kaleidoscope ofheavy electrons: super- conductivity ... · 2 0.6 ('92 ge) cerh 2si 2 0.4...
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Kaleidoscope of Heavy Electrons: Super-conductivity, Magnetism, Quantum Critical Points
F. SteglichMPI for Chemical Physics of Solids, Dresden, Germany
In collaboration with:J. Custers, P. Gegenwart, C. Geibel, T. Cichorek, M. Grosche§, R. Küchler, M. Lang#,T. Lühmann, T. Nakanishi, M. Nicklas, S. Paschen, N. Sato+, R. Shiina§§, J. Sichelschmidt, G. Sparn, O. Stockert, T. Tayama##, K. Tenya++, P. Thalmeier, Y. Tokiwa, H. Wilhelm, H.Q. Yuan, S. Wirth
at present: § Royal Holloway College, Univ. of London; # Univ. of Frankfurt, + Nagoya Univ.,§§ Tokyo Metropolitan Univ.; ## ISSP, Univ. of Tokyo; ++ Hokkaido Univ.
M.M. Abd-Elmeguid, Univ. of Cologne K. Neumaier, WMI GarchingK. Ishida, Kyoto Univ. Y. Kitaoka, Osaka Univ.D.E. MacLaughlin, UC Riverside T. Komatsubara, Tohoku Univ.P. Coleman, Rutgers Univ. P. Fulde, MPI-PKS DresdenK. Miyake, Osaka Univ. C. Pépin, CEA SaclayQ. Si, Rice Univ. G. Varelogiannis, MPI-PKS DresdenG. Zwicknagl, TU Braunschweig
Crystal structures and phenomena
ferroelectricity
charge density wave
quantum Hall effect
conductivity in polymers
superfluidity
superconductivity (SC)
high-Tc SC in cuprates
colossal magnetoresistance
heavy fermions
quantum phase transitions
C60
1985, 98
2000 (C)
1996, 2003
1913, 72, 73, 20031987
YBa2Cu3O7UPd2Al3
Outline
• Heavy-fermion (HF) metals
• Superconductivity
• Quantum criticality
• Outlook
Superconductivity in CeCu2Si2
100 at% Ce3+ ions necessaryfor superconductivity
(LaCu2Si2 is not a superconductor)
Superconductivity of Heavy Fermions
(J/K2mole) ~ m*
TK ≈ 15 K
• Superconducting phase transition(B = 0)∆C/Tc ≈ (Tc)Cooper pairs formed by "HeavyFermions"Anisotropic order parameter
• Normal state(Bc2 ≈ 3 Tesla)
→ 1 J/K2mole (Cu: 0.7 · 10-3 J/K2mole)Heavy Electrons("Heavy Fermions")
Heavy-Fermion metals
T >> TK (10 ... 100 K)
T << TK: Heavy electrons ("compositefermions")
→ m* ≈ 1000 mel: "strongly correlated electron system"
vF ≈ 106sm
vF* ≈ 103sm
Groundstate properties - Heavy Landau Fermi liquid (LFL) : CeCu6- Non-Fermi liquid (NFL) : YbRh2Si2- Magnetic order : NpBe13- Superconductivity : UPd2Al3
Heavy-Fermion Superconductors
U-basedTc(K)
UBe13 0.9 ('83 Z/LANL)
Ce-basedTc(K)
CeCu2Si2 0.7 ('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)CePt3Si 0.7 ('03 VI)
p > 0CeCu2Ge2 0.6 ('92 GE)CeRh2Si2 0.4 ('95 LANL)CePd2Si2 0.4 ('94 CA)CeIn3 0.2 ('98 CA)CeRhIn5 2.1 ('00 LANL)Ce2RhIn8 1.1 ('03 LANL)
UPt3 0.5 ('84 LANL)URu2Si2 1.4 ('84 K)UNi2Al3 1.2 ('91 DA)UPd2Al3 2.0 ('91 DA)
Pr-basedPrOs4Sb12 1.85 ('01 UCSD)
Pu-basedPuCoGa5 18.5 ('02 LANL)PuRhGa5 8.7 ('03 KA)
Non-Fermi-Liquid Superconductor: CePd2Si2[N.D. Mathur et al., Nature 394, 39 (1998)]
p →
↑T CePd2Si2
• AF QCP at pc = 28 kbar• Tc = 0.4 K at p=pc
• NFL normal state• SC mediated by strong spin-fluctuations ?
