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

2. Contents Introduction - History of superconductivity - Heavy fermion system - Transuranic HF compounds - Motivation Measurement - NMR (Nuclear Magnetic Resonance) Experimental Results (PuCoGa 5 ) Summary 2

3. under high pressure 0 50 100 150 200 SmO 0.9 F 0.11 FeAs LaO 0.89 F 0.11 FeAs LaOFeP Hg-Ba-Ca-Cu-O （） Tl-Ba-Ca-Cu-O Bi-Sr-Ca-Cu-O Y-Ba-Cu-O MgB 2 NbGe NbN NbC Nb Pb high-T c cuprate metal iron-based system Transition temperature (K) 1900192019401960198020002020 Year Hg La-Ba-Cu-O Discovery of superconducting phenomenon 1911 1986 High-T c cuprate superconductor 2006 Iron-based high-T c superconductor 77 163 1979 Heavy fermion superconductor CeCu 2 Si 2 heavy fermion system PuCoGa 5 History of Superconductivity introduction 3

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

5. Heavy Fermion System introduction Example of heavy fermion superconductor compounds UPt 3 UPd 2 Al 3 CeCu 2 Si 2 CePd 2 Si 2 CeRh 2 Si 2 CeIn 3 CeRhIn 5 PrOs 4 Sb 12 PuCoGa 5 f-electrons. All of HF compounds have f-electrons. lanthanide compounds ⇒ some 4f electrons actinide compounds ⇒ some 5f electrons 5

6. transuranium elements ( 超ウラン元素 ) don’t exist in nature Handling is difficult because of strong radioactivity Transuranic HF Compounds example : PuCoGa 5, PuRhGa 5, NpPd 5 Al 2 introduction 6

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

8. m=+1/2 m=-1/2 ℏ H0ℏ H0 Zeeman splitting NMR Intensity ω Introduction I =1/2 NMR spectra measurement 8

9. NMR Intensity H electron Knight shift measurement 9

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

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

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

13. 1/T 1 T in 115 compounds result LuCoGa 5 1/T 1 T = const conduction electrons ⇒ metallic PuCoGa 5 conduction electrons + 5f-electrons ⇒ heavy fermion state Anisotropy (T 1 T) ∥ -1 / (T 1 T) ⊥ -1 reaches a maximum just above T c. PuCoGa 5 LuCoGa 5 5f-electrons 5個5個 0個0個 LuCoGa 5 Spin fluctuations develop as temperature decrease. 13

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

15. Anisotropic nature result PuCoGa 5 : tetragonal structure (a=b≠c) new spin-lattice relaxation rate in-plane component : R a out-of-plane component : R c (1/T 1 T ) H ∥ c = 2R a (1/T 1 T ) H ⊥ c = R a +R c AFM spin fluctuation is strong In XY-plane. 15

16. Ratio of spin fluctuation energy : ρ result 115 HF compounds XY-like anisotropy ρ > 1 ⇒ XY-like anisotropy Cuprates : YBa 2 Cu 3 O 7 isotropic ρ ⋍ 1 ⇒ isotropic Spin fluctuation energy : ratio : χ″(q=Q,ω) ω Γ 16 Magnetic order

17. T c versus Γ a /Γ c for 115 HF superconductors result Reduced dimensionality could enhance T c. Anisotropy Γ c /Γ a is a good parameter for determining T c. 17

18. Summary 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/T 1 are strongly anisotropic. The ratio Γ c /Γ a (spin fluctuation energy) is a characteristic quantity in 115 HF compounds. This suggest the possibility that anisotropic spin-fluctuations enhance T c. PuCoGa 5 : 59 CoNMR study in the normal state 18

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

22. 1/T 1 温度依存性 ～ T 0.35 ～T3～T3

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

24. (T 1 T ) -1 /(T 1 T ) -1 0 versus T/T c (T 1 T ) -1 0 is given by the value of (T 1 T ) -1 at 1.25T c

25. T c versus the characteristic spin fluctuation energy T 0 T 0 = Γq B 2 /2π

27. c/a ratio of tetragonal structure parameter versus T c

28. Temperature - pressure phase diagram

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

30. Crystal structure in 115 compounds

31. 遍歴的局在的

32. Cooper pairing state ψ(r 1 -r 2 ;s 1,s 2 ) = Φ(r 1 -r 2 ) σ (s 1,s 2 ) orbitalspin What can we know from Knight shift ? ~Symmetry of Cooper pair~ s-wave d-wave p-wave orbital partspin part even function (s, d wave) Φ (-(r 1 -r 2 )) =Φ (r 1 -r 2 ) spin-singlet  (s 2,s 1 ) = -  (s 1,s 2 ) odd function (p wave) Φ (-(r 1 -r 2 )) = － Φ (r 1 -r 2 ) spin-triplet  (s 2,s 1 ) =  (s 1,s 2 ) S=0 S=1

33. N0N0 N S (E)EFEF E F +Δ 0 1/T 1 in various superconductors Conventional type (BCS) s-wave d-wave p-wave unconventional superconductors (non BCS) N0N0 N S (E) EFEF E F +Δ 0 Line nodes EFEF E F +Δ 0 Point nodes