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Anisotropic Spin Fluctuations and Superconductivity in ‘115’ Heavy Fermion Compounds :

Anisotropic Spin Fluctuations and Superconductivity in ‘115’ Heavy Fermion Compounds : 59 Co NMR Study in PuCoGa 5. S.-H. Baek et. al. PRL 105 ,217002(2010). Kazuhiro Nishimoto Kitaoka lab. 1. Contents. Introduction - History of superconductivity

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Anisotropic Spin Fluctuations and Superconductivity in ‘115’ Heavy Fermion Compounds :

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  1. Anisotropic Spin Fluctuations and Superconductivity in ‘115’ Heavy Fermion Compounds : 59Co NMR Study in PuCoGa5 S.-H. Baek et. al. PRL 105,217002(2010) Kazuhiro Nishimoto Kitaoka lab. 1

  2. Contents • Introduction • - History of superconductivity • - Heavy fermion system • - Transuranic HF compounds • - Motivation • Measurement • - NMR (Nuclear Magnetic Resonance) • Experimental Results (PuCoGa5) • Summary 2

  3. introduction 1900 1920 1940 1960 1980 2000 2020 Year History of Superconductivity 200 metal Discovery of superconducting phenomenon heavy fermion system high-Tc cuprate 1911 163 Hg-Ba-Ca-Cu-O iron-based system under high pressure （ ） 150 Hg-Ba-Ca-Cu-O Tl-Ba-Ca-Cu-O Heavy fermion superconductor Bi-Sr-Ca-Cu-O 1979 1986 100 Transition temperature (K) Y-Ba-Cu-O 77 SmO F FeAs High-Tc cuprate superconductor 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 3

  4. introduction f f f f f f c-fhybridization ( c-f混成） Heavy Fermion System What does “Heavy” mean? Heavy Fermion system Normal metal ＋ ＋ ＋ ＋ ＋ ＋ ＋ ＋ ＋ ＋ ＋ ＋ Strong electron correlation makes effective mass large. “Heavy” ⇒large effective mass 4

  5. introduction Heavy Fermion System Example of heavy fermion superconductor compounds CeCu2Si2 CePd2Si2CeRh2Si2CeIn3CeRhIn5 PrOs4Sb12 lanthanide compounds ⇒some 4f electrons UPt3UPd2Al3 PuCoGa5 actinide compounds ⇒some 5f electrons All of HF compounds have f-electrons. 5

  6. introduction Transuranic HF Compounds transuranium elements (超ウラン元素) • don’t exist in nature • Handling is difficult because of • strong radioactivity example : PuCoGa5 , PuRhGa5 , NpPd5Al2 6

  7. introduction Motivation iso-structural superconductor PuCoGa5 : Pu-115 compounds CeCoIn5 : Ce-115 compounds 5f-electron : 5個 Tc = 18.5 K 4f-electron: 1個 Tc = 2.3 K Amazingly high Tc in HF 115 compounds NMR study (PuCoGa5 in normal state) • Spectra • K (Knight shift) • 1/T1T 7

  8. measurement Introduction NMR spectra I =1/2 m=-1/2 gℏH0 m=+1/2 Zeeman splitting NMR Intensity ω 8

  9. measurement Knight shift NMR Intensity H electron Knight shift 9

  10. measurement Release the energy Excitation energy T1~spin-lattice relation time I=-1/2 I=+1/2 nuclear spin electronic spin spin-lattice interaction Energy- transfer 1/T1 is quite sensitive to spin fluctuations 10

  11. result 59Co NMR Spectra at 19 K Co : I =7/2 g = 10.103MHz/T Spectra • Quadrupole Interaction : I >1 • （電気四重極相互作用） • νQ = 1.02 MHZ νQ 11

  12. result Knight shifts and 1/T1 ～T3 • Knight shifts show strongly anisotropic behavior. • At Tc both sifts drop sharply , indicating spin-singlet pairing. • 1/T1⇒d-wave superconductor Spin singlet S=0 anisotropic : 異方性 12

