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Magnetic pair breaking and local lattice distortion in Cr-containing high-entropy alloy superconductors

Nikita Sharma*, Tirthankar Chakraborty, and Sourav Marik

  • *Contact author: nsharma_phd23@thapar.edu
  • Contact author: soumarik@thapar.edu

Phys. Rev. Materials 10, 064803 – Published 4 June, 2026

DOI: https://doi.org/10.1103/ngx6-vxlq

Abstract

High-entropy alloys provide an ideal platform for investigating superconductivity in the presence of extreme chemical disorder, lattice distortion, and magnetic impurity effects. Herein, we report a systematic study of the structural, normal-state, and superconducting-state properties of (TiVTa)0.6Nb0.4xCrx high-entropy alloys with x=0, 0.05, and 0.20. All compositions crystallize in a single-phase body-centered-cubic structure, with space group Im-3m. Our detailed analysis includes magnetization, resistivity, and specific-heat capacity measurements. The superconducting transition temperature is progressively suppressed from 4.68 to 2.59 K and the upper critical field is decreased from 5.77 to 3.87 T with increasing Cr content in the structure. Heat capacity measurements confirm s-wave weak-coupling superconductivity with a superconducting gap within the BCS limit in all the materials. The suppression of transition temperature follows Abrikosov-Gor'kov behavior, identifying magnetic impurity scattering from Cr as the dominant pair breaking mechanism. First-principles calculation reveals severe local lattice distortion characterized by a large atomic size mismatch δ=5.5% and a substantial average atomic displacement (Δd=0.22Å). The interatomic distance distribution exhibits broadened coordination shells with partially filled gaps between nearest-neighbor shells, reflecting strong deviations from ideal lattice positions while retaining long-range crystalline order.

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References (68)

