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  • Letter
  • Open Access

Interplay of charge and spin fluctuations in a Hund's coupled impurity

Victor Drouin-Touchette1, Elio J. König2,*, Yashar Komijani3, and Piers Coleman1,4

  • 1Center for Materials Theory, Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
  • 2Max-Planck Institute for Solid State Research, 70569 Stuttgart, Germany
  • 3Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221-0011, USA
  • 4Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom

  • *elio.j.koenig@gmail.com
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Phys. Rev. Research 4, L042011 – Published 20 October, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L042011

Abstract

In Hund's metals, the local ferromagnetic interaction between orbitals leads to an emergence of complex electronic states with large and slowly fluctuating magnetic moments. Introducing the Hund's coupled mixed-valence quantum impurity, we gain analytic insight into recent numerical renormalization group studies. We show that valence fluctuations drastically impede the development of a large fluctuating moment over a wide range of temperatures and energy, characterized by quenched orbital degrees of freedom and a singular logarithmic behavior of the spin susceptibility χsp(ω)∝[ωln(ω/TKeff)2]−1, closely resembling power-law scaling χsp(ω)∼ω−γ. Finally, we outline how such singular spin fluctuations can play an important role in generating a superconducting state through Hund's driven Cooper pairing.

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References (74)

  1. K. Haule and G. Kotliar, Coherence–incoherence crossover in the normal state of iron oxypnictides and importance of Hund's rule coupling, New J. Phys. 11, 025021 (2009).
  2. Z. Yin, K. Haule, and G. Kotliar, Fractional power-law behavior and its origin in iron-chalcogenide and ruthenate superconductors: Insights from first-principles calculations, Phys. Rev. B 86, 195141 (2012).
  3. L. Fanfarillo and E. Bascones, Electronic correlations in Hund metals, Phys. Rev. B 92, 075136 (2015).
  4. H. T. Dang, J. Mravlje, A. Georges, and A. J. Millis, Electronic correlations, magnetism, and Hund's rule coupling in the ruthenium perovskites SrRuO3 and CaRuO3, Phys. Rev. B 91, 195149 (2015).
  5. X. Deng, K. Haule, and G. Kotliar, Transport Properties of Metallic Ruthenates: A DFT+DMFT Investigation, Phys. Rev. Lett. 116, 256401 (2016).
  6. Y. Wang, C.-J. Kang, H. Miao, and G. Kotliar, Hund's metal physics: From SrNiO2 to LaNiO2, Phys. Rev. B 102, 161118(R) (2020).
  7. L. de' Medici, Hund's coupling and its key role in tuning multiorbital correlations, Phys. Rev. B 83, 205112 (2011).
  8. A. Georges, L. de Medici, and J. Mravlje, Strong correlations from Hund's coupling, Annu. Rev. Condens. Matter Phys. 4, 137 (2013).
  9. K. M. Stadler, G. Kotliar, A. Weichselbaum, and J. von Delft, Hundness versus mottness in a three-band Hubbard–Hund model: On the origin of strong correlations in Hund metals, Ann. Phys. 405, 365 (2019).
  10. P. Werner, E. Gull, M. Troyer, and A. J. Millis, Spin Freezing Transition and Non-Fermi-Liquid Self-Energy in a Three-Orbital Model, Phys. Rev. Lett. 101, 166405 (2008).
  11. C. Watzenböck, M. Edelmann, D. Springer, G. Sangiovanni, and A. Toschi, Characteristic Timescales of the Local Moment Dynamics in Hund's Metals, Phys. Rev. Lett. 125, 086402 (2020).
  12. P. Hansmann, R. Arita, A. Toschi, S. Sakai, G. Sangiovanni, and K. Held, Dichotomy between Large Local and Small Ordered Magnetic Moments in Iron-Based Superconductors, Phys. Rev. Lett. 104, 197002 (2010).
