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Kitaoka Lab. M1 Ryuji Michizoe

59 Co NMR shift anomalies and spin dynamics in the normal state of superconducting CeCoIn5. H. Sakai et al., PHYSICAL REVIEW B 8 2 , 020501 (2010). Kitaoka Lab. M1 Ryuji Michizoe. Contents. ・ Introduction - Heavy fermion system(HF) - Superconductivity(SC) in CeCoIn 5

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Kitaoka Lab. M1 Ryuji Michizoe

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  1. 59Co NMR shift anomalies and spin dynamics in the normal state of superconducting CeCoIn5 H. Sakai et al., PHYSICAL REVIEW B 82, 020501 (2010) KitaokaLab. M1 Ryuji Michizoe

  2. Contents ・Introduction - Heavy fermion system(HF) -Superconductivity(SC) in CeCoIn5 ・Experimental results - The relationship between Tcandspin fluctuation energy - The relationship between Tcandanisotropy ・Summary

  3. 4f 5p 5d n(r) 6s r Heavy Fermion compounds The interaction between localized f electrons and itinerant conduction electrons is very important . CeCu2Si2 CePd2Si2CeRh2Si2CeIn3CeRhIn5 f electrons PuCoGa5etc UPt3UPd2Al3

  4. RKKY interaction H=-JcfSc・Sf(Jcf= - t2 / U ) The interplay between two 4f electrons mediated by conduction electrons. Conduction electrons polarization Jcf Jcf 4felectrons Magnetic order U :Coulomb energy t : Transition integrate

  5. Kondo effect H=-JcfSc・Sf(Jcf = - t2 / U ) E Heavy Fermion state 4f and conduction electrons form a spin-singlet state E4f + U EF Conduction electrons E4f D(E) 4felectrons m* : effective mass EF: Fermi energy Ef: Energy of f electrons D(E) : Density of states m* ∝ D(E)

  6. Phase Diagram of HF system H=-JcfSc・Sf(Jcf = - t2 / U ) TK ∝ W exp(-1/JcfD(εF)) TRKKY ∝ D(εF) Jcf2 SC Local Itinerant AFM : antiferromagnetism QCP : quantumcritical point

  7. Tcmax = 2.6K Superconductivity in CeCoIn5 CeCoIn5 Tc ~ 2.3 K CeIrIn5 Tc~ 0.4 K PuCoGa5 Tc~ 18.5 K PuRhGa5 Tc ~ 8.5 K M. Nicklaset al., PRB 76, 052401 (2007). V. A Sidorov et al., PRL 89, 157004 (2002). SC may be mediated by AFM spin fluctuations

  8. The relationship between spin fluctuation(SF) energyand Tc Χ(ω） ω Γ John L. SARRAO et al,. JPSJ-76-051013(2007) As SF energy increases, Tc becomes high.

  9. SF energy Γaand Γc

  10. The relationship between magnetic anisotropy and Tc PuRhGa5 CeCoIn5 PuRhGa5 CeCoIn5 S.-H. Baek et al., PRL 105, 217002 (2010) ρ> 1 indicates 2D magnetic anisotropy

  11. The relationship between magnetic anisotropy and Tc PuRhGa5 CeCoIn5 S.-H. Baek et al., PRL 105, 217002 (2010) Is the magnetic anisotropy favorable for SC ?

  12. Summary ○CeCoIn5 has 2D AFM spin fluctuations. ○As Γc/ Γaincreases, Tcbecomes higher and higher. PuRhGa5 PuRhGa5 CeCoIn5 CeCoIn5 ○The magnetic anisotropy may be favorable for SC.