  1. D. Agarwal, Nickel and nickel alloys, in Handbook of Advanced Materials: Enabling New Designs (Wiley Online Library, New Jersey, United States, 2004), pp. 217–270.
  2. A. Jayakumar, S. Radoor, J. T. Kim, J.-W. Rhim, J. Parameswaranpillai, and S. Siengchin, Lightweight and Sustainable Composite Materials (Elsevier, Amsterdam, 2023), pp. 1–18.
  3. E. Ezugwu and Z. Wang, Titanium alloys and their machinability—a review, J. Mater. Process. Technol. 68, 262 (1997).
  4. E. P. George, D. Raabe, and R. O. Ritchie, High-entropy alloys, Nat. Rev. Mater. 4, 515 (2019).
  5. 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).
  6. X. Wang, W. Guo, and Y. Fu, High-entropy alloys: Emerging materials for advanced functional applications, J. Mater. Chem. A 9, 663 (2021).
  7. N. Ishizu and J. Kitagawa, New high-entropy alloy superconductor Hf21Nb25Ti15V15Zr24, Results Phys. 13, 102275 (2019).
  8. Y. F. Ye, Q. Wang, J. Lu, C. Liu, and Y. Yang, High-entropy alloy: Challenges and prospects, Mater. Today 19, 349 (2016).
  9. 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).
  10. D. H. Cook, P. Kumar, M. I. Payne, C. H. Belcher, P. Borges, W. Wang, F. Walsh, Z. Li, A. Devaraj, M. Zhang, A. Mark, A. M. Minor, E. J. Lavernia, D. Apelian, and R. O. Ritchie, Kink bands promote exceptional fracture resistance in a NbTaTiHf refractory medium-entropy alloy, Science 384, 178 (2024).
  11. C. P. Lee, Y. Y. Chen, C. Y. Hsu, J. W. Yeh, and H. C. Shih, The effect of boron on the corrosion resistance of the high-entropy alloys Al0.5CoCrCuFeNiBx, J. Electrochem. Soc. 154, C424 (2007).
  12. F. O. von Rohr and R. J. Cava, Isoelectronic substitutions and aluminium alloying in the Ta–Nb–Hf–Zr–Ti high-entropy alloy superconductor, Phys. Rev. Mater. 2, 034801 (2018).
  13. P. Koželj, S. Vrtnik, A. Jelen, S. Jazbec, Z. Jagličič, S. Maiti, M. Feuerbacher, W. Steurer, and J. Dolinšek, Discovery of superconductivity in high-entropy alloys, Phys. Rev. Lett. 113, 107001 (2014).
  14. L. Zeng, J. Wang, H. Liu, L. Li, J. Qin, Y. Li, R. Chen, J. Song, Y. Hou, and H. Luo, Ambient-pressure superconductivity onset at 10 K and robust TC under high pressure in TiNbTaN3 medium-entropy nitride, Adv. Sci. 12, e06089 (2025).
  15. L. Zeng, Z. Wang, J. Song, G. Lin, R. Guo, S.-C. Luo, S. Guo, K. Li, P. Yu, C. Zhang, W.-M. Guo, J. Ma, Y. Hou, and H. Luo, Discovery of the high-entropy carbide ceramic topological superconductor candidate (Ti0.2Zr0.2Nb0.2Hf0.2Ta0.2)C, Adv. Funct. Mater. 33, 2301929 (2023).
  16. J. Guo, H. Wang, F. von Rohr, Z. Wang, S. Cai, Y. Zhou, K. Yang, A. Li, S. Jiang, Q. Wu, R. J. Cava, and L. Sun, Robust zero resistance in a superconducting high-entropy alloy at pressures up to 190 GPa, Proc. Natl. Acad. Sci. USA 114, 13144 (2017).
  17. N. Sharma, K. Kargeti, N. Sharma, P. Chourasia, B. Vignolle, O. Toulemonde, T. Chakraborty, S. K. Panda, and S. Marik, Multiband superconductivity and high critical current density in entropy-stabilized Nb0.25Ta0.25Ti0.25Zr0.25, Phys. Rev. B 112, 224515 (2025).
  18. 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).
  19. N. Sharma, J. Link, K. Kargeti, N. Sharma, I. Heinmaa, S. K. Panda, R. Stern, T. Chakraborty, T. Chakrabarty, and S. Marik, Normal state and superconducting state properties of high entropy Ta0.2Nb0.2V0.2Ti0.2X0.2 (X=Zr and Hf), Phys. Rev. Mater. 9, 064801 (2025).
  20. N. Sharma, N. Sharma, T. Chakraborty, and S. Marik, Superconductivity in medium entropy alloy (TiV)0.5Nb0.4Ta0.1, Mater. Today Commun. 44, 111968 (2025).
  21. J. Kitagawa, K. Hoshi, Y. Kawasaki, R. Koga, Y. Mizuguchi, and T. Nishizaki, Superconductivity and hardness of the equiatomic high-entropy alloy HfMoNbTiZr, J. Alloys Compd. 924, 166473 (2022).
