Kondo problem to heavy fermions and local quantum criticality (Experiment I)

F. SteglichMPI 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

Kondo effect:

(J. Kondo 1964)

D.K.C. MacDonald et al., Proc. Roy. Soc. A266, 161 (1962)resistivity susceptibility

Curie Weiss law

χ(T) ~ (T + θ)-1, θ = f (TK) > 0

effective moment µeff(T):

(T)/T

T 0 µeff(T) 0

2effμχ(T) ~

2 CrFe[J/K -mole ]

γ

1.0

CuFe

16

CuCr

T = TK: local Fermi liquid (P. Nozières 1974)

Incremental specific heat of Cu1-xMx (M: Cr, Fe):

ΔC(T) = C(T) – CCu(T)

per mole M: ΔC(T)/x = γT

> 1970: Rare earth impuritiesJ. Moeser, F. Steglich, G.v. MinnigerodeJ. Low Temp. Phys. 15, 9 (1974)giant thermoelectric power

K. Winzer, Z. Phys. 265, 139 (1973)resistivity

x = 0.00626re-entrant superconductivity ( ) [ ( ) ( )]

( )ce La

cece

T S T T SST

ρ ρ ρρ

− −=

Gorter-Nordheim:

(La1-xCex)Al2

outline:

Kondo effect

Superconductivity vs. magnetism

Heavy fermions

Heavy-fermion superconductors

Superconductivity vs. magnetism

IA VIIIA1

H1.008 IIA IIIA IVA VA VIA VIIA

2

He4.003

3

Li6.941

4

Be9.012

5

B10.81

6

C12.01

7

N14.01

8

O16.00

9

F19.00

10

Ne20.18

11

Na22.99

12

Mg24.31 IIIB IVB VB VIB VIIB VIIIB IB IIB

13

Al26.98

14

Si28.09

15

P30.97

16

S32.07

17

Cl35.45

18

Ar39.95

19

K39.10

20

Ca40.08

21

Sc44.96

22

Ti47.87

23

V50.94

24

Cr52.00

25

Mn54.94

26

Fe55.85

27

Co58.93

28

Ni58.69

29

Cu63.55

30

Zn65.39

31

Ga69.72

32

Ge72.61

33

As74.92

34

Se78.96

35

Br79.90

36

Kr83.80

37

Rb85.47

38

Sr87.62

39

Y88.91

40

Zr91.22

41

Nb92.91

42

Mo95.94

43

Tc(98)

44

Ru101.1

45

Rh102.9

46

Pd106.4

47

Ag107.9

48

Cd112.4

49

In114.8

50

Sn118.7

51

Sb121.8

52

Te127.6

53

I126.9

54

Xe131.3

55

Cs132.9

56

Ba137.3

57

La138.9

72

Hf178.5

73

Ta180.9

74

W183.8

75

Re186.2

76

Os190.2

77

Ir192.2

78

Pt195.1

79

Au197.0

80

Hg200.6

81

Tl204.4

82

Pb207.2

83

Bi209.0

84

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

Ce140.1

59

Pr140.9

60

Nd144.2

61

Pm(145)

62

Sm150.4

63

Eu152.0

64

Gd157.3

65

Tb158.9

66

Dy162.5

67

Ho164.9

68

Er167.3

69

Tm168.9

70

Yb173.0

71

Lu175.0

90

Th232.0

91

Pa(231)

92

U238.0

93

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)

Tc of La0.99RE0.01

Pairbreaking by magnetic impurities (theory)

Hint = 2 J S . s

α ~ x S(S + 1)

J > 0

TK ~ TFexp (-1/NFJ)

)1S(S()T/T(ln)1S(Sx~

2

K

2

2

+π++π

α

Pairbreaking by magnetic impurities (experiment)

outline:

Kondo effect

Superconductivity vs. magnetism

Heavy fermions

Heavy-fermion superconductors

TK increases by a factor of 250CeAl2 (x = 1): ≈ 0.3

⇒ TK ≈ 5 K

Volume dependence of Kondo effect, cf.[(La1-zYz)1-xCex]Al2

F.S. et al., Physica 86-88B, 503 (1977). F.S., Adv. Solid State Phys. (1977), Vol. XVII, p.319.

T<< TK : Δρ = ρ0 (1-AT2)

A = π2/(4 )(M. Larsen '75)

)V/()VV(=v22 YAlLaAl 2LaAlV --

v2

KT

Specific heat of CeAl2

γ = 0.135 J/K2mole

F. S. et al., J. Phys. (Paris) 40, C5-301 (1979).

C.D. Bredl et al., Z. Phys. B 29, 327 (1978).