  13. result 1/T1T in 115 compounds • LuCoGa5 • 1/T1T = const • conduction electrons ⇒metallic • PuCoGa5 • conduction electrons + 5f-electrons • ⇒heavy fermion state PuCoGa5 LuCoGa5 Spin fluctuations develop as temperature decrease. Anisotropy (T1T)∥-1 / (T1T)⊥-1reaches a maximum just above Tc . 13

  14. result Korringa ratio Korringa ratio RK > 1 ⇒ antiferromagnetic RK～ 1 ⇒Fermi gas RK < 1 ⇒ ferromagnetic From K(T) and 1/T1T , Rk ranges from 5 to 16 Strong AFM fluctuations in PuCoGa5 14

  15. result Anisotropic nature PuCoGa5 : tetragonal structure (a=b≠c) new spin-lattice relaxation rate • in-plane component : Ra • out-of-plane component : Rc (1/T1T )H∥c = 2Ra (1/T1T )H⊥c = Ra+Rc AFM spin fluctuation is strong In XY-plane. 15

  16. result Ratio of spin fluctuation energy : ρ χ″(q=Q,ω) Γ Magnetic order ratio : ω 115 HF compounds ρ> 1　⇒　XY-like anisotropy Cuprates : YBa2Cu3O7 ρ ⋍ 1　⇒ isotropic Spin fluctuation energy : 16

  17. result Tc versus Γa/Γc for 115 HF superconductors • Reduced dimensionality could enhance Tc . • Anisotropy Γc/Γa is a good parameter for determining Tc. 17

  18. Summary PuCoGa5 : 59CoNMR study in the normal state • Spin fluctuations promote d-wave superconductivity in the • iso-structural 115 HF compounds. • Both the Knight shift K and the spin-lattice relaxation rate 1/T1 • are strongly anisotropic. • The ratio Γc/Γa (spin fluctuation energy) is a characteristic quantity in 115 HF compounds. This suggest the possibility • that anisotropic spin-fluctuations enhance Tc. 18

  19. b : The normal-state magnetic shift K tot of the 59Co and 71Ga(1) versus bulk susceptibility x. a : 71Ga NMR spectra in 8T c : The total magnetic shift K tot of the 59Co and 71Ga(1) versus temperature.

  20. 1/T1温度依存性 ～T0.35 ～T3

  21. Normalized spin susceptibility in the superconducting state. 71Ga 59Co

  22. (T 1T )-1/(T 1T )-10 versus T/Tc (T 1T )-10 is given by the value of (T 1T )-1 at 1.25Tc

  23. Tc versus the characteristic spin fluctuation energy T0 T0 = ΓqB2/2π

  24. c/a ratio of tetragonal structure parameter versus Tc

  25. Temperature - pressure phase diagram

  26. 電気四重極相互作用 C軸となす角度 H∥c θ=0° H⊥c θ=90°

  27. Crystal structure in 115 compounds

  28. 遍歴的 局在的

  29. What can we know from Knight shift ?~Symmetry of Cooper pair~ Cooper pairing state S=0 orbital part spin part even function (s, d wave) Φ(-(r1-r2)) =Φ(r1-r2) spin-singlet s (s2,s1) = -s (s1,s2) S=1 s-wave d-wave odd function (p wave) Φ(-(r1-r2)) = －Φ(r1-r2) spin-triplet s (s2,s1) = s(s1,s2) ψ(r1-r2;s1,s2) = Φ(r1-r2) σ(s1,s2) p-wave orbital spin

  30. 1/T1 in various superconductors unconventional superconductors (non BCS) NS(E) NS(E) Point nodes Line nodes N0 N0 EF EF +Δ0 EF +Δ0 EF EF +Δ0 d-wave p-wave EF Conventional type (BCS) s-wave

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