Kondo breakdown in the cubic heavy fermion compound...
Transcript of Kondo breakdown in the cubic heavy fermion compound...
Kondo breakdown in the cubic heavy fermioncompound Ce3Pd20Si6
Silke Paschen
Institute of Solid State Physics, Vienna University of Technology
G
JK
PS PL
AFS AFL
CPP
CeIn3/LaIn
3
Dimensionality
CPS CeIn3
YRS CCA
Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 1
Kondo breakdown in the cubic heavy fermioncompound Ce3Pd20Si6
Silke Paschen
Institute of Solid State Physics, Vienna University of Technology
• Heavy fermion quantum criticality
• The case of YbRh2Si2
• The new cubic material Ce3Pd20Si6
• Materials in the global phase diagram
Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 2
.
Ce3Pd20Si6: J. Custers∗, J. Hanel, K.-A. Lorenzer, M. Muller, A. Prokofiev,A. Sidorenko, H. Winkler
Institut fur Festkorperphysik, Technische Universitat Wien
A. M. Strydom
Univ. of Johannesburg
Y. Shimura, T. Sakakibara
ISSP, Tokio, Japan
P.P. Deen1, E. Ressouche2, J.R. Stewart2, S. Rols2, D. T. Adroja3,W. Kockelmann3, J.-M. Mignot4
1: ESS, Lund, 2: ILL, Grenoble, 3: ISIS, Oxon, 4: LLB, Saclay
R. Yu, Q. Si
Rice University, USA
YbRh2Si2: S. Friedemann∗, P. Gegenwart∗, C. Geibel, S. Hartmann∗, C. Krellner∗,N. Oeschler∗, S. Wirth, A. Pikul∗, S. Kirchner (& PKS), F. Steglich
Max-Planck-Institut fur Chemische Physics fester Stoffe, Dresden
P. Coleman
Rutgers University, USA
Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 3
Kondo effect and heavy fermion compounds
a
b
(Coleman, Nature Mater. 11 (2012) 185, news & views)Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 4
NFL behaviour at quantum critical pointsCeCu6−xAux (Schroder et al, Nature 2000)
x
00.51
0
1
2
3
T (K
)
CeCu6–xAux
free spins
heavyfermion
AF
magnetic order
?
a
YbRh2Si2 (Custers et at., Nature 2001)B 0.3
0.2
0.1
0.0
YbRh2Si
2
TN
B c
T (
K)
B (T)0 1 2
CeIn3−xSnx (Kuchler et al, PRL 2006)
0 0.5 10
5
10
TI LFL
AF
T*
TN
CeIn3-x
Snx
T(K
)
x
CeRhIn5 (Park et at., Nature 2006)
Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 5
Standard scenario: Spin density wave (SDW) formation
(i) SDW
Paramagnet Itinerant antiferromagnet
Alternative scenario in 2D: Kondo breakdown (Coleman, Si, Schroder, ...)
(ii) KD
Paramagnet Local moment antiferromagnet
(Coleman, Nature Mater. 11 (2012) 185, news & views)
Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 6
Hall effect in tetragonal YbRh2Si2 with 2D spin fluctuations
Hall coefficient vs field
0.0 0.5 1.0 1.5 2.0 2.50.7
0.8
0.9
1.0
1.1
1.2
1.3
T (mK): 45, 65, 75, 93
YbRh2Si2
RH /R
H(B
0)
B2/B0
Phase diagram
0 1 2 30.0
0.1
0.2
0.3
B = B1 = 11 B
2
TN
T *
THall
LFLAF
YbRh2Si2
T (K)
B (T)
(SP et al., Nature 432 (2004) 881)
c
a
Yb
Rh
Si
Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 7
Hall effect in tetragonal YbRh2Si2 with 2D spin fluctuations:
Experiments on purest samples with enhanced resolution
Phase diagram
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Crossover width
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FWHM ∼ T (valid up to 1 K)
Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 8
Suggested scenarios (list incomplete ...):
Kondo breakdown/Orbital selective Mott transition:
Kondo lattice, Kondo-Heisenberg, PAM, Bose-Fermi Kondo models, ...
Coleman, Fabrizio, Kim, Kotliar, Pepin, Senthil, Si, Zaanen, ...
Lifshitz transition/Topological transition:
2D Kondo lattice model, band picture ...
Assaad, Vojta, Watanabe, ...
Valence transition/Valence criticality:
PAM with Ufc, band picture ...
Miyake, Norman, Watanabe, ...
Quantum tricritical point:
Self-consistent renormalization theory for spin fluctuations
Imada, Misawa, Yamaji
Weak-field breakdown:
Boltzmann transport theory
Schofield
...Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 9
A new cubic material: Ce3Pd20Si6
Magnetic susceptibility
0.1 1 10 1000
5
10
15
20
25
30
35
TN
TQ
T (K)
103χS
I
Inverse susceptibility
0 50 100 150 200 250 3000
50
100
150
200
250
300
350
400
450
0.0 0.2 0.4 0.6 0.8 1.0 1.23
4
5
6
-1 (
mol C
e/e
mu)
T (K)
ΘP
µ0H = 0.5 T-1
(m
ol C
e/e
mu)
T (K)
TN
TQ
χ0 = 2.27 · 10−6 m3/mol Ce
Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 10
A new cubic material: Ce3Pd20Si6
Electrical resistivity
0.1 1 10 1000
10
20
30
40
50
60
0.1 0.2 0.3 0.4 0.5 0.60
20
40
TQ
mag = -
ph
(µ
Ωcm
)
T (K)
TN
Tmax
∂/∂
T (
µΩ
cm
K-1)
T (K)
TQ
TN
Electronic specific heat
0.0 0.2 0.4 0.6 0.8 1.00
1
2
3
4
TQ
TN
T (K)
B = 0.5 T
∆C (J/mol CeK2)
ρ = ρ0 + AT 2, A