γ = 1.62 J/K2mole A = 35 µΩcm/K2

Superconductivity in CeCu2Si2

100 at% Ce3+ ions necessaryfor superconductivity

(LaCu2Si2 is not a superconductor)

Heavy-Fermion metals

T >> TK (10 ... 100 K)

T << TK: Heavy electrons ("composite fermions")

→ m* ≈ 1000 mel: "strongly correlated electron system"

Groundstate properties - Heavy Landau Fermi liquid (LFL) : CeCu6- Non-Fermi liquid (NFL) : YbRh2Si2- Magnetic order : NpBe13- Superconductivity : UPd2Al3

vF ≈ 106sm

vF* ≈ 103sm

outline:

Kondo effect

Superconductivity vs. magnetism

Heavy fermions

Heavy-fermion superconductors

Superconductivity in CeCu2Si2

100 at% Ce3+ ions necessaryfor superconductivity

(LaCu2Si2 is not a superconductor)

Heavy-fermion superconductivity in CeCu2Si2

Heavy-fermion superconductivity in UBe13

Heavy-fermion superconductivity in UPt3

Heavy-fermion superconductivity in URu2Si2[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 superconductorsTc(K)

CeCu2Si2 0.6 ('79 DA/K)[p = 2.9 GPa: 2.3 ('84 GE/GR)]CeNi2Ge2 0.2 ('97 DA, '98 CA/GR) CeIrIn5 0.4 ('00 LANL)CeCoIn5 2.3 ('00 LANL)Ce2CoIn8 0.4 ('02 NA)Ce2PdIn8 0.7 ('09 WR)CePt3Si 0.7 ('03 VI)p > 0CeCu2Ge2 0.6 ('92 GE)CePd2Si2 0.4 ('94 CA) CeRh2Si2 0.4 ('95 LANL)CeCu2 0.15 ('97 GE/KA)CeIn3 0.2 ('98 CA)CeRhIn5 2.1 ('00 LANL)Ce2RhIn8 1.1 ('03 LANL)CeRhSi3 0.8 ('05 SE)CeIrSi3 1.6 ('06 OS)CeCoGe3 0.7 ('06 OS)Ce2Ni3Ge5 0.26 ('06 OS)CeNiGe3 0.4 ('06 OS)CePd5Al2 0,57 (‘08 OS)CeRhGe2 0.45 ('09 OS)CePt2In7 2.1 (‘10 LANL)CeIrGe3 1.5 (’10 OS)

UBe13 0.9 ('83 Z/LANL)UPt3 0.5 ('84 LANL)URu2Si2 1.4 ('84 K/DA)UNi2Al3 1.2 ('91 DA)UPd2Al3 2.0 ('91 DA)URhGe 0.3 ('01 GR)UCoGe 3.0 ('07 AM/KA)p > 0UGe2 0.7 ('00 CA/GR)UIr 0.14 ('04 OS)

NpPd5Al2 5.0 ('07 OS)

PuCoGa5 18.5 ('02 LANL)PuRhGa5 8.7 ('03 KA)

p > 0Am metal 2.2 ('05 KA)

Tc(K) PrOs4Sb12 1.85 ('01 UCSD)

β-YbAlB4 0.08 ('08 TO/IR)

p > 0Eu metal 1.8-2.8 (’09 SL, OS)

Magnetic Cooper pairing in UPd2Al3

C. Geibel et. al., 1991

Tmagn ≈ 14 Kµs ≈ 0.85 µB

γ ≈ 140 mJ/K2molTc ≈ 2 K2∆0/kBTc ≈ 6 (Kyougaku

et al., 1993)

•Two more localized ("core") electrons: magnetism• one less localized ("heavy" itinerant) electron:

heavy LFL state (Tc< T < TN)heavy-fermion SC (T < Tc)

U3+ (5f3)coexisting with local AF

Quasiparticle tunneling[M. Jourdan et. al., Nature 398, 47 (1999)]

tunnel diode UPd2Al3 - AlOx - 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")

= = (0, 0, 1/2)Tc = 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

Q 0Q

Non-Fermi-liquid superconductor UBe13[F. Kromer et al., PRL 81, 4476 (1998); N. Oeschler et al., Acta Phys. Pol. 34, 255 (2003)]

ΔCT vs T C vs T

TL 0 at B* ≈ 4.2 T: QCP

4T ≤ B ≤ 10 T : ρ/ρ(1K) vs T universal

ΔC/T = γ0-βT0.5 (B = 12 T)

P. Gegenwart et al. (2004)

(α =l-1 δl/δT)

α vs T

T 0 : Δρ ~ T1.5

(3D-SDW)

Double transition in (U1-xThx)Be13 0.019 < x < 0.046 [H.R. Ott et al., Phys. Rev. B 31, 1651 (1985)]

Phase diagram of U1-xThxBe13[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