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 heavyelectrons ("itinerant" 5f electrons)
superconducting glue provided bymagnetic excitons in the system of
"localized" 5f electrons
Q 0Q
Itinerant (SDW) scenario
g
T
TN
gc
TK
NFL
LFLSDW
Moriya, Hertz,Millis,Continentino,Lonzarich, …
• local moments screened• heavy QPs formed ("itinerant f-electrons")• weak coupling: SDW phase• QPs scattered off critical spin fluctuations
• in wide regions of phase diagram (T, lg-gcl)• thermal excitation of quantum critical modes• coupling of statics and dynamics: τc ~ ξz (AF: z = 2); deff = d + z
T < TK
NFL
0
CeCu2Si2: "A-S" transition at p < 0.7 GPa[G. Sparn et al., Rev. High Press. Sci. Technol. 7, 431 (1998)]
p > pc:
∆ρ = αT1.5
γ = γ0- βT0.5
(3D-SDW scenario)
SC
Tc
0.1
-2 0 2 4 6 80.0
0.5
1.0
1.5
2.0
2.5CeCu2(Si1-xGex)2
Tc
Tem
pera
ture
[K]
∆p=p-pc1(x) [GPa]
Tc TN x 0
Tc
AFM
S C
TN
0.1 0.25
Observation of two distinct superconductingphases in CeCu2Si2
[H. Q. Yuan et al., Science 302, 2104 (2003)]
Locally critical (local moment) scenario
T TK
NFL
LFL
• Two QCPs coinciding:
• New quantum criticality dominating: local spin fluctuations• At QCP: Kondo resonance not fully developed• NFL: fluctuations between small and large Fermi surface
Schröder, Coleman, Si,Pépin,Ingersent,Ramazashvili
TN
T*
ggc0
AFM - PMLFL - NFL
experimental techniques: T-dependence (at g = gc)g (p or B) -dependence (at T = 0)
YbRh2(Si0.95Ge0.05)2[P. Gegenwart et al., Acta Pol. Phys. B 34, 323 (2003)]
χ = C/(T−θ)θ = − 0.3 KC → µpara = 1.4 µB/Yb3+
χ−1 ∼ Tα with α ≈ 0.75
c
a
Yb
Rh
Si
-0.4 0 1 2 3 40.0
0.2
0.4
0.6
0.8
~ T0.75χ-1
(106 m
ol/m
3 )
T (K)
0.01 0.1 1 40
2
4
6
8
YbRh2(Si1-xGex)2x=0x = 0.05χ
(10-6
m3 /m
ol)
T (K)
0.12 0.18 0.24 0.30
B (T)
T=12K
T=5K
YbRh2Si2
dP/d
B (a
rb. u
nits
)
B ⊥ c (T)
0.3 0.6 0.9
-90
0
90
Θ (d
eg.)
Yb3+ ESR in YbRh2Si2[J.Sichelschmidt et al., PRL 91, 156401 (2003)]
B
a a
cΘ
g⊥ = 3.561 ± 0.006g|| = 0.17 ± 0.07
linewidth ∆Bexp = 0.02T << ∆BK = kBTK/µB = 37 T (TK = 25 K)
intensity I ~ χ (ω = 0, q = 0)
anisotropy
large local Yb3+ moments exist well below TK = 25 K
Kondo temperature TK from thermodynamics
0.1 1 10 100 3000.0
0.5
1.0
B = 0
YbRh2Si2
∆C /
T (J
/ m
ol K
2 )
T (K)
0 100 2000
1
2
3
4
RLn8
∆S
(Rln
2)
T (K)
TK = 20-30 K
~ log(T0/T)
T0 = 24 K
Rln8
Kondo temperature TK from transport
0 50 100 150 200 250 300
-100
-80
-60
-40
-20
0
S (µ
V/K
)
T (K)0 100 200 300
0
20
40
60
80
YbRh2Si2
j // c
j // a
ρ (µ
Ω c
m)
T (K)
0.02 0.1 10
1
2
3
a
x =0.05
x = 0 YbRh2(Si1−xGex)2
C el/T (J
mol−1
K− 2)
T (K)0 2 4 6 8 10
0
5
10
15
20