  22. S. Marik, M. Varghese, K. Sajilesh, D. Singh, and R. Singh, Superconductivity in equimolar Nb-Re-Hf-Zr-Ti high entropy alloy, J. Alloys Compd. 769, 1059 (2018).
  23. S. Vrtnik, P. Koželj, A. Meden, S. Maiti, W. Steurer, M. Feuerbacher, and J. Dolinšek, Superconductivity in thermally annealed Ta-Nb-Hf-Zr-Ti high-entropy alloys, J. Alloys Compd. 695, 3530 (2017).
  24. K. Stolze, F. A. Cevallos, T. Kong, and R. J. Cava, High-entropy alloy superconductors on an α-Mn lattice, J. Mater. Chem. C 6, 10441 (2018).
  25. K. Stolze, J. Tao, F. O. Von Rohr, T. Kong, and R. J. Cava, Sc–Zr–Nb–Rh–Pd and Sc–Zr–Nb–Ta–Rh–Pd high-entropy alloy superconductors on a CsCl-type lattice, Chem. Mater. 30, 906 (2018).
  26. A. Yamashita, T. D. Matsuda, and Y. Mizuguchi, Synthesis of new high-entropy alloy-type Nb3 (Al, Sn, Ge, Ga, Si) superconductors, J. Alloys Compd. 868, 159233 (2021).
  27. S. Jung, Y. Han, J. H. Kim, R. Hidayati, J. Rhyee, J. M. Lee, W. N. Kang, W. S. Choi, H. Jeon, J. Suk, and T. Park, High critical current density and high-tolerance superconductivity in high-entropy alloy thin films, Nat. Commun. 13, 3373 (2022).
  28. 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).
  29. T. Boutboul, S. Le Naour, D. Leroy, L. Oberli, and V. Previtali, Critical current density in superconducting Nb-Ti strands in the 100 mT to 11 T applied field range, IEEE Trans. Appl. Supercond. 16, 1184 (2006).
  30. N. Banno, Low-temperature superconductors: Nb3Sn, Nb3Al, and NbTi, Superconductivity 6, 100047 (2023).
  31. 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).
  32. S. Bazargan, H. Javanmard, and M. Akhavan, Localization length-doping dependence in GdBa2Cu3xCrxO7δ, Physica C 466, 157 (2007).
  33. C. Hsieh, C. Ke, D. Zhou, C. Cheng, H. Zhang, and Y. Zhao, Cr doping effects on structure and superconductivity of Ba2Ti2Fe2As4O, J. Alloys Compd. 745, 460 (2018).
  34. A. A. Abrikosov and L. P. Gor'kov, Contribution to the theory of superconducting alloys with paramagnetic impurities, Sov. Phys. JETP 12, 1243 (1961).
  35. B. Liu, J. Wu, Y. Cui, Q. Zhu, G. Xiao, S. Wu, G. han Cao, and Z. Ren, Superconductivity and paramagnetism in Cr-containing tetragonal high-entropy alloys, J. Alloys Compd. 869, 159293 (2021).
  36. H. Wang, Q. He, X. Gao, Y. Shang, W. Zhu, W. Zhao, Z. Chen, H. Gong, and Y. Yang, Multifunctional high entropy alloys enabled by severe lattice distortion, Adv. Mater. 36, 2305453 (2024).
  37. H. Song, F. Tian, Q.-M. Hu, L. Vitos, Y. Wang, J. Shen, and N. Chen, Local lattice distortion in high-entropy alloys, Phys. Rev. Mater. 1, 023404 (2017).
  38. A. van de Walle, M. Asta, and G. Ceder, The alloy theoretic automated toolkit: A user guide, Calphad 26, 539 (2002).
  39. A. van de Walle, Multicomponent multisublattice alloys, nonconfigurational entropy and other additions to the alloy theoretic automated toolkit, Calphad 33, 266 (2009).
  40. A. van de Walle, P. Tiwary, M. de Jong, D. L. Olmsted, M. Asta, A. Dick, D. Shin, Y. Wang, L. Q. Chen, and Z. K. Liu, Efficient stochastic generation of special quasirandom structures, Calphad 42, 13 (2013).
  41. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  42. L. He, C. Wang, M. Zhang, J. Li, T. Chen, and X. Zhou, Design of BCC/FCC dual-solid solution refractory high-entropy alloys through CALPHAD, machine learning and experimental methods, npj Comput. Mater. 11, 105 (2025).
  43. O. Senkov, J. Scott, S. Senkova, D. Miracle, and C. Woodward, Microstructure and room temperature properties of a high-entropy TaNbHfZrTi alloy, J. Alloys Compd. 509, 6043 (2011).
  44. A. Jacko, J. Fjærestad, and B. Powell, A unified explanation of the Kadowaki-Woods ratio in strongly correlated metals, Nat. Phys. 5, 422 (2009).
