Kondo problem to heavy fermions and local quantum criticality - PowerPoint PPT Presentation

Kondo problem to heavy fermions and local quantum criticality (Experiment I) F. Steglich MPI for Chemical Physics of Solids, 01187 Dresden, Germany outline : Kondo effect Superconductivity vs. magnetism Heavy fermions Heavy-fermion superconductors

1930: T- dependence of the electrical resistivity in pure metals?

≤ 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): 2 μ χ (T) ~ (T)/T eff T  0 µ eff (T)  0 Kondo effect: (J. Kondo 1964)

Incremental specific heat of Cu 1-x M x (M: Cr, Fe): Δ C(T) = C(T) – C Cu (T) per mole M: Δ C(T)/x = γ T γ Cu Cr Cu Fe 2 Cr [J/K -mole ] Fe 16 1.0 T = T K : local Fermi liquid (P. Nozières 1974)

> 1970: Rare earth impurities K. Winzer, Z. Phys. 265 , 139 (1973) J. Moeser, F. Steglich, G.v. Minnigerode resistivity J. Low Temp. Phys. 15 , 9 (1974) giant thermoelectric power (La 1-x Ce x )Al 2 Gorter-Nordheim: x = 0.00626 ρ − ρ − ρ ( ) T S [ ( ) T ( )] T S re-entrant superconductivity = ce La S ce ρ ( ) T ce

outline : Kondo effect Superconductivity vs. magnetism Heavy fermions Heavy-fermion superconductors

Superconductivity vs. magnetism IA VIIIA 1 2 1.008 IIA H He IIIA IVA VA VIA VIIA 4.003 10 3 4 5 6 7 8 9 Li Be Ne .012 B C N O F 6.941 9 10.81 1 2.01 14.01 1 6.00 1 9.00 20.18 1 2 3 4 5 6 7 18 1 1 1 1 1 1 1 Na Mg Al Si P S Cl Ar VIIIB 4.31 IIIB IVB VB VIB VIIB IB IIB 22.99 2 26.98 2 8.09 30.97 3 2.07 3 5.45 39.95 1 9 2 0 2 1 2 2 23 2 4 2 5 2 6 2 7 2 8 2 9 3 0 3 1 3 2 3 3 3 4 3 5 36 K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 39.10 4 0.08 44.96 4 7.87 50.94 5 2.00 5 4.94 5 5.85 58.93 5 8.69 6 3.55 65.39 69.72 7 2.61 74.92 7 8.96 7 9.90 83.80 3 7 3 8 3 9 4 0 41 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 5 0 5 1 5 2 5 3 54 Rb Sr Zr Nb Tc Ru Rh Pd Ag Cd In Sn Sb Te Xe Y Mo I 85.47 7.62 88.91 1.22 92.91 5.94 01.1 102.9 06.4 07.9 112.4 114.8 18.7 121.8 27.6 26.9 131.3 8 9 9 (98) 1 1 1 1 1 1 5 6 7 2 73 4 5 6 7 8 9 0 1 2 3 4 5 86 5 5 5 7 7 7 7 7 7 7 8 8 8 8 8 8 Cs Ba La Hf Ta Re Au Hg Tl Pb Bi Po At Rn W Os Ir Pt 132.9 37.3 138.9 78.5 180.9 83.8 86.2 90.2 192.2 95.1 97.0 200.6 204.4 07.2 209.0 209) 210) (222) 1 1 1 1 1 1 1 2 ( ( 8 7 8 8 8 9 104 1 05 106 1 07 1 08 1 09 Fr Ra Ac Rf Db Sg Bh Hs Mt (223) 226) (227) 261) (262) 266) 264) 269) (268) ( ( ( ( ( 8 59 0 1 2 3 4 5 6 7 8 9 0 1 5 6 6 6 6 6 6 6 6 6 6 7 7 Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu 1 40.1 140.9 1 44.2 ( 145) 1 50.4 152.0 1 57.3 1 58.9 162.5 164.9 1 67.3 168.9 1 73.0 1 75.0 9 0 91 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 100 1 01 102 103 Th Np Pu Am Cm Bk Cf No Lr Pa U Es Fm Md 32.0 (231) 38.0 237) 244) (243) 247) 247) (251) (252) 257) (258) 259) 262) 2 2 ( ( ( ( ( ( (

T c of La 0.99 RE 0.01

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) π + 2 S ( S 1 ) α ~ x + π + ln 2 ( T / T ) 2 ( S ( S 1 ) K

Pairbreaking by magnetic impurities (experiment)

outline : Kondo effect Superconductivity vs. magnetism Heavy fermions Heavy-fermion superconductors

Volume dependence of Kondo effect, cf.[(La 1-z Y z ) 1-x Ce x ]Al 2 F.S., Adv. Solid State Phys. (1977), F.S. et al., Physica 86-88B , 503 (1977). Vol. XVII, p.319. v = ( V V ) /( V ) - - V T<< T K : Δρ = ρ 0 (1-AT 2 ) LaAl YAl LaAl 2 2 2 T K increases by a factor of 250 A = π 2 /(4 ) 2 T K ≈ 0.3 CeAl 2 (x = 1): v (M. Larsen '75) ⇒ T K ≈ 5 K

Specific heat of CeAl 2 γ = 0.135 J/K 2 mole F. S. et al., C.D. Bredl et al., J. Phys. (Paris) 40 , C5-301 (1979). Z. Phys. B 29 , 327 (1978).

