Kondo problem to heavy fermions and local quantum criticality (Experiment I)
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1 Kondo problem to heavy fermions and local quantum criticality (Experiment I) F. Steglich MPI for Chemical Physics of Solids, Dresden, Germany outline: Kondo effect Superconductivity vs. magnetism Heavy fermions Heavy-fermion superconductors
2 1930: T- dependence of the electrical resistivity in pure metals?
3 1970: Noble metals with transition-metal impurities D.K.C. MacDonald et al., Proc. Roy. Soc. A266, 161 (1962) resistivity susceptibility Curie Weiss law χ(t) ~ (T + θ) -1, θ = f (T K ) > 0 effective moment µ eff (T): χ(t) ~ 2 μ eff (T)/T T 0 µ eff (T) 0 Kondo effect: (J. Kondo 1964)
4 CuCr Incremental specific heat of Cu 1-x M x (M: Cr, Fe): ΔC(T) = C(T) C Cu (T) per mole M: ΔC(T)/x = γt γ 2 Cr [J/K -mole Fe ] CuFe T = T K : local Fermi liquid (P. Nozières 1974)
5 > 1970: Rare earth impurities K. Winzer, Z. Phys. 265, 139 (1973) resistivity J. Moeser, F. Steglich, G.v. Minnigerode J. Low Temp. Phys. 15, 9 (1974) giant thermoelectric power (La 1-x Ce x )Al 2 Gorter-Nordheim: x = re-entrant superconductivity ρ( T) S [ ρ( T) ρce ( T)] S Sce = ρ ( T ) ce La
6 outline: Kondo effect Superconductivity vs. magnetism Heavy fermions Heavy-fermion superconductors
7 Superconductivity vs. magnetism IA VIIIA 1 H IIA IIIA IVA VA VIA VIIA 2 He Li Be B C N O F Ne Na Mg IIIB IVB VB VIB VIIB VIIIB IB IIB 13 Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc (98) 44 Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po (209) 85 At (210) 86 Rn (222) 87 Fr (223) 88 Ra (226) 89 Ac (227) 104 Rf (261) 105 Db (262) 106 Sg (266) 107 Bh (264) 108 Hs (269) 109 Mt (268) 58 Ce Pr Nd Pm (145) 62 Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Th Pa (231) 92 U Np (237) 94 Pu (244) 95 Am (243) 96 Cm (247) 97 Bk (247) 98 Cf (251) 99 Es (252) 100 Fm (257) 101 Md (258) 102 No (259) 103 Lr (262)
8 Tc of La0.99RE0.01
9 Pairbreaking by magnetic impurities (theory) H int = 2 J S. s α ~ x S(S + 1) J > 0 T K ~ T F exp (-1/N F J) α 2 π S(S + 1) x 2 ln (T / T ) + π (S(S + 1) ~ 2 K
10 Pairbreaking by magnetic impurities (experiment)
11
12 outline: Kondo effect Superconductivity vs. magnetism Heavy fermions Heavy-fermion superconductors
13 Volume dependence of Kondo effect, cf.[(la 1-z Y z ) 1-x Ce x ]Al 2 F.S. et al., Physica 86-88B, 503 (1977). F.S., Adv. Solid State Phys. (1977), Vol. XVII, p.319. T<< T K : Δρ = ρ 0 (1-AT 2 ) (M. Larsen '75) T K A = π 2 2 /(4 ) v = (V - V )/(V 2 YAl2 - V LaAl LaAl 2 T K increases by a factor of 250 v CeAl 2 (x = 1): 0.3 T K 5 K )
14 Specific heat of CeAl 2 γ = J/K 2 mole F. S. et al., J. Phys. (Paris) 40, C5-301 (1979). C.D. Bredl et al., Z. Phys. B 29, 327 (1978).
15 γ = 1.62 J/K2mole A = 35 µωcm/k2
16 Superconductivity in CeCu 2 Si at% Ce 3+ ions necessary for superconductivity (LaCu 2 Si 2 is not a superconductor)
17 Heavy-Fermion metals T >> T K ( K) v F 10 6 m s T << T K : Heavy electrons ("composite fermions") v F * 10 3 m s m* 1000 m el : "strongly correlated electron system" Groundstate properties - Heavy Landau Fermi liquid (LFL) : CeCu 6 - Non-Fermi liquid (NFL) : YbRh 2 Si 2 - Magnetic order : NpBe 13 - Superconductivity : UPd 2 Al 3
18 outline: Kondo effect Superconductivity vs. magnetism Heavy fermions Heavy-fermion superconductors
19 Superconductivity in CeCu 2 Si at% Ce 3+ ions necessary for superconductivity (LaCu 2 Si 2 is not a superconductor)
20 Heavy-fermion superconductivity in CeCu2Si2
21 Heavy-fermion superconductivity in UBe13
22 Heavy-fermion superconductivity in UPt3
23 Heavy-fermion superconductivity in URu 2 Si 2 [W. Schlabitz et al., Poster ICVF, Cologne 1984 (unpublished)] cf. also, T.T.M. Palstra et al., PRL 55, 2727 (1985) M.B. Maple et al., PRL 56, 185 (1986).