25
x=0.05
b
ρ (µΩ
cm)
T (K)
0.0 0.1 0.20.8
1.2
j // c
x=0 j ⊥c
Disparity between Cel/T and ρ in YbRh2Si2[J. Custers et. al., Nature 524, 424 (2003)]
Characteristic energy scale T0(b) ~ b vanishes at QCP
Scaling behavior in Cel(T,b)/T; b = B - Bc
0.02 0.1 1 20
1
2
B (T)
0.8
B ⊥ c
0.40.2
0.1
0.05
YbRh2 (Si0.95 Ge0.05 )2
Cel /
T (J
mol
-1 K
-2 )
T (K) 0.1 1 10 1000.2
1
B (T)0.050.10.20.40.8
φ(T
0.33
J K
-2 m
ol-1
T / (B - Bc ) (KT-1)
T0(b)
⇒T/T0 scaling for Φ(T,b) with Φ(T,b) = b1/3⋅C(T,b)/T)
⇒ no residual entropy at QCP⇒ S(T,b)=b2/3 S(T/T0) →0 at QCP
b 0:
0.02 0.1 1 100
1
2
a
γ 0 (J
mol
-1 K -2
)
(B - Bc ) (T)
~b−1/3
b =
γ0 YbRh2(Si.95Ge.05)2
Field dependence of γ0(b), b⊥ c (Bc = 0.027 T)
0.02 0.1 1 20
1
2
3
TN
B ⊥ c
B (T) 0 0.025
YbRh2 (Si0.95 Ge0.05 )2
Cel /
T (J
mol
-1 K
-2 )
T (K)
~ T−1/3
T 0:
Similar: ~12
−=∆
ATρ
T (b → 0)b (T → 0)
⇒ b-dependence at T=0 similar to
T-dependence at b=0
γ ~ (-log b) for b ≥ 0.3 Tb−1/3 (b → 0)
⇒ contradiction to 2D-SDW scenario
Scaling behavior in ρ(T,b), b = B - Bc
0 5 100
5
10
15
~ 1/b B ⊥ c 1/10 B || c
A(µΩcmK-2)
B (T) 0.1 1 10 1000.1
1
5B ⊥ cj ⊥ c
B (T) 0.1 0.2 0.4 0.5 0.7 1
dρ/d
T (µ
Ωcm
/K)
T / (B - Bc ) (K T -1 )
b>0: ∆ρ=A(b)T2
Grüneisen ratio[R. Küchler et al., PRL 91, 066405 (2003)]
Specific heat: C/T ∼ ∂S/ ∂TThermal expansion: β ~ (– ∂S/ ∂p)( β = 1/V dV/dT) LFLAF
p
T
0 2 4
100
150
Γ
T (K)
CeNi2Ge2
Γcr ~ 1/T
L. Zhu, M. Garst, A. Rosch, Q. Si, PRL 91, 066404 (2003):Grüneisen ratio Γcr = βcr/Ccr diverges at any QCP, Γcr ~ T-x
Critical exponent x nature of QCP
x = 1:
3D-SDW scenario
Outlook
Importance of local f-degrees of freedom, e.g.,
UPd2Al3 - Cooper pairing via (propagating) local 5f-excitation
break-up of heavy ("composite") quasiparticles
Is local QCP unfavorable for superconductivity?
CeCu2Si2 - compatible with (3D) SDW scenario, superconductors
CeNi2Ge2...
- no superconductor
YbRh2(Si, Ge)2 - suggestive of local QCP
non-Kondo-screened fluctuating Yb3+ moments
fractional exponent for Grüneisen ratio
However:
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)
• Pairbreaking by magneticimpurities (xc < 1 at%)
LaAl2 TCo = 3.3 KGd-doping: xc = 0.6 at%Ce-doping: xc = 0.9 at%
TK = 0.5 K MHZ
(Riblet, Winzer 1971)
CeCu2Si2: Phase diagrams
chemical (C. Geibel et al., 1995)
physical (P. Gegenwart et al., 1998)
29Si NMR[K. Ishida et al., PRL 89, 107202 (2002)]
(1/T1T)4f ∝ T-½
0.1 1 10 100
0.1
1
10
~ T − 1/2
T (K)
NMR 0.15 T 0.50 T 2.42 T
(1/T
1T)4f
NM
R (s
-1K-1
)
0.1
1
10 ESR
0.19 T 0.68 T
(Im χ
/ω) 4f
ES
R
(arb
. uni
ts)
B →Bc+
B > Bc : LFL state below T*(B)
T → 0