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La substitution studies on the heavy-fermion superconductor
Phys. Rev. B 114, 115129 – Published 25 August, 2026
DOI: https://doi.org/10.1103/f79y-ssdx
Abstract
has been receiving considerable attention due to its unusual two-phase superconductivity. The superconducting (SC) phase appears at K in an ordered state (phase I) of the moments, which develops below K. The microscopic nature of phase I has not been fully established yet. We report a single-crystal study of the effect of La substitution on these low-temperature phases in up to . The lattice parameters increase monotonically with , corresponding to an effective negative pressure of approximately GPa for . While the local valence state and the non-Fermi-liquid behavior are preserved, the resistivity coherence maximum K in the pristine sample shifts to lower temperatures with increasing , indicating a suppression of the Kondo energy scale upon lattice expansion. On the other hand, both and are rapidly suppressed to below 0.1 K for . Notably, such a rapid decrease of under moderate negative pressure is unexpected, but is rather consistent with a substitution-induced disorder effect which leads to strong pair breaking in unconventional superconductors. The observed fragility of phase I under both pressure and disorder may imply its itinerant origin.
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References (55)
- S. Khim, J. F. Landaeta, J. Banda, N. Bannor, M. Brando, P. M. R. Brydon, D. Hafner, R. Küchler, R. Cardoso-Gil, U. Stockert, A. P. Mackenzie, D. F. Agterberg, C. Geibel, and E. Hassinger, Field-induced transition from even to odd parity superconductivity in , Science 373, 1012 (2021).
- J. F. Landaeta, P. Khanenko, D. C. Cavanagh, C. Geibel, S. Khim, S. Mishra, I. Sheikin, P. M. R. Brydon, D. F. Agterberg, M. Brando, and E. Hassinger, Field-angle dependence reveals odd-parity superconductivity in , Phys. Rev. X 12, 031001 (2022).
- R. Madar, P. Chaudouet, J. Senateur, S. Zemni, and D. Tranqui, New ternary pnictides with the -type structure in the systems, rare-earth-Rh-P and rare-earth-Rh-As, J. Less-Common Met. 133, 303 (1987).
- T. Yoshida, M. Sigrist, and Y. Yanase, Pair-density wave states through spin-orbit coupling in multilayer superconductors, Phys. Rev. B 86, 134514 (2012).
- D. Maruyama, M. Sigrist, and Y. Yanase, Locally non-centrosymmetric superconductivity in multilayer systems, J. Phys. Soc. Jpn. 81, 034702 (2012).
- M. Sigrist, D. F. Agterberg, M. H. Fischer, J. Goryo, F. Loder, S.-H. Rhim, D. Maruyama, Y. Yanase, T. Yoshida, and S. J. Youn, Superconductors with staggered non-centrosymmetricity, J. Phys. Soc. Jpn. 83, 061014 (2014).
- E. G. Schertenleib, M. H. Fischer, and M. Sigrist, Unusual phase diagram of : The role of staggered noncentrosymmetricity, Phys. Rev. Res. 3, 023179 (2021).
- D. Möckli and A. Ramires, Two scenarios for superconductivity in , Phys. Rev. Res. 3, 023204 (2021).
- D. C. Cavanagh, T. Shishidou, M. Weinert, P. M. R. Brydon, and D. F. Agterberg, Nonsymmorphic symmetry and field-driven odd-parity pairing in , Phys. Rev. B 105, L020505 (2022).
- M. H. Fischer, M. Sigrist, D. F. Agterberg, and Y. Yanase, Superconductivity and local inversion-symmetry breaking, Annu. Rev. Condens. Matter Phys. 14, 153 (2023).
- K. Nogaki, A. Daido, J. Ishizuka, and Y. Yanase, Topological crystalline superconductivity in locally noncentrosymmetric , Phys. Rev. Res. 3, L032071 (2021).
- J. Ishizuka, K. Nogaki, M. Sigrist, and Y. Yanase, Correlation-induced Fermi surface evolution and topological crystalline superconductivity in , Phys. Rev. B 110, L140505 (2024).
- G. Chajewski and D. Kaczorowski, Discovery of magnetic phase transitions in heavy-fermion superconductor , Phys. Rev. Lett. 132, 076504 (2024).
- M. Kibune, S. Kitagawa, K. Kinjo, S. Ogata, M. Manago, T. Taniguchi, K. Ishida, M. Brando, E. Hassinger, H. Rosner, C. Geibel, and S. Khim, Observation of antiferromagnetic order as odd-parity multipoles inside the superconducting phase in , Phys. Rev. Lett. 128, 057002 (2022).
- S. Ogata, S. Kitagawa, K. Kinjo, K. Ishida, M. Brando, E. Hassinger, C. Geibel, and S. Khim, Parity transition of spin-singlet superconductivity using sublattice degrees of freedom, Phys. Rev. Lett. 130, 166001 (2023).
- S. Khim, O. Stockert, M. Brando, C. Geibel, C. Baines, T. J. Hicken, H. Luetkens, D. Das, T. Shiroka, Z. Guguchia, and R. Scheuermann, Coexistence of local magnetism and superconductivity in the heavy-fermion compound revealed by studies, Phys. Rev. B 111, 115134 (2025).
