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 Contents Introduction - History of superconductivity - Heavy fermion system - Transuranic HF compounds - Motivation Measurement - NMR (Nuclear Magnetic Resonance) Experimental Results (PuCoGa 5 ) Summary 2 under high pressure 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) Year Hg La-Ba-Cu-O Discovery of superconducting phenomenon High-T c cuprate superconductor 2006 Iron-based high-T c superconductor Heavy fermion superconductor CeCu 2 Si 2 heavy fermion system PuCoGa 5 History of Superconductivity introduction 3 Normal metal Heavy Fermion system f ff f f f c-f hybridization ( c-f What does Heavy mean? Heavy Heavy large effective mass Heavy Fermion System introduction Strong electron correlation makes effective mass large. 4 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 transuranium elements ( ) dont exist in nature Handling is difficult because of strong radioactivity Transuranic HF Compounds example : PuCoGa 5, PuRhGa 5, NpPd 5 Al 2 introduction 6 Motivation PuCoGa 5 : Pu-115 compounds 5f-electron : 5 T c = 18.5 K CeCoIn 5 : Ce-115 compounds 4f-electron : 1 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 m=+1/2 m=-1/2 H0 H0 Zeeman splitting NMR Intensity Introduction I =1/2 NMR spectra measurement 8 NMR Intensity H electron Knight shift measurement 9 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 59 Co NMR Spectra at 19 K result Co : I =7/2 = MHz/T QQ Quadrupole Interaction : I >1 Q = 1.02 MHZ Spectra 11 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 : T3T3 12 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 55 00 LuCoGa 5 Spin fluctuations develop as temperature decrease. 13 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 Anisotropic nature result PuCoGa 5 : tetragonal structure (a=bc) 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 Ratio of spin fluctuation energy : result 115 HF compounds XY-like anisotropy > 1 XY-like anisotropy Cuprates : YBa 2 Cu 3 O 7 isotropic 1 isotropic Spin fluctuation energy : ratio : (q=Q,) 16 Magnetic order T c versus a / c for 115 HF superconductors result Reduced dimensionality could enhance T c. Anisotropy c / a is a good parameter for determining T c. 17 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 c / 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 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. 1/T 1 T 0.35 T3T3 Normalized spin susceptibility in the superconducting state. 59 Co 71 Ga (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 T c versus the characteristic spin fluctuation energy T 0 T 0 = q B 2 /2 c/a ratio of tetragonal structure parameter versus T c Temperature - pressure phase diagram C H c =0 H c =90 Crystal structure in 115 compounds Cooper pairing state (r 1 -r 2 ;s 1,s 2 ) = (r 1 -r 2 ) (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) (-(r 1 -r 2 )) = (r 1 -r 2 ) spin-singlet (s 2,s 1 ) = - (s 1,s 2 ) odd function (p wave) (-(r 1 -r 2 )) = (r 1 -r 2 ) spin-triplet (s 2,s 1 ) = (s 1,s 2 ) S=0 S=1 N0N0 N S (E)EFEF E F + 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 + 0 Line nodes EFEF E F + 0 Point nodes