  13. F. Hardy, A. Böhmer, D. Aoki, P. Burger, T. Wolf, P. Schweiss, R. Heid, P. Adelmann, Y. Yao, G. Kotliar, J. Schmalian, C. Meingast, Evidence of Strong Correlations and Coherence-Incoherence Crossover in the Iron Pnictide Superconductor KFe2As2, Phys. Rev. Lett. 111, 027002 (2013).
  14. F. Hardy, A. Böhmer, L. de'Medici, M. Capone, G. Giovannetti, R. Eder, L. Wang, M. He, T. Wolf, P. Schweiss, R. Heid, A. Herbig, P. Adelmann, R. A. Fisher, C. Meingast, Strong correlations, strong coupling, and s-wave superconductivity in hole-doped BaFe2As2 single crystals, Phys. Rev. B 94, 205113 (2016).
  15. R. Yang, Z. Yin, Y. Wang, Y. Dai, H. Miao, B. Xu, X. Qiu, and C. C. Homes, Observation of an emergent coherent state in the iron-based superconductor KFe2As2, Phys. Rev. B 96, 201108(R) (2017).
  16. G. R. Stewart, Superconductivity in iron compounds, Rev. Mod. Phys. 83, 1589 (2011).
  17. H. Hosono, A. Yamamoto, H. Hiramatsu, and Y. Ma, Recent advances in iron-based superconductors toward applications, Mater. Today 21, 278 (2018).
  18. C. M. Puetter and H.-Y. Kee, Identifying spin-triplet pairing in spin-orbit coupled multi-band superconductors, EPL (Europhysics Letters) 98, 27010 (2012).
  19. S. Hoshino and P. Werner, Superconductivity from Emerging Magnetic Moments, Phys. Rev. Lett. 115, 247001 (2015).
  20. O. Vafek and A. V. Chubukov, Hund Interaction, Spin-Orbit Coupling, and the Mechanism of Superconductivity in Strongly Hole-Doped Iron Pnictides, Phys. Rev. Lett. 118, 087003 (2017).
  21. A. K. C. Cheung and D. F. Agterberg, Superconductivity in the presence of spin-orbit interactions stabilized by hund coupling, Phys. Rev. B 99, 024516 (2019).
  22. P. Coleman, Y. Komijani, and E. J. König, Triplet Resonating Valence Bond State and Superconductivity in Hund's Metals, Phys. Rev. Lett. 125, 077001 (2020).
  23. J. Schrieffer, The Kondo effect–the link between magnetic and nonmagnetic impurities in metals?, J. Appl. Phys. 38, 1143 (1967).
  24. I. Okada and K. Yosida, Singlet ground state of the localized d-electrons coupled with conduction electrons in metals, Prog. Theor. Phys. 49, 1483 (1973).
  25. P. Nozières and A. Blandin, Kondo effect in real metals, J. de Physique 41, 193 (1980).
  26. C. Jayaprakash, H. R. Krishna-Murthy, and J. W. Wilkins, Two-Impurity Kondo Problem, Phys. Rev. Lett. 47, 737 (1981).
  27. A. H. Nevidomskyy and P. Coleman, Kondo Resonance Narrowing in d-and f-Electron Systems, Phys. Rev. Lett. 103, 147205 (2009).
  28. V. Drouin-Touchette, E. J. König, Y. Komijani, and P. Coleman, Emergent moments in a hund's impurity, Phys. Rev. B 103, 205147 (2021).
  29. C. Aron and G. Kotliar, Analytic theory of Hund's metals: A renormalization group perspective, Phys. Rev. B 91, 041110(R) (2015).
  30. A. Horvat, R. Zitko, and J. Mravlje, Non-Fermi-liquid fixed point in multi-orbital Kondo impurity model relevant for Hund's metals, arXiv:1907.07100.
  31. Y. Wang, E. Walter, S. S. B. Lee, K. M. Stadler, J. von Delft, A. Weichselbaum, and G. Kotliar, Global Phase Diagram of a Spin-Orbital Kondo Impurity Model and the Suppression of Fermi-Liquid Scale, Phys. Rev. Lett. 124, 136406 (2020).
  32. E. Walter, K. M. Stadler, S. S. B. Lee, Y. Wang, G. Kotliar, A. Weichselbaum, and J. von Delft, Uncovering Non-Fermi-Liquid Behavior in Hund Metals: Conformal Field Theory Analysis of an SU (2)× SU (3) Spin-Orbital Kondo Model, Phys. Rev. X 10, 031052 (2020).
  33. S. Ryee, S. Choi, and M. J. Han, Frozen spin ratio and the detection of Hund correlations, arXiv:2207.10421.
  34. Y. Komijani and P. Coleman, Model for a Ferromagnetic Quantum Critical Point in a 1D Kondo Lattice, Phys. Rev. Lett. 120, 157206 (2018).