  13. END

  14. What’s T1? H Nuclear spin T1 : Spin-lattice relaxation time

  15. T dependence of χ (γnA⊥(T))-2 ∝ T Quasi-2D AFM spin fluctuation(SF) ○:59Co ( H // c ) ●: 115In(1) 1/T1(γnA⊥(T))-2 ∝ T1/4 ⇒ Quasi-2D AFM spin fluctuation(SF) 1/T1(γnA⊥(T))-2 ∝ T1/2 ⇒ 3D AFM spin fluctuation(SF)

  16. What’s the Knight Shift(K)? Hhf H Ce Co Ce ω ω0 ω0+ Δω ω0: resonance frequency Hhf : hyperfine field

  17. T dependence of K , χ H. Shishido et al., JPSJ 71, 162 (2002) Magnetic anisotropy Ka: H // a Kc : H // c

  18. T dependence of A K = Aχ A is estimated from K-χ plot A : hyperfine coupling constant

  19. T dependence of T1 In(1) H = 50 kOe (γnA⊥(T))2 T Im[χ⊥(q,ω0)] ∝ ∝ T1/2

  20. Spin fluctuation energy ( ) = spin-lattice relaxation rate Χ(ω） Γ ω

  21. T dependence of Ra , Rc = Ra + Rc = 2Ra

  22. Spin Fluctuation energy

  23. N. J. Curro et al.,PRB 64, 180514(2001)

  24. Y. Kohori et al., PRB 64,134526(2001)

  25. CeRhIn5

  26. The spin-lattice relaxation rate Rα Ra = Rb = Ra + Rc = 2Ra

  27. Heavy Fermion system Kondo effect 4f and conduction electrons form a spin-singlet state Conduction electron Jcf Fermi Liquid 4f electron

  28. Heavy Fermion system RKKY interaction The interplay between two 4f electrons mediated by conduction electrons Conduction electron Polarization Jcf Jcf Magnetic Order 4f electron

  29. RKKY interaction Kondo effect Conduction electron Conduction electron 4f electron 4f electron 4f and conduction electrons form a spin-singlet state. The interplay between two 4f electrons mediated by conduction electrons Heavy fermion system (RKKY:Rudermann-Kittel-Kasuya-Yoshida) Magnetic Order Fermi Liquid heavy fermion system : 重い電子系

  30. 1900 1920 1940 1960 1980 2000 2020 Year History of Superconductivity(SC) Discovery of superconducting phenomenon 200 metal 1911 heavy fermion system high-Tc cuprate 163 Hg-Ba-Ca-Cu-O iron-based system under high pressure （ ） 150 Hg-Ba-Ca-Cu-O Heavy fermion superconductor Tl-Ba-Ca-Cu-O 1986 1979 Bi-Sr-Ca-Cu-O 100 SC transition temperature-Tc(K) Y-Ba-Cu-O 77 High-Tccuprate superconductor SmO F FeAs 50 0.9 0.11 MgB2 La-Ba-Cu-O LaO F FeAs PuCoGa5 2006 Nb Ge 0.11 0.89 Nb Pb CeCu2Si2 NbN LaOFeP Hg NbC Iron-based high-Tc superconductor 0

  31. Heavy Fermion state Normal metal ＋ ＋ ＋ ＋ ＋ ＋ Heavy fermion state f f f ＋ ＋ ＋ c-f hybridization f f f ＋ ＋ ＋ conduction electron

  32. parallel polarization antiparallel J J 4f electron Coulomb interaction

  33. Development of magnetic moment E E4f + U EF E4f t : Hopping integrate D(E) U :Coulomb interaction EF: Fermi energy Ef: Energy of f electrons D(E) : Density of states

  34. BCS superconductivity - SC in Heavy Fermion system is not BCS type. + - Cooper pare BCS superconductivity is mediated by lattice viblation

  35. Kondo effect H=-JcfSc・Sf(Jcf = - t2 / U ) itinerant E TK > TRKKY E4f + U Heavy Fermion state EF Conduction electron E4f singlet 4f electron D(E) m* ∝ D(EF) m* : effective mass

  36. Heavy Fermion state E m* ∝ D(EF) E4f + U EF E4f D(E)

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