr (CRC Press, Boca Raton, 2010).
  3. M. Vojta, Quantum phase transitions, Rep. Prog. Phys. 66, 2069 (2003) .
  4. P. Coleman and A. J. Schofield, Quantum criticality, Nature (London) 433, 226 (2005) .
  5. S. Sachdev and B. Keimer, Quantum criticality, Phys. Today 64 (2), 29 (2011) .
  6. T. Park, F. Ronning, H. Q. Yuan, M. B. Salamon, R. Movshovich, J. L. Sarrao, and J. D. Thompson, Hidden magnetism and quantum criticality in the heavy fermion superconductor CeRhIn5, Nature (London) 440, 65 (2006) .
  7. H. von Löhneysen, A. Rosch, M. Vojta, and P. Wölfle, Fermi-liquid instabilities at magnetic quantum phase transitions, Rev. Mod. Phys. 79, 1015 (2007).
  8. P. Gegenwart, Q. Si, and F. Steglich, Quantum criticality in heavy-fermion metals, Nat. Phys. 4, 186 (2008) .
  9. S. Vrtnik, M. Krnel, P. Koželj, Z. Jagličić, L. Kelhar, A. Meden, M.-C. de Weerd, P. Boulet, J. Ledieu, V. Fournée, J.-M. Dubois, and J. Dolinšek, Anisotropic quantum critical point in the Ce3Al system with a large magnetic anisotropy, J. Phys. Commun. 4, 105016 (2020) .
  10. M. Brando, D. Belitz, F. M. Grosche, and T. R. Kirkpatrick, Metallic quantum ferromagnets, Rev. Mod. Phys. 88, 039901 (2016) .
  11. M. Majumder, M. Wagner-Reetz, R. Cardoso-Gil, P. Gille, F. Steglich, Y. Grin, and M. Baenitz, Towards ferromagnetic quantum criticality in FeGa3−xGex: Ga71 NQR as a zero-field microscopic probe, Phys. Rev. B 93, 064410 (2016) .
  12. B. Koo, K. Bader, U. Burkhardt, M. Baenitz, P. Gille, and J. Sichelschmidt, Spin dynamics of FeGa3−xGex studied by electron spin resonance, J. Phys.: Condens. Matter 30, 045601 (2018).
  13. Y. Kishimoto, D. Kasinathan, H. Yasuoka, K. Bader, P. Gille, U. Burkhardt, and M. Baenitz, Site selective substitution and charge differentiation around Ge atom in FeGa3−xGex proved by Ga-NQR with super-cell calculation, J. Phys. Soc. Jpn. 89, 083701 (2020).
  14. J. C. Alvarez-Quiceno, M. Cabrera-Baez, R. A. Ribeiro, M. A. Avila, G. M. Dalpian, and J. M. Osorio-Guillén, Emergence of competing magnetic interactions induced by Ge doping in the semiconductor FeGa3, Phys. Rev. B 94, 014432 (2016) .
  15. K. Umeo, Y. Hadano, S. Narazu, T. Onimaru, M. A. Avila, and T. Takabatake, Ferromagnetic instability in a doped band gap semiconductor FeGa3, Phys. Rev. B 86, 144421 (2012) .
  16. A. Takeuchi and A. Inoue, Classification of bulk metallic glasses by atomic size difference, heat of mixing and period of constituent element and its application to characterization of the main alloying element, Mater. Trans. 46, 2817 (2005) .
  17. K. Bader and P. Gille, Single crystal growth of FeGa3 and FeGa3−xGex from high-temperature solution using the Czochralski method, Cryst. Res. Technol. 55, 1900067 (2019) .
  18. U. Häussermann, M. Boström, P. Viklund, Ö. Rapp, and T. Björnägen, FeGa3 and RuGa3: Semiconducting intermetallic compounds, J. Solid State Chem. 165, 94 (2002) .
  19. Y. Hadano, S. Narazu, M. A. Avila, T. Onimaru, and T. Takabatake, Thermoelectric and magnetic properties of a narrow-gap semiconductor FeGa3, J. Phys. Soc. Jpn. 78, 013702 (2009) .
  20. N. Tsujii, H. Yamaoka, M. Matsunami, R. Eguchi, Y. Ishida, Y. Senba, H. Ohashi, S. Shin, T. Furubayashi, H. Abe, and H. Kitazawa, Observation of energy gap in FeGa3, J. Phys. Soc. Jpn. 77, 024705 (2008) .
