Field-Induced Quantum Critical Point in CeCoIn5 J.Paglione et al,Phys.Rev.Lett. 91.246405 (2003) F. Ronning et al,Phys.Rev. B 71, 104528 (2005) Kitaoka Laboratory Takuya Fujii 1 Contents Introduction - QCP - Heavy Fermion & Fermi Liquid Experimental Data - Resistivity and specific heat of CeCoIn5 under fields - Phase diagram Summary 2 Physical properties around QCP Metal Semiconductor Insulator Parameter Magnetic field(H) Material Pressure(P) Superconductor The ground states are changed ! Carrier doping Magnetism 3 QCP (Quantum Critical Point) Heavy-fermion system High-Tc cuprates QCP by carrier doping QCP by Pressure Unconventional SC around QCP QCP (Quantum Critical Point): Phase transition of ground state (T=0K) 4 (ex) magnetic order-disorder, normal phase-SC Temperature (K) Physical properties around QCP Non Fermi liquid Magnetic fluctuations happen. magnetic order QCP 0 Fermi Liquid Parameters Physical properties around QCP are not described by Fermi Liquid theory. 5 Heavy Fermion & Fermi Liquid localize : 局在する <Heavy electron systems> itinerant : 遍歴した f-electron: (RKKY interaction) localize at the atom. (Kondo effect) become itinerant by the hybridization between conduction electrons and f-electrons. RKKY interaction conduction electron Kondo effect conduction electron rare earth ion f-electron Magnetic order 6 Fermi liquid state by heavy electrons Crystal structure of CeCoIn5 H // ab Normal SC H // c Heavy fermions superconductor •Tc=2.3 K at P=0. •C/T=350 mJ/mol K2 •H//abc2 ~ 11.8 T, H//cc2 ~ 5 T Tc=2.3K S. Ikeda et al., J. Phys. Soc. Jpn. 71 (2002) 1023. 7 Comparison with isostructural CeRhIn5 isostructural AFM compound: CeRhIn5 (TN=3.8K) CeCoIn5 is in the vicinity of QCP at ambient pressure. QCP of CeCoIn5 M. Yashima et al. 8 FL and NFL behavior Fermi-liquid (3D, 2D) Non Fermi-liquid r =r0+AT2 2D AFM C/T=const r =r0+AT, C/T~ -log T A(slope): interaction between electrons 3D AFM r = r0+AT3/2, C/T=r0-aT1/2 9 Resistivity in high fields ( H // c) 2 ρ T Temperature range of Hex wider Fermi liquid: ρ = ρ0 AT 2 A decreases as increasing field. By applying magnetic field, a FL regime is recovered ! 10 Field dependence of T2 coefficient A( H ) ( H H *) critical behavior divergence close to H* (H*=5.1,α=-1.37) 11 Specific heat in high fields ( H // c ) High-Hex Fermi liquid: C/T=const C/T=const Hex is close to H* C/T~ -log T Non Fermi liquid: C/T~ -log T 12 H-T phase diagram H // c FL H* SC H* coincides with the critical field of SC Hc2(0). 13 QCP in H // ab H // ab Hc2ab~11.8 T H // c Hc2c~5 T FLNFL was also observed around Hc2. 14 H-T phase diagram ＋ H // ab × Tc ● TFL H // c ＋ Tc ○ TFL ＋ SC ＋ FL: H // c FL: H // ab 15 What is unique about CeCoIn5 ? comparison with YbRh2Si2 H-T phase diagram of YbRh2Si2 Hex approaches to critical field value H＊ . critical behavior ! In CeCoIn5 : H＊ Hc2(0) T (K) SC QCP FL FL AF NFL SC H＊ FL 0 H＊ H(T) AF QCP FL 16 P.Gegenwart el et al. (2002) Summary We observed a suppression of the non-Fermi liquid behaviors with increasing field, and the development of a Fermi liquid state. It was a field-induced quantum critical point. It coincides with the superconducting critical field Hc2(0). 17 The end THE END 18 SC FL: H // c H＊ Hc2(0) FL: H // ab 19 Motivation Motivation Quantum critical behavior in the H-T phase diagram ? Measurements Specific heat and resistivity in high magnetic field. 20 - the QCP of CeCoIn5 under Pressure QCP at negative P? V.A.Sidorov et al. 2002 21 -Heavy Fermion & Fermi Liquid ・ ・ ・ ・・ ・ εF F * Interaction ・・ ・ Fermi liquid ・ ・ ・ Fermi gas Fermi gas : No dynamic interaction between particles. The interaction between electrons becomes very strong. itinerancy Fermi liquid : The electrons can’t move easily. The effective mass seems heavy. Heavy fermion is described by Fermi Liquid theory. 22 QCP by the competition between RKKY interaction and Kondo effect 23 - Resistivity of CeCoIn5 under fields resistivity of metal at low temperature ρ(T ) =ρ0 ρphonon (T ) ρe e (T ) ρphonon = T 5 ( scattering by the phonon vibration) 0 (T = low) ρe e (T ) = AT 2 (T = low) ρ(T ) =ρ0 AT ( scattering between conduction electrons) 2 24 - Resistivity of CeCoIn5 under fields ρ T2 ρ T Tc H ex ab , H c 2 = 5T H ex = 0; ρ T (Tc T 10K ) H ex 0; ρ drastic change ρ(T ) ρ0 AT NFL ρ = ρ0 AT n 25 2 -Resistivity of CeCoIn5 under fields MR:magnetoresistance T 30K ; MR : small T 30K ; MR : develop H ex H c 2 ; going up H ex H c 2 ; up down 26 - Resistivity of CeCoIn5 under fields Crossover from positive to negative MR T(K)=16 14.5 13 11.5 initial increase an increase of spin disorder a suppression of AF correlations 10 8.5 7 5.5 4 T>Tc 2 0.1 polarization of spins by increasing field strength a field-aligned state 27 : London penetration depth : Coherence length = BS = B (π 2 ) 0 0 Hc = , = 2 π Hc Hc2(//ab)=11.8T,(//c)=5T ab< c Hex 28 Non Fermi liquid behavior • The single-impurity multichannel Kondo model theory • Disorder-induced theory • Spin-fluctuation theory Landau Fermi-liquid (3D, 2D) Non Femi-liquid r =r0+AT2, C/T=const. c=const. 2D AFM r =r0+AT, C/T~ -log T 3D AFM r = r0+AT3/2, C/T=r0-aT1/2 29 - H-T phase diagram of CeCoIn5 FL NFL:near QCP,due to spin critical fluctuations, n 0 ρ = ρ AT SC 30 H* 31
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