- D. Hafner, P. Khanenko, E.-O. Eljaouhari, R. Küchler, J. Banda, N. Bannor, T. Lühmann, J. F. Landaeta, S. Mishra, I. Sheikin, E. Hassinger, S. Khim, C. Geibel, G. Zwicknagl, and M. Brando, Possible quadrupole density wave in the superconducting Kondo lattice , Phys. Rev. X 12, 011023 (2022).
- K. Semeniuk, D. Hafner, P. Khanenko, T. Lühmann, J. Banda, J. F. Landaeta, C. Geibel, S. Khim, E. Hassinger, and M. Brando, Decoupling multiphase superconductivity from normal state ordering in , Phys. Rev. B 107, L220504 (2023).
- J. Bławat, G. Chajewski, D. Gnida, J. Singleton, O. Ayala Valenzuela, D. Kaczorowski, and R. D. McDonald, Competing electronic ground states in the heavy-fermion superconductor , Phys. Rev. X 15, 041057 (2025).
- P. Khanenko, J. F. Landaeta, S. Ruet, T. Lühmann, K. Semeniuk, M. Pelly, A. W. Rost, G. Chajewski, D. Kaczorowski, C. Geibel, S. Khim, E. Hassinger, and M. Brando, Phase diagram of for out-of-plane magnetic field, Phys. Rev. B 112, L060501 (2025).
- D. S. Christovam, M. Ferreira-Carvalho, A. Marino, M. Sundermann, D. Takegami, A. Melendez-Sans, K. D. Tsuei, Z. Hu, S. Rößler, M. Valvidares, M. W. Haverkort, Y. Liu, E. D. Bauer, L. H. Tjeng, G. Zwicknagl, and A. Severing, Spectroscopic evidence of Kondo-induced quasiquartet in , Phys. Rev. Lett. 132, 046401 (2024).
- B. Schmidt and P. Thalmeier, Anisotropic magnetic and quadrupolar phase diagram of , Phys. Rev. B 110, 075154 (2024).
- P. Thalmeier, A. Akbari, and B. Schmidt, Thermodynamics, elastic anomalies and excitations in the field induced phases of , New J. Phys. 27, 033026 (2025).
- P. Khanenko, D. Hafner, K. Semeniuk, J. Banda, T. Lühmann, F. Bärtl, T. Kotte, J. Wosnitza, G. Zwicknagl, C. Geibel, J. F. Landaeta, S. Khim, E. Hassinger, and M. Brando, Origin of the non-Fermi-liquid behavior in , Phys. Rev. B 111, 045162 (2025).
- A. Amin, H. Wu, T. Shishidou, and D. F. Agterberg, Kramers' degenerate magnetism and superconductivity, Phys. Rev. B 109, 024502 (2024).
- A. L. Szabó and A. Ramires, Superconductivity-induced improper orders in nonsymmorphic systems, Phys. Rev. B 110, L180503 (2024).
- C. Lee, D. F. Agterberg, and P. M. R. Brydon, Unified picture of superconductivity and magnetism in , Phys. Rev. Lett. 135, 026003 (2025).
- H. Siddiquee, Z. Rehfuss, C. Broyles, and S. Ran, Pressure dependence of superconductivity in , Phys. Rev. B 108, L020504 (2023).
- K. Semeniuk, M. Pfeiffer, J. F. Landaeta, M. Nicklas, C. Geibel, M. Brando, S. Khim, and E. Hassinger, Exposing the odd-parity superconductivity in with hydrostatic pressure, Phys. Rev. B 110, L100504 (2024).
- M. Pfeiffer, K. Semeniuk, J. F. Landaeta, R. Borth, C. Geibel, M. Nicklas, M. Brando, S. Khim, and E. Hassinger, Pressure-tuned quantum criticality in the locally noncentrosymmetric superconductor , Phys. Rev. Lett. 133, 126506 (2024).
- L. Akselrud and Y. Grin, WinCSD: Software package for crystallographic calculations (version 4), J. Appl. Cryst. 47, 803 (2014).
- F. C. Ragel, P. D. V. du Plessis, and A. M. Strydom, Effects of La dilution on the Kondo lattice, J. Phys.: Condens. Matter 20, 055218 (2008).
- Y. Ōnuki, T. Hirai, T. Kumazawa, T. Komatsubara, and Y. Oda, Heavy fermion state and superconductivity in , J. Phys. Soc. Jpn. 56, 1454 (1987).
- B. Andraka, C. Jee, J. Kim, H. Li, M. Meisel, and G. Stewart, Heavy-fermion, magnetic and superconducting behavior of ; = , La, Th, Physica B 171, 384 (1991).
- M. Očko, D. Drobac, B. Buschinger, C. Geibel, and F. Steglich, Transport properties of the heavy-fermion alloy system, Phys. Rev. B 64, 195106 (2001).
- C. Petrovic, S. L. Bud'ko, V. G. Kogan, and P. C. Canfield, Effects of La substitution on the superconducting state of , Phys. Rev. B 66, 054534 (2002).