  45. 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).
  46. 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).
  47. 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).
  48. D. Yan, D. Geng, Q. Gao, Z. Cui, C. Yi, Y. Feng, C. Song, H. Luo, M. Yang, M. Arita, S. Kumar, E. F. Schwier, K. Shimada, L. Zhao, K. Wu, H. Weng, L. Chen, X. J. Zhou, Z. Wang, Y. Shi, et al., Superconductivity and Fermi-surface nesting in the candidate Dirac semimetal NbC, Phys. Rev. B 102, 205117 (2020).
  49. K. Maki, Effect of Pauli paramagnetism on magnetic properties of high-field superconductors, Phys. Rev. 148, 362 (1966).
  50. C. P. Bean, Magnetization of high-field superconductors, Rev. Mod. Phys. 36, 31 (1964).
  51. D. Dew-Hughes, Flux pinning mechanisms in type II superconductors, Philos. Mag. 30, 293 (1974).
  52. C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, Hoboken, NJ, 2005).
  53. W. L. McMillan, Transition temperature of strong-coupled superconductors, Phys. Rev. 167, 331 (1968).
  54. Y. Yuan, Y. Wu, H. Luo, Z. Wang, X. Liang, Z. Yang, H. Wang, X. Liu, and Z. Lu, Superconducting Ti15Zr15Nb35Ta35 high-entropy alloy with intermediate electron-phonon coupling, Front. Mater. 5, 72 (2018).
  55. H. X. Liu, J. Y. Yao, J. M. Shi, Z. L. Yang, D. Y. Yan, Y. Li, D. H. Chen, H. L. Feng, S. L. Li, Z. J. Wang, and Y. G. Shi, Vanadium-based superconductivity in the breathing kagome compound Ta2V3.1Si0.9, Phys. Rev. B 108, 104504 (2023).
  56. R. J. Radtke, K. Levin, H.-B. Schüttler, and M. R. Norman, Predictions for impurity-induced Tc suppression in the high-temperature superconductors, Phys. Rev. B 48, 653 (1993).
  57. 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).
  58. H. Khan, C. Raub, W. Däumer, K. Lüders, H. Riesemeier, and G. Roth, Superconductivity and electronic structure of V-solid solutions with 3d-, 4d- and 5d-metals, Physica B+C 107, 469 (1981).
  59. B. T. Matthias, Empirical relation between superconductivity and the number of valence electrons per atom, Phys. Rev. 97, 74 (1955).
  60. M. M. Collver and R. H. Hammond, Superconductivity in “amorphous” transition metal alloy films, Phys. Rev. Lett. 30, 92 (1973).
  61. L. Zeng, J. Zhan, M. Boubeche, K. Li, L. Li, P. Yu, K. Wang, C. Zhang, K. Jin, Y. Sun, and H. Luo, Superconductivity in the bcc-type high-entropy alloy TiHfNbTaMo, Adv. Quantum Technol. 6, 2300213 (2023).
  62. F. von Rohr, M. J. Winiarski, J. Tao, T. Klimczuk, and R. J. Cava, Effect of electron count and chemical complexity in the TaNbHfZrTi high-entropy alloy superconductor, Proc. Natl. Acad. Sci. USA 113, E7144 (2016).
  63. O. Senkov and D. Miracle, Effect of the atomic size distribution on glass forming ability of amorphous metallic alloys, Mater. Res. Bull. 36, 2183 (2001).
  64. S. Marik, K. Motla, M. Varghese, K. P. Sajilesh, D. Singh, Y. Breard, P. Boullay, and R. P. Singh, Superconductivity in a new hexagonal high-entropy alloy, Phys. Rev. Mater. 3, 060602(R) (2019).
  65. C. Lee, G. Song, M. C. Gao, R. Feng, P. Chen, J. Brechtl, Y. Chen, K. An, W. Guo, J. D. Poplawsky, et al., Lattice distortion in a strong and ductile refractory high-entropy alloy, Acta Mater. 160, 158 (2018).
  66. W. Guo, W. Dmowski, J.-Y. Noh, P. Rack, P. K. Liaw, and T. Egami, Local atomic structure of a high-entropy alloy: An X-ray and neutron scattering study, Metall. Mater. Trans. A 44, 1994 (2013).
  67. 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).
  68. C. Varvenne, A. Luque, and W. A. Curtin, Theory of strengthening in fcc high entropy alloys, Acta Mater. 118, 164 (2016).

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