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

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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

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SLIDE 1

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

  • F. Steglich

MPI for Chemical Physics of Solids, 01187 Dresden, Germany

  • utline:

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

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SLIDE 2

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

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SLIDE 3

≤ 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

2 eff

μ

χ(T) ~

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SLIDE 4

2 Cr Fe

[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

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SLIDE 5

> 1970: Rare earth impurities

  • J. Moeser, F. Steglich, G.v. Minnigerode
  • J. Low Temp. Phys. 15, 9 (1974)

giant thermoelectric power

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

resistivity x = 0.00626 re-entrant superconductivity

( ) [ ( ) ( )] ( )

ce La ce ce

T S T T S S T ρ ρ ρ ρ − − =

Gorter-Nordheim:

(La1-xCex)Al2

slide-6
SLIDE 6
  • utline:

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

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SLIDE 7

Superconductivity vs. magnetism

IA VIIIA

1

H

1.008 IIA

IIIA IVA VA VIA VIIA

2

He

4.003 3

Li

6.941 4

Be

9 .012 5

B

10.81 6

C

1 2.01 7

N

14.01 8

O

1 6.00 9

F

1 9.00 10

Ne

20.18 1 1

Na

22.99 1 2

Mg

2 4.31 IIIB IVB VB VIB VIIB

VIIIB IB IIB

1 3

Al

26.98 1 4

Si

2 8.09 1 5

P

30.97 1 6

S

3 2.07 1 7

Cl

3 5.45 18

Ar

39.95 1 9

K

39.10 2

Ca

4 0.08 2 1

Sc

44.96 2 2

Ti

4 7.87 23

V

50.94 2 4

Cr

5 2.00 2 5

Mn

5 4.94 2 6

Fe

5 5.85 2 7

Co

58.93 2 8

Ni

5 8.69 2 9

Cu

6 3.55 3

Zn

65.39 3 1

Ga

69.72 3 2

Ge

7 2.61 3 3

As

74.92 3 4

Se

7 8.96 3 5

Br

7 9.90 36

Kr

83.80 3 7

Rb

85.47 3 8

Sr

8 7.62 3 9

Y

88.91 4

Zr

9 1.22 41

Nb

92.91 4 2

Mo

9 5.94 4 3

Tc

(98) 4 4

Ru

1 01.1 4 5

Rh

102.9 4 6

Pd

1 06.4 4 7

Ag

1 07.9 4 8

Cd

112.4 4 9

In

114.8 5

Sn

1 18.7 5 1

Sb

121.8 5 2

Te

1 27.6 5 3

I

1 26.9 54

Xe

131.3 5 5

Cs

132.9 5 6

Ba

1 37.3 5 7

La

138.9 7 2

Hf

1 78.5 73

Ta

180.9 7 4

W

1 83.8 7 5

Re

1 86.2 7 6

Os

1 90.2 7 7

Ir

192.2 7 8

Pt

1 95.1 7 9

Au

1 97.0 8

Hg

200.6 8 1

Tl

204.4 8 2

Pb

2 07.2 8 3

Bi

209.0 8 4

Po

( 209) 8 5

At

( 210) 86

Rn

(222) 8 7

Fr

(223) 8 8

Ra

( 226) 8 9

Ac

(227) 104

Rf

( 261) 1 05

Db

(262) 106

Sg

( 266) 1 07

Bh

( 264) 1 08

Hs

( 269) 1 09

Mt

(268) 5 8

Ce

1 40.1 59

Pr

140.9 6

Nd

1 44.2 6 1

Pm

( 145) 6 2

Sm

1 50.4 6 3

Eu

152.0 6 4

Gd

1 57.3 6 5

Tb

1 58.9 6 6

Dy

162.5 6 7

Ho

164.9 6 8

Er

1 67.3 6 9

Tm

168.9 7

Yb

1 73.0 7 1

Lu

1 75.0 9

Th

2 32.0 91

Pa

(231) 9 2

U

2 38.0 9 3

Np

( 237) 9 4

Pu

( 244) 9 5

Am

(243) 9 6

Cm

( 247) 9 7

Bk

( 247) 9 8

Cf

(251) 9 9

Es

(252) 100

Fm

( 257) 1 01

Md

(258) 102

No

( 259) 103

Lr

( 262)

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SLIDE 8

Tc of La0.99RE0.01

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SLIDE 9

Pairbreaking by magnetic impurities (theory)

Hint = 2 J S . s α ~ x S(S + 1) J > 0 TK ~ TFexp (-1/NFJ) ) 1 S ( S ( ) T / T ( ln ) 1 S ( S x ~

2 K 2 2

+ π + + π α

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SLIDE 10

Pairbreaking by magnetic impurities (experiment)

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SLIDE 11
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SLIDE 12
  • utline:

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

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SLIDE 13

TK increases by a factor of 250 CeAl2 (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 /( ) V V ( = v

2 2

YAl LaAl

2

LaAl

V

  • v

2 K

T

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SLIDE 14

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).
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SLIDE 15

γ = 1.62 J/K2mole A = 35 µΩcm/K2

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SLIDE 16

Superconductivity in CeCu2Si2

100 at% Ce3+ ions necessary for superconductivity (LaCu2Si2 is not a superconductor)

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SLIDE 17

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 ≈ 106

s m

vF* ≈ 103 s

m

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SLIDE 18
  • utline:

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

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SLIDE 19

Superconductivity in CeCu2Si2

100 at% Ce3+ ions necessary for superconductivity (LaCu2Si2 is not a superconductor)

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SLIDE 20

Heavy-fermion superconductivity in CeCu2Si2

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SLIDE 21

Heavy-fermion superconductivity in UBe13

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SLIDE 22

Heavy-fermion superconductivity in UPt3

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SLIDE 23

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).

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SLIDE 24
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SLIDE 25

Heavy-fermion superconductors

Tc(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 > 0 CeCu2Ge2 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 > 0 UGe2 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 > 0 Am metal 2.2 ('05 KA) Tc(K) PrOs4Sb12 1.85 ('01 UCSD) β-YbAlB4 0.08 ('08 TO/IR) p > 0 Eu metal 1.8-2.8 (’09 SL, OS)

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SLIDE 26

Magnetic Cooper pairing in UPd2Al3

  • C. Geibel et. al., 1991

Tmagn ≈ 14 K µs ≈ 0.85 µB γ ≈ 140 mJ/K2mol Tc ≈ 2 K 2∆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

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SLIDE 27

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)

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SLIDE 28

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

Q

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SLIDE 29

Non-Fermi-liquid superconductor UBe13

[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 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)

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SLIDE 30

Double transition in (U1-xThx)Be13 0.019 < x < 0.046

[H.R. Ott et al., Phys. Rev. B 31, 1651 (1985)]

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SLIDE 31

Phase diagram of U1-xThxBe13

[F. Kromer et al., PRB 62, 12477 (2000); JLTP 126, 815 (2002)] α vs T

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SLIDE 32

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