γ = 1.62 J/K 2 mole A = 35 µ Ω cm/K 2

Superconductivity in CeCu 2 Si 2 100 at% Ce 3+ ions necessary for superconductivity (LaCu 2 Si 2 is not a superconductor)

Heavy-Fermion metals T >> T K (10 ... 100 K) m v F ≈ 10 6 s T << T K : Heavy electrons ("composite fermions") m v F * ≈ 10 3 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

outline : Kondo effect Superconductivity vs. magnetism Heavy fermions Heavy-fermion superconductors

Superconductivity in CeCu 2 Si 2 100 at% Ce 3+ ions necessary for superconductivity (LaCu 2 Si 2 is not a superconductor)

Heavy-fermion superconductivity in CeCu 2 Si 2

Heavy-fermion superconductivity in UBe 13

Heavy-fermion superconductivity in UPt 3

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).

Heavy-fermion superconductors T c (K) T c (K) CeCu 2 Si 2 0.6 ('79 DA/K) PrOs 4 Sb 12 1.85 ('01 UCSD) [p = 2.9 GPa: 2.3 ('84 GE/GR)] CeNi 2 Ge 2 0.2 ('97 DA, '98 CA/GR) 0.08 ( ' 08 TO/IR) β -YbAlB 4 CeIrIn 5 0.4 ('00 LANL) CeCoIn 5 2.3 ('00 LANL) p > 0 Ce 2 CoIn 8 0.4 ('02 NA) Eu metal 1.8-2.8 (’09 SL, OS) Ce 2 PdIn 8 0.7 ('09 WR) CePt 3 Si 0.7 ('03 VI) UBe 13 0.9 ('83 Z/LANL) p > 0 UPt 3 0.5 ('84 LANL) CeCu 2 Ge 2 0.6 ('92 GE) URu 2 Si 2 1.4 ('84 K/DA) CePd 2 Si 2 0.4 ('94 CA) UNi 2 Al 3 1.2 ('91 DA) CeRh 2 Si 2 0.4 ('95 LANL) UPd 2 Al 3 2.0 ('91 DA) CeCu 2 0.15 ('97 GE/KA) URhGe 0.3 ('01 GR) UCoGe 3.0 ('07 AM/KA) CeIn 3 0.2 ('98 CA) p > 0 CeRhIn 5 2.1 ('00 LANL) UGe 2 0.7 ('00 CA/GR) Ce 2 RhIn 8 1.1 ('03 LANL) UIr 0.14 ('04 OS) CeRhSi 3 0.8 ('05 SE) CeIrSi 3 1.6 ('06 OS) NpPd 5 Al 2 5.0 ('07 OS) CeCoGe 3 0.7 ('06 OS) Ce 2 Ni 3 Ge 5 0.26 ('06 OS) PuCoGa 5 18.5 ('02 LANL) CeNiGe 3 0.4 ('06 OS) PuRhGa5 8.7 ('03 KA) CePd 5 Al 2 0,57 (‘08 OS) p > 0 CeRhGe 2 0.45 ('09 OS) Am metal 2.2 ('05 KA) CePt 2 In 7 2.1 (‘10 LANL) CeIrGe 3 1.5 (’10 OS)

Magnetic Cooper pairing in UPd 2 Al 3 C. Geibel et. al., 1991 ≈ 14 K T magn ≈ 0.85 µ B µ s γ ≈ 140 mJ/K 2 mol ≈ 2 K T c 2 ∆ 0 /k B T c ≈ 6 (Kyougaku et al., 1993) • Two more localized ("core") electrons: magnetism • one less localized ("heavy" itinerant) electron: U 3+ (5f 3 ) heavy LFL state (T c < T < T N ) coexisting with local AF heavy-fermion SC (T < T c )

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)

Inelastic neutron scattering [N.K. Sato et al., Nature 410 , 340 (2001)] acoustic magnon ("magnetic exciton") Q Q = = (0, 0, 1/2) 0 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

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 C vs T α vs T vs T T ( α = l -1 δ l/ δ T) P. Gegenwart et al. (2004) 4T ≤ B ≤ 10 T : ρ / ρ (1K) vs T universal T  0 : Δρ ~ T 1.5 T L  0 at B* ≈ 4.2 T: QCP (3D-SDW) Δ C/T = γ 0 - β T 0.5 (B = 12 T)

Double transition in (U 1-x Th x )Be 13 0.019 < x < 0.046 [H.R. Ott et al., Phys. Rev. B 31 , 1651 (1985)]

Phase diagram of U 1-x Th x Be 13 [F. Kromer et al., PRB 62 , 12477 (2000); JLTP 126 , 815 (2002)] α vs T

Kondo problem to heavy fermions and local quantum criticality (Experiment II): Interplay of incipient magnetism and superconductivity in heavy-fermion metals