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Superconducting ground state study of Cr-based equiatomic high-entropy alloy through μSR

Sonika Jangid1, Rhea Stewart2, Adrian D. Hillier2, and R. P. Singh1,*

  • *Contact author: rpsingh@iiserb.ac.in
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APS Open Sci. 1, 000137 – Published 16 September, 2026

DOI: https://doi.org/10.1103/ft3z-h51w

Abstract

High-entropy alloy superconductors, characterized by extreme chemical disorder and complex electronic environments, have attracted significant attention as model systems for exploring superconductivity in disordered materials. Here, we investigate a Cr-based equiatomic high-entropy alloy, Cr-V-Ti-Nb-Ta, which contains a magnetic 3d element, providing an opportunity to examine the influence of magnetic elements on superconductivity in highly disordered systems. Despite expected magnetic pair breaking, this alloy exhibits bulk type-II superconductivity with a transition temperature of Tc=2.33(3)K and a high upper critical field. Transverse-field μSR measurements reveal an s-wave superconducting gap close to the BCS value, while zero-field μSR suggests preserved time-reversal symmetry. These results establish Cr-V-Ti-Nb-Ta as a promising platform for exploring the interplay between disorder, magnetism, and superconductivity in high-entropy alloys.

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References (66)

  1. P. Koželj, S. Vrtnik, A. Jelen, S. Jazbec, Z. Jagličić, S. Maiti, M. Feuerbacher, W. Steurer, and J. Dolinšek, Discovery of a superconducting high-entropy alloy, Phys. Rev. Lett. 113, 107001 (2014).
  2. J. W. Yeh, S. K. Chen, S. J. Lin, J. Y. Gan, T. S. Chin, T. T. Shun, C. H. Tsau, and S. Y. Chang, Nanostructured high-entropy alloys with multiple principal elements: Novel alloy design concepts and outcomes, Adv. Eng. Mater. 6, 299 (2004).
  3. J. W. Yeh, S. J. Lin, T. S. Chin, J. Y. Gan, S. K. Chen, T. T. Shun, C. H. Tsau, and S. Y. Chou, Formation of simple crystal structures in Cu-Co-Ni-Cr-Al-Fe-Ti-V alloys with multiprincipal metallic elements, Metall. Mater. Trans. A 35, 2533 (2004).
  4. J. W. Yeh, Recent progress in high entropy alloys, Ann. Chim. Sci. Mater. 31, 633 (2006).
  5. B. Cantor, I. T. Chang, P. Knight, and A. Vincent, Microstructural development in equiatomic multicomponent alloys, Mater. Sci. Eng. A 375–377, 213 (2004).
  6. Y. Zhang, Y. J. Zhou, J. P. Lin, G. L. Chen, and P. K. Liaw, Solid-solution phase formation rules for multi-component alloys, Adv. Eng. Mater. 10, 534 (2008).
  7. F. Otto, Y. Yang, H. Bei, and E. P. George, Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy alloys, Acta Mater. 61, 2628 (2013).
  8. B. Gludovatz, A. Hohenwarter, D. Catoor, E. H. Chang, E. P. George, and R. O. Ritchie, A fracture-resistant high-entropy alloy for cryogenic applications, Science 345, 1153 (2014).
  9. S. Huang, H. Huang, W. Li, D. Kim, S. Lu, X. Li, E. Holmström, S. K. Kwon, and L. Vitos, Twinning in metastable high-entropy alloys, Nat. Commun. 9, 2381 (2018).
  10. Y. Zou, H. Ma, and R. Spolenak, Ultrastrong ductile and stable high-entropy alloys at small scales, Nat. Commun. 6, 7748 (2015).
  11. C. Lee, Y. Chen, C. Hsu, J. Yeh, and H. Shih, The effect of boron on the corrosion resistance of the high entropy alloys Al0.5CoCrCuFeNiBx, J. Electrochem. Soc. 154, C424 (2007).
  12. K. Y. Tsai, M. H. Tsai, and J. W. Yeh, Sluggish diffusion in Co-Cr-Fe-Mn-Ni high-entropy alloys, Acta Mater. 61, 4887 (2013).