24
25 Heavy-fermion superconductors T c (K) CeCu 2 Si ('79 DA/K) [p = 2.9 GPa: 2.3 ('84 GE/GR)] CeNi 2 Ge ('97 DA, '98 CA/GR) CeIrIn ('00 LANL) CeCoIn ('00 LANL) Ce 2 CoIn ('02 NA) Ce 2 PdIn ('09 WR) CePt 3 Si 0.7 ('03 VI) p > 0 CeCu 2 Ge ('92 GE) CePd 2 Si ('94 CA) CeRh 2 Si ('95 LANL) CeCu ('97 GE/KA) CeIn ('98 CA) CeRhIn ('00 LANL) Ce 2 RhIn ('03 LANL) CeRhSi ('05 SE) CeIrSi ('06 OS) CeCoGe ('06 OS) Ce 2 Ni 3 Ge ('06 OS) CeNiGe ('06 OS) CePd 5 Al 2 0,57 ( 08 OS) CeRhGe ('09 OS) CePt 2 In ( 10 LANL) CeIrGe ( 10 OS) T c (K) PrOs 4 Sb ('01 UCSD) β-ybalb ('08 TO/IR) p > 0 Eu metal ( 09 SL, OS) UBe ('83 Z/LANL) UPt ('84 LANL) URu 2 Si ('84 K/DA) UNi 2 Al ('91 DA) UPd 2 Al ('91 DA) URhGe 0.3 ('01 GR) UCoGe 3.0 ('07 AM/KA) p > 0 UGe ('00 CA/GR) UIr 0.14 ('04 OS) NpPd 5 Al ('07 OS) PuCoGa ('02 LANL) PuRhGa5 8.7 ('03 KA) p > 0 Am metal 2.2 ('05 KA)
26 Magnetic Cooper pairing in UPd 2 Al 3 C. Geibel et. al., 1991 T magn 14 K µ s 0.85 µ B γ 140 mj/k 2 mol T c 2 K 2 0 /k B T c 6 (Kyougaku U 3+ (5f 3 ) et al., 1993) Two more localized ("core") electrons: magnetism one less localized ("heavy" itinerant) electron: heavy LFL state (T c < T < T N ) coexisting with local AF heavy-fermion SC (T < T c )
27 Quasiparticle tunneling [M. Jourdan et. al., Nature 398, 47 (1999)] tunnel diode UPd 2 Al 3 - AlO x - Pb (Pb normal conducting : B = 0.3 T) di/dv (T = 0.15 K)
28 Inelastic neutron scattering [N.K. Sato et al., Nature 410, 340 (2001)] acoustic magnon ("magnetic exciton") Q= Q 0 = (0, 0, 1/2) T c = 1.8 K Cooper pairs formed by heavy electrons ("itinerant" 5f electrons) superconducting glue provided by magnetic excitons in the system of "localized" 5f electrons
29 Non-Fermi-liquid superconductor UBe 13 [F. Kromer et al., PRL 81, 4476 (1998); N. Oeschler et al., Acta Phys. Pol. 34, 255 (2003)] ΔC T vs T C vs T α vs T (α = l -1 δl/δt) P. Gegenwart et al. (2004) 4T B 10 T : ρ/ρ(1k) vs T universal T L 0 at B* 4.2 T: QCP (3D-SDW) T 0 : Δρ ~ T 1.5 ΔC/T = γ 0 -βt 0.5 (B = 12 T)
30 Double transition in (U 1-x Th x )Be < x < [H.R. Ott et al., Phys. Rev. B 31, 1651 (1985)]
31 α vs T Phase diagram of U 1-x Th x Be 13 [F. Kromer et al., PRB 62, (2000); JLTP 126, 815 (2002)]
32 Kondo problem to heavy fermions and local quantum criticality (Experiment II): Interplay of incipient magnetism and superconductivity in heavy-fermion metals
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