  21. G. A. Bain and J. F. Berry, Diamagnetic corrections and Pascal's constants, J. Chem. Educ. 85, 532 (2008) .
  22. M. Wagner-Reetz, D. Kasinathan, W. Schnelle, R. Cardoso-Gil, H. Rosner, and Y. Grin, Phonon-drag effect in FeGa3, Phys. Rev. B 90, 195206 (2014) .
  23. Y. Imai and A. Watanabe, Electronic structures of semiconducting FeGa3, RuGa3, OsGa3, and RuIn3 with the CoGa3- or the FeGa3-type structure, Intermetallics 14, 722 (2006) .
  24. J. M. D. Coey, Magnetism and Magnetic Materials (Cambridge University Press, Cambridge, 2010), pp. 171–172.
  25. M. Hagiwara, Cole–Cole plot analysis of the spin-glass system NiC2O4·2(2MIz)0.49(H2O)0.51, J. Magn. Magn. Mater. 177, 89 (1998) .
  26. O. Petracic, S. Sahoo, Ch. Binek, W. Kleemann, J. B. Sousa, S. Cardoso, and P. P. Freitas, Cole–Cole analysis of the superspin glass system Co80Fe20/Al2O3, Ph. Transit. 76, 367 (2003) .
  27. S. Havriliak and S. Negami, A complex plane analysis of α-dispersions in some polymer systems, J. Polym. Sci. C 14, 99 (1966) .
  28. S. Havriliak and S. Negami, A complex plane representation of dielectric and mechanical relaxation processes in some polymers, Polymer 8, 161 (1967) .
  29. R. Zorn, Applicability of distribution functions for the Havriliak–Negami spectral function, J. Polym. Sci. B 37, 1043 (1999) .
  30. K. C. Kao, Dielectric Phenomena in Solids (Elsevier Academic Press, London, 2004), pp. 92–93.
  31. U. Mizutani, Introduction to the Electron Theory of Metals (Cambridge University Press, Cambridge, 2001), p. 39.
  32. A. Tari, The Specific Heat of Matter at Low Temperatures (Imperial College Press, London, 2003), pp. 167–174.
  33. J. A. Mydosh, Spin Glasses: An Experimental Introduction (Taylor & Francis, London, 1993), p. 7 and p. 31.
  34. F. R. Wagner, R. Cardoso-Gil, B. Boucher, M. Wagner-Reetz, J. Sichelschmidt, P. Gille, M. Baenitz, and Y. Grin, On Fe–Fe dumbbells in the ideal and real structures of FeGa3, Inorg. Chem. 57, 12908 (2018) .
  35. K. Binder and A. P. Young, Spin glasses: Experimental facts, theoretical concepts, and open questions, Rev. Mod. Phys. 58, 801 (1986) .
  36. T. R. Kirkpatrick and D. Belitz, Ferromagnetic quantum critical point in noncentrosymmetric systems, Phys. Rev. Lett. 124, 147201 (2020) .
  37. A. Steppke, R. Küchler, S. Lausberg, E. Lengyel, L. Steinke, R. Borth, T. Lühmann, C. Krellner, M. Nicklas, C. Geibel, F. Steglich, and M. Brando, Ferromagnetic quantum critical point in the heavy-fermion metal YbNi4(P1−xAsx)2, Science 339, 933 (2013) .
  38. M. Nicklas, M. Brando, G. Knebel, F. Mayr, W. Trinkl, and A. Loidl, Non-Fermi-liquid behavior at a ferromagnetic quantum critical point in NixPd1−x, Phys. Rev. Lett. 82, 4268 (1999) .
  39. M. Nicklas, Nicht-Fermi-Flüssigkeitsverhalten am quantenkritischen Punkt in Nickel-Palladium. Ph.D. thesis, University of Augsburg, Germany, 2000.
  40. M. Sato, Magnetic properties and electrical resistivity of (Ni1−xPdx)3Al, J. Phys. Soc. Jpn. 39, 98 (1975) .
  41. J. Yang, B. Chen, H. Ohta, C. Michioka, K. Yoshimura, H. Wang, and M. Fang, Spin fluctuations on the verge of a ferromagnetic quantum phase transition in Ni3Al1−xGax, Phys. Rev. B 83, 134433 (2011) .