  35. J. Rech, P. Coleman, G. Zarand, and O. Parcollet, Schwinger Boson Approach to the Fully Screened Kondo Model, Phys. Rev. Lett. 96, 016601 (2006).
  36. Y. Komijani and P. Coleman, Emergent Critical Charge Fluctuations at the Kondo Breakdown of Heavy Fermions, Phys. Rev. Lett. 122, 217001 (2019).
  37. J. Wang, Y.-Y. Chang, C.-Y. Mou, S. Kirchner, and C.-H. Chung, Quantum phase transition in a two-dimensional Kondo-Heisenberg model: A dynamical Schwinger-boson large-N approach, Phys. Rev. B 102, 115133 (2020).
  38. B. Shen, Y. Zhang, Y. Komijani, M. Nicklas, R. Borth, A. Wang, Y. Chen, Z. Nie, R. Li, X. Lu et al., Strange-metal behaviour in a pure ferromagnetic Kondo lattice, Nature (London) 579, 51 (2020).
  39. Y. Komijani, Isolating kondo anyons for topological quantum computation, Phys. Rev. B 101, 235131 (2020).
  40. J. Wang and Y.-f. Yang, Nonlocal kondo effect and quantum critical phase in heavy-fermion metals, Phys. Rev. B 104, 165120 (2021).
  41. R. Han, D. Hu, J. Wang, and Y.-f. Yang, Schwinger boson approach for the dynamical mean-field theory of the kondo lattice, Phys. Rev. B 104, 245132 (2021).
  42. Y. Ge and Y. Komijani, Emergent Spinon Dispersion and Symmetry Breaking in Two-Channel Kondo Lattices, Phys. Rev. Lett. 129, 077202 (2022).
  43. K. P. Stadler, Z. M. Yin, J. Von Delft, G. Kotliar, and A. Weichselbaum, Dynamical Mean-Field Theory Plus Numerical Renormalization-Group Study of Spin-Orbital Separation in a Three-Band Hund Metal, Phys. Rev. Lett. 115, 136401 (2015).
  44. C. Varma, Z. Nussinov, and W. Van Saarloos, Singular or non-Fermi liquids, Phys. Rep. 361, 267 (2002).
  45. P. Coleman and C. Pépin, Singular Fermi liquid behavior in the underscreened Kondo model, Phys. Rev. B 68, 220405 (2003).
  46. P. Mehta, N. Andrei, P. Coleman, L. Borda, and G. Zarand, Regular and singular Fermi-liquid fixed points in quantum impurity models, Phys. Rev. B 72, 014430 (2005).
  47. P. Coleman and I. Paul, Quantum replica approach to the underscreened kondo model, Phys. Rev. B 71, 035111 (2005).
  48. P. Coleman, Introduction to Many-Body Physics (Cambridge University Press, Cambridge, England, 2015).
  49. P. Werner, E. Gull, and A. J. Millis, Metal-insulator phase diagram and orbital selectivity in three-orbital models with rotationally invariant Hund coupling, Phys. Rev. B 79, 115119 (2009).
  50. N. Lanata, H. U. Strand, G. Giovannetti, B. Hellsing, L. De'Medici, and M. Capone, Orbital selectivity in Hund's metals: The iron chalcogenides, Phys. Rev. B 87, 045122 (2013).
  51. F. B. Kugler, S.-S. B. Lee, A. Weichselbaum, G. Kotliar, and J. Von Delft, Orbital differentiation in Hund metals, Phys. Rev. B 100, 115159 (2019).
  52. F. B. Kugler and G. Kotliar, Is the Orbital-Selective Mott Phase Stable Against Interorbital Hopping?, Phys. Rev. Lett. 129, 096403 (2022).
  53. One could include realistic crystal field splitting effects in our model by breaking the degeneracy of the three orbitals. The isotropic holon energy term in Eq. (2) would become εf[Xa,a(1)+Xa,a(1)]+(εf+Δcf)Xa,a(3), which leads to an additional self-energy equation for the holons. We expect that a finite Δcf will lead to orbital differentiation, with different Torb crossover temperatures for each orbital subset, but that the S.O.S. regime would remain. The detailed effects of such perturbations are beyond the scope of our work.
  54. P. Coleman, I. Paul, and J. Rech, Sum rules and Ward identities in the Kondo lattice, Phys. Rev. B 72, 094430 (2005).