- J. F. Landaeta, A. M. León, S. Zwickel, T. Lühmann, M. Brando, C. Geibel, E.-O. Eljaouhari, H. Rosner, G. Zwicknagl, E. Hassinger, and S. Khim, Conventional type-II superconductivity in locally noncentrosymmetric single crystals, Phys. Rev. B 106, 014506 (2022).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/f79y-ssdx for a detailed description of the data analyses, which include Refs. [49, 50, 51, 52, 53, 54, 55].
- M. L. Ali, M. K. Alam, M. Khan, M. N. M. Nobin, N. Islam, U. Faruk, and M. Z. Rahaman, Pressure-dependent structural, electronic, optical, and mechanical properties of superconductor : A first-principles study, Physica B 668, 415224 (2023).
- U. Ahlheim, M. Winkelmann, P. van Aken, C. Bredl, F. Steglich, and G. Stewart, Pair breaking in the heavy-fermion superconductors and (M = Th, La, Y and Gd), J. Magn. Magn. Mater. 76–77, 520 (1988).
- F. Steglich, U. Ahlheim, U. Rauchschwalbe, and H. Spille, Heavy fermions and superconductivity: “Superconducting spectroscopy” of non-magnetic impurities in , Physica B+C 148, 6 (1987).
- A. A. Abrikosov and L. P. Gor'kov, Contribution to the theory of superconducting alloys with paramagnetic impurities, Zh. Eksp. Teor. Fiz. 39, 1781 (1960), [Sov. Phys. JETP 12, 1243 (1961)].
- L. A. Openov, Critical temperature of an anisotropic superconductor containing both nonmagnetic and magnetic impurities, Phys. Rev. B 58, 9468 (1998).
- T. Chen, H. Siddiquee, Q. Xu, Z. Rehfuss, S. Gao, C. Lygouras, J. Drouin, V. Morano, K. E. Avers, C. J. Schmitt, A. Podlesnyak, J. Paglione, S. Ran, Y. Song, and C. Broholm, Quasi-two-dimensional antiferromagnetic spin fluctuations in the spin-triplet superconductor candidate , Phys. Rev. Lett. 133, 266505 (2024).
- Y. Wu, Y. Zhang, S. Ju, Y. Hu, Y. Huang, Y. Zhang, H. Zhang, H. Zheng, G. Yang, E.-O. Eljaouhari, B. Song, N. C. Plumb, F. Steglich, M. Shi, G. Zwicknagl, C. Cao, H. Yuan, and Y. Liu, Fermi surface nesting with heavy quasiparticles in the locally noncentrosymmetric superconductor , Chin. Phys. Lett. 41, 097403 (2024).
- B. Chen, H. Liu, Q.-Y. Wu, C. Zhang, X.-Q. Ye, Y.-Z. Zhao, J.-J. Song, X.-Y. Tian, B.-L. Tan, Z.-T. Liu, M. Ye, Z.-H. Chen, Y.-B. Huang, D.-W. Shen, Y.-H. Yuan, J. He, Y.-X. Duan, and J.-Q. Meng, Exploring possible Fermi surface nesting and the nature of heavy quasiparticles in the spin-triplet superconductor candidate , Phys. Rev. B 110, L041120 (2024).
- X. Chen, L. Wang, J. Ishizuka, R. Zhang, K. Nogaki, Y. Cheng, F. Yang, Z. Chen, F. Zhu, Z. Liu, J. Mei, Y. Yanase, B. Lv, and Y. Huang, Coexistence of near- flat band and van Hove singularity in a two-phase superconductor, Phys. Rev. X 14, 021048 (2024).
- S. L. Ravi Sankar, Data for the manuscript titled: “La substitution studies on the heavy-fermion superconductor ”, Edmond (2026), https://doi.org/10.17617/3.HMFH1A.
- N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976).
- R. J. Radtke, K. Levin, H.-B. Schüttler, and M. R. Norman, Predictions for impurity-induced suppression in the high-temperature superconductors, Phys. Rev. B 48, 653(R) (1993).
- A. Ranna, R. Grasset, M. Gonzalez, K. Lee, B. Y. Wang, E. Abarca Morales, F. Theuss, Z. H. Filipiak, M. Moravec, M. Konczykowski, H. Y. Hwang, A. P. Mackenzie, and B. H. Goodge, Disorder-induced suppression of superconductivity in infinite-layer nickelates, Phys. Rev. Lett. 135, 126501 (2025).
- M. T. Hutchings, Point-charge calculations of energy levels of magnetic ions in crystalline electric fields, Solid State Phys. 16, 227 (1964).
- K. W. H. Stevens, Matrix elements and operator equivalents connected with the magnetic properties of rare earth ions, Proc. Phys. Soc. A 65, 209 (1952).
- F. Marabelli, P. Wachter, and J. Franse, Electronic structure of : A low energy optical study, J. Magn. Magn. Mater. 62, 287 (1986).
- F. Marabelli and P. Wachter, Temperature dependence of the optical conductivity of the heavy-fermion system , Phys. Rev. B 42, 3307 (1990).