  42. L. Schoop, M. Hirschberger, J. Tao, C. Felser, N. P. Ong, and R. J. Cava, Paramagnetic to ferromagnetic phase transition in lightly Fe-doped Cr2B, Phys. Rev. B 89, 224417 (2014) .
  43. D. A. Sokolov, M. C. Aronson, W. Gannon, and Z. Fisk, Critical phenomena and the quantum critical point of ferromagnetic Zr1−xNbxZn2, Phys. Rev. Lett. 96, 116404 (2006) .
  44. S. Jia, P. Jiramongkolchai, M. R. Suchomel, B. H. Toby, J. G. Checkelsky, N. P. Ong, and R. J. Cava, Ferromagnetic quantum critical point induced by dimer-breaking in SrCo2(Ge1−xPx)2, Nat. Phys. 7, 207 (2011) .
  45. J. A. Mydosh and P. M. Oppeneer, Colloquium: Hidden order, superconductivity, and magnetism: The unsolved case of URu2Si2, Rev. Mod. Phys. 83, 1301 (2013) .
  46. N. P. Butch and M. B. Maple, The suppression of hidden order and the onset of ferromagnetism in URu2Si2 via Re substitution, J. Phys.: Condens. Matter 22, 164204 (2010).
  47. T. C. Kobayashi, S. Fukushima, H. Hidaka, H. Kotegawa, T. Akazawa, E. Yamamoto, Y. Haga, R. Settai, and Y. Onuki, Pressure-induced superconductivity in ferromagnet UIr without inversion symmetry, Physica B 378, 355 (2006) .
  48. V. A. Sidorov, P. H. Tobash, C. Wang, B. L. Scott, T. Park, E. D. Bauer, F. Ronning, J. D. Thompson, and Z. Fisk, Quenching of ferromagnetism in β−UB2C and UNiSi2 at high pressure, J. Phys.: Conf. Series 273, 012014 (2011).
  49. H. Hidaka, S. Takahashi, Y. Shimizu, T. Yanagisawa, and H. Amitsuka, Pressure-induced quantum critical point in ferromagnet U4Ru7Ge6, J. Phys. Soc. Jpn. 80, SA102 (2011) .
  50. H. Kotegawa, E. Matsuoka, T. Uga, M. Takemura, M. Manago, N. Chikuchi, H. Sugawara, H. Tou, and H. Harima, Indication of ferromagnetic quantum critical point in Kondo lattice CeRh6Ge4, J. Phys. Soc. Jpn. 88, 093702 (2019) .
  51. B. Shen, Y. Zhang, Y. Komijani, M. Nicklas, R. Borth, A. Wang, Y. Chen, Z. Nie, R. Li, X. Lu, H. Lee, M. Smidman, F. Steglich, P. Coleman, and H. Yuan, Strange-metal behaviour in a pure ferromagnetic Kondo lattice, Nature (London) 579, 51 (2020) .
  52. Y. J. Zhang, Z. Y. Nie, R. Li, Y. C. Li, D. L. Yang, B. Shen, Y. Chen, F. Du, S. S. Luo, H. Su, R. Shi, S. Y. Wang, M. Nicklas, F. Steglich, M. Smidman, and H. Q. Yuan, Suppression of ferromagnetism and influence of disorder in silicon-substituted CeRh6Ge4, Phys. Rev. B 106, 054409 (2022) .
  53. R. B. Griffiths, Nonanalytic behavior above the critical point in a random Ising ferromagnet, Phys. Rev. Lett. 23, 17 (1969) .
  54. A. J. Bray, Nature of the Griffiths phase, Phys. Rev. Lett. 59, 586 (1987) .
  55. A. J. Millis, D. K. Morr, and J. Schmalian, Quantum Griffiths effects in metallic systems, Phys. Rev. B 66, 174433 (2002) .
  56. T. Vojta, Quantum Griffiths effects and smeared phase transitions in metals: Theory and experiment, J. Low Temp. Phys. 161, 299 (2010) .
  57. M. Randeria, J. P. Sethna, and R. G. Palmer, Low-frequency relaxation in Ising spin-glasses, Phys. Rev. Lett. 54, 1321 (1985) .

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