  55. E. Lebanon, J. Rech, P. Coleman, and O. Parcollet, Conserving many body approach to the infinite-U Anderson model, Phys. Rev. Lett. 97, 106604 (2006).
  56. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L042011 for further information on the bare mixed valence problem, the derivation of spin and orbital susceptibilities, details on the single iteration approach, the scaling of the spin susceptibility and the quasi-power-law exponent.
  57. K. M. Stadler, A model study of strong correlations in Hund metals, Ph.D. thesis, lmu (2019).
  58. Another definition of L̂γ=∑Lγmm′XabmXbam′ purely in terms of orbital charge can generically be written. For the antisymmetric Lγ matrices, this leads to an identically zerow operator.
  59. I. Affleck, A. W. W. Ludwig, H.-B. Pang, and D. L. Cox, Relevance of anisotropy in the multichannel Kondo effect: Comparison of conformal field theory and numerical renormalization-group results, Phys. Rev. B 45, 7918 (1992).
  60. I. Affleck and A. W. W. Ludwig, Exact conformal-field-theory results on the multichannel Kondo effect: Single-fermion Green's function, self-energy, and resistivity, Phys. Rev. B 48, 7297 (1993).
  61. P. Coleman, L. B. Ioffe, and A. M. Tsvelik, Simple formulation of the two-channel Kondo model, Phys. Rev. B 52, 6611 (1995).
  62. A. Georges and A. M. Sengupta, Solution of the Two-Impurity, Two-Channel Kondo Model, Phys. Rev. Lett. 74, 2808 (1995).
  63. O. Parcollet and A. Georges, Transition from Overscreening to Underscreening in the Multichannel Kondo Model: Exact Solution at Large N, Phys. Rev. Lett. 79, 4665 (1997).
  64. O. Parcollet, A. Georges, G. Kotliar, and A. Sengupta, Overscreened multichannel SU (N) Kondo model: Large-N solution and conformal field theory, Phys. Rev. B 58, 3794 (1998).
  65. W. Koller, A. C. Hewson, and D. Meyer, Singular dynamics of underscreened magnetic impurity models, Phys. Rev. B 72, 045117 (2005).
  66. T.-H. Lee, A. Chubukov, H. Miao, and G. Kotliar, Pairing Mechanism in Hund's Metal Superconductors and the Universality of the Superconducting Gap to Critical Temperature Ratio, Phys. Rev. Lett. 121, 187003 (2018).
  67. Y.-M. Wu, A. Abanov, and A. V. Chubukov, Pairing in quantum critical systems: Transition temperature, pairing gap, and their ratio, Phys. Rev. B 99, 014502 (2019).
  68. In reality, Gχ has a frequency dependent behavior, as we saw in the rest of the paper, but it can be approximated as nearly instantaneous with respect to the other propagators.
  69. A. Migdal, Interaction between electrons and lattice vibrations in a normal metal, Sov. Phys. JETP 7, 996 (1958).
  70. G. Eliashberg, Interactions between electrons and lattice vibrations in a superconductor, Sov. Phys. JETP 11, 696 (1960).
  71. R. Combescot, Strong-coupling limit of eliashberg theory, Phys. Rev. B 51, 11625 (1995).
  72. E.-G. Moon and A. Chubukov, Quantum-critical pairing with varying exponents, J. Low Temp. Phys. 161, 263 (2010).
  73. Y. Wang, A. Abanov, B. L. Altshuler, E. A. Yuzbashyan, and A. V. Chubukov, Superconductivity near a Quantum-Critical Point: The Special Role of the First Matsubara Frequency, Phys. Rev. Lett. 117, 157001 (2016).
  74. H. Miao, L.-M. Wang, P. Richard, S.-F. Wu, J. Ma, T. Qian, L.-Y. Xing, X.-C. Wang, C.-Q. Jin, C.-P. Chou, Z. Wang, W. Ku, H. Ding, Coexistence of orbital degeneracy lifting and superconductivity in iron-based superconductors, Phys. Rev. B 89, 220503 (2014).

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Phys. Rev. Research 4, L042011– Published 20 October, 2022
  • Received 22 April 2022
  • Revised 8 September 2022
  • Accepted 9 September 2022
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