  13. K. Motla, Arushi, S. Jangid, P. K. Meena, R. K. Kushwaha, and R. P. Singh, Superconducting properties of new hexagonal and noncentrosymmetric cubic high entropy alloys, Supercond. Sci. Technol. 36, 115024 (2023).
  14. S. Jangid, P. K. Meena, R. K. Kushwaha, S. Srivastava, P. Manna, P. Mishra, S. Sharma, and R. P. Singh, Superconductivity with a high upper critical field in an equiatomic high-entropy alloy Sc-V-Ti-Hf-Nb, Appl. Phys. Lett. 124, 192602 (2024).
  15. S. Jangid, P. K. Meena, R. K. Kushwaha, S. Srivastava, P. Manna, S. Sharma, P. Mishra, and R. P. Singh, Lightweight 3d-element-rich high-entropy alloy superconductor with high critical field and current density, Phys. Rev. Mater. 9, 094804 (2025).
  16. S. G. Jung, Y. Han, J. H. Kim, R. Hidayati, J. S. Rhyee, J. M. Lee, W. N. Kang, W. S. Choi, H. R. Jeon, and J. Suk, High critical current density and high-tolerance superconductivity in high-entropy alloy thin films, Nat. Commun. 13, 3373 (2022).
  17. C. K. Leung, X. Zhang, F. von Rohr, R. Lortz, and B. Jäck, Evidence for isotropic s-wave superconductivity in high-entropy alloys, Sci. Rep. 12, 12773 (2022).
  18. J. Guo, H. Wang, F. Von Rohr, Z. Wang, S. Cai, Y. Zhou, K. Yang, A. Li, S. Jiang, and Q. Wu, Robust zero resistance in a superconducting high-entropy alloy at pressures up to 190 GPa, Proc. Natl. Acad. Sci. USA 114, 13144 (2017).
  19. F. Marques, M. Balcerzak, F. Winkelmann, G. Zepon, and M. Felderhoff, Review and outlook on high-entropy alloys for hydrogen storage, Energy Environ. Sci. 14, 5191 (2021).
  20. E. J. Pickering, A. W. Carruthers, P. J. Barron, S. C. Middleburgh, D. E. Armstrong, and A. S. Gandy, High-entropy alloys for advanced nuclear applications, Entropy 23, 98 (2021).
  21. D. Castro, P. Jaeger, A. C. Baptista, and J. P. Oliveira, An overview of high-entropy alloys as biomaterials, Metals 11, 648 (2021).
  22. M. B. Maple, Interplay between superconductivity and magnetism, Physica B 215, 110 (1995).
  23. P. Rosa, C. Adriano, T. M. Garitezi, M. M. Piva, K. Mydeen, T. Grant, Z. Fisk, M. Nicklas, R. Urbano, and R. M. Fernandes, Possible unconventional superconductivity in substituted BaFe2As2 revealed by magnetic pair-breaking studies, Sci. Rep. 4, 6252 (2014).
  24. C. C. Hsieh, C. Ke, D. J. Zhou, C. H. Cheng, H. Zhang, and Y. Zhao, Cr doping effects on structure and superconductivity of Ba2Ti2Fe2As4O, J. Alloys Compd. 745, 460 (2018).
  25. G. Ding, H. Wo, Y. Gu, Y. Gu, and J. Zhao, Effect of chromium doping on superconductivity and charge density wave order in the kagome metal Cs(V1−xCrx)3Sb5, Phys. Rev. B 106, 235151 (2022).
  26. B. Li, S. Li, and H. H. Wen, Chemical doping effect in the LaRu3Si2 superconductor with a kagome lattice, Phys. Rev. B 94, 094523 (2016).
  27. S. Bazargan, H. Javanmard, and M. Akhavan, Localization length-doping dependence in GdBa2Cu3−xCrxO7−δ, Physica C 466, 157 (2007).
  28. B. Liu, J. Wu, Y. Cui, Q. Zhu, G. Xiao, S. Wu, G.-H. Cao, and Z. Ren, Superconductivity and paramagnetism in Cr-containing tetragonal high-entropy alloys, J. Alloys Compd. 869, 159293 (2021).
  29. R. Y. Chen and N. L. Wang, Progress in Cr- and Mn-based superconductors: A key issues review, Rep. Prog. Phys. 82, 012503 (2019).
  30. Y. Liang, J. Wang, Z. Yang, T. Huang, and P. Song, A new Cr-based high entropy coating with high wear and corrosion resistance, Ceram. Int. 51, 27112 (2025).
  31. A. D. Hillier, J. S. Lord, K. Ishida, and C. Rogers, Muons at ISIS, Philos. Trans. R. Soc. A 377, 20180064 (2019).
  32. A. Le Bail, H. Duroy, and J. L. Fourquet, Ab initio structure determination of LiSbWO6 by x-ray powder diffraction, Mater. Res. Bull. 23, 447 (1988).
  33. S. Jangid, P. K. Meena, N. P. Atale, R. Stewart, A. D. Hillier, and R. P. Singh, Superconducting properties of an equiatomic hexagonal high-entropy alloy via muon spin relaxation and rotation measurement, Phys. Rev. B 111, 214504 (2025).
  34. G. Xiao, W. Yang, Q. Zhu, S. Song, G.-H. Cao, and Z. Ren, Superconductivity with large upper critical field in noncentrosymmetric Cr-bearing high-entropy alloys, Scr. Mater. 223, 115099 (2023).
  35. N. Sarkar, C. Prajapat, P. Ghosh, N. Garg, P. Babu, S. Wajhal, P. Krishna, M. Gonal, R. Tewari, and P. Mishra, Investigations on superconductivity in an equi-atomic disordered Hf-Nb-Ta-Ti-V high entropy alloy, Intermetallics 144, 107503 (2022).
  36. K. Motla, Arushi, P. K. Meena, D. Singh, P. K. Biswas, A. D. Hillier, and R. P. Singh, Probing the superconducting ground state of noncentrosymmetric high-entropy alloys using muon-spin rotation and relaxation, Phys. Rev. B 104, 094515 (2021).
  37. K. Motla, V. Soni, P. K. Meena, and R. P. Singh, Boron based new high entropy alloy superconductor Mo0.11W0.11V0.11Re0.34B0.33, Supercond. Sci. Technol. 35, 074002 (2022).
  38. K. Motla, P. K. Meena, Arushi, D. Singh, P. K. Biswas, A. D. Hillier, and R. P. Singh, Superconducting and normal-state properties of the high-entropy alloy Nb-Re-Hf-Zr-Ti investigated by muon spin relaxation and rotation, Phys. Rev. B 105, 144501 (2022).
  39. A. Ślebarski, M. Fijałkowski, M. M. Maśka, M. Mierzejewski, B. D. White, and M. B. Maple, Superconductivity of La3Co4Sn13 and La3Rh4Sn13: A comparative study, Phys. Rev. B 89, 125111 (2014).
  40. A. Bianchi, R. Movshovich, M. Jaime, J. D. Thompson, P. G. Pagliuso, and J. L. Sarrao, Origin of the zero-resistance anomaly in heavy fermion superconducting CeIrIn5:A clue from magnetic-field and Rh-doping studies, Phys. Rev. B 64, 220504(R) (2001).
  41. C. P. Bean, Magnetization of hard superconductors, Phys. Rev. Lett. 8, 250 (1962).
  42. G. Kim, M. H. Lee, J. H. Yun, P. Rawat, S. G. Jung, W. Choi, T. S. You, S. J. Kim, and J. S. Rhyee, Strongly correlated and strongly coupled s-wave superconductivity of the high entropy alloy Ta1/6Nb2/6Hf1/6Zr1/6Ti1/6 compound, Acta Mater. 186, 250 (2020).
  43. M. Tinkham and V. Emery, in Introduction to Superconductivity (American Institute of Physics, New York, 1996), Vol. 49, p. 65.
  44. T. Klimczuk, F. Ronning, V. Sidorov, R. J. Cava, and J. D. Thompson, Physical properties of the noncentrosymmetric superconductor Mg10Ir19B16, Phys. Rev. Lett. 99, 257004 (2007).
  45. N. R. Werthamer, E. Helfand, and P. C. Hohenberg, Temperature and purity dependence of the superconducting critical field, Hc2. III. Electron spin and spin-orbit effects, Phys. Rev. 147, 295 (1966).
  46. E. Helfand and N. R. Werthamer, Temperature and purity dependence of the superconducting critical field, Hc2. II, Phys. Rev. 147, 288 (1966).
  47. B. S. Chandrasekhar, A note on the maximum critical field of high-field superconductors, Appl. Phys. Lett. 1, 7 (1962).
  48. A. M. Clogston, Upper limit for the critical field in hard superconductors, Phys. Rev. Lett. 9, 266 (1962).
  49. K. Maki, Effect of Pauli paramagnetism on magnetic properties of high-field superconductors, Phys. Rev. 148, 362 (1966).
  50. G. Blatter, M. V. Feigel'man, V. B. Geshkenbein, A. I. Larkin, and V. M. Vinokur, Vortices in high-temperature superconductors, Rev. Mod. Phys. 66, 1125 (1994).
  51. C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, New York, 2005).
  52. W. L. McMillan, Transition temperature of strong-coupled superconductors, Phys. Rev. 167, 331 (1968).
  53. A. D. Hillier, S. J. Blundell, I. McKenzie, I. Umegaki, L. Shu, J. A. Wright, T. Prokscha, F. Bert, K. Shimomura, and A. Berlie, Muon spin spectroscopy, Nat. Rev. Methods Primers 2, 4 (2022).
  54. A. Maisuradze, R. Khasanov, A. Shengelaya, and H. Keller, Comparison of different methods for analyzing μSR line shapes in the vortex state of type-II superconductors, J. Phys.: Condens. Matter 21, 075701 (2009).
  55. M. Weber, A. Amato, F. N. Gygax, A. Schenck, H. Maletta, V. N. Duginov, V. G. Grebinnik, A. B. Lazarev, V. G. Olshevsky, V. Y. Pomjakushin, S. N. Shilov, V. A. Zhukov, B. F. Kirillov, A. V. Pirogov, A. N. Ponomarev, V. G. Storchak, S. Kapusta, and J. Bock, Magnetic-flux distribution and the magnetic penetration depth in superconducting polycrystalline Bi2Sr2Ca1−xYxCu2O8+δ and Bi2−xPbxSr2CaCu2O8+δ, Phys. Rev. B 48, 13022 (1993).
  56. J. E. Sonier, J. H. Brewer, and R. F. Kiefl, μSR studies of the vortex state in type-II superconductors, Rev. Mod. Phys. 72, 769 (2000).
  57. E. H. Brandt, Flux distribution and penetration depth measured by muon spin rotation in high-Tc superconductors, Phys. Rev. B 37, 2349 (1988).
  58. V. Fesenko, V. Gorbunov, and V. Smilga, Analytical properties of muon polarization spectra in type-II superconductors and experimental data interpretation for mono- and polycrystalline HTSCs, Physica C 176, 551 (1991).
  59. A. Carrington and F. Manzano, Magnetic penetration depth of MgB2, Physica C 385, 205 (2003).
  60. S. K. Ghosh, M. Smidman, T. Shang, J. F. Annett, A. D. Hillier, J. Quintanilla, and H. Yuan, Recent progress on superconductors with time-reversal symmetry breaking, J. Phys.: Condens. Matter 33, 033001 (2021).
  61. R. S. Hayano, Y. J. Uemura, J. Imazato, N. Nishida, T. Yamazaki, and R. Kubo, Zero-and low-field spin relaxation studied by positive muons, Phys. Rev. B 20, 850 (1979).
  62. Y. J. Uemura, V. J. Emery, A. R. Moodenbaugh, M. Suenaga, D. C. Johnston, A. J. Jacobson, J. T. Lewandowski, J. H. Brewer, R. F. Kiefl, S. R. Kreitzman, G. M. Luke, T. Riseman, C. E. Stronach, W. J. Kossler, J. R. Kempton, X. H. Yu, D. Opie, and H. E. Schone, Systematic variation of magnetic-field penetration depth in high-Tc superconductors studied by muon-spin relaxation, Phys. Rev. B 38, 909 (1988).
  63. Y. J. Uemura, G. M. Luke, B. J. Sternlieb, J. H. Brewer, J. F. Carolan, W. N. Hardy, R. Kadono, J. R. Kempton, R. F. Kiefl, S. R. Kreitzman, et al., Universal correlations between Tc and nsm* (carrier density over effective mass) in high-Tc cuprate superconductors, Phys. Rev. Lett. 62, 2317 (1989).
  64. Y. J. Uemura, L. P. Le, G. M. Luke, B. J. Sternlieb, W. D. Wu, J. H. Brewer, T. M. Riseman, C. L. Seaman, M. B. Maple, M. Ishikawa, D. G. Hinks, J. D. Jorgensen, G. Saito, and H. Yamochi, Basic similarities among cuprate, bismuthate, organic, Chevrel-phase, and heavy-fermion superconductors shown by penetration-depth measurements, Phys. Rev. Lett. 66, 2665 (1991).
  65. A. Hillier and R. Cywinski, The classification of superconductors using muon spin rotation, Appl. Magn. Reson. 13, 95 (1997).
  66. R. P. Singh et al., Microscopic study of equiatomic high entropy alloy superconductors using μSR measurement, STFC ISIS Neutron and Muon Source (2024), https://doi.org/10.5286/ISIS.E.RB2410706-1.

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APS Open Sci. 1, 000137– Published 16 September, 2026
Vol. 1
  • Received 17 April 2026
  • Accepted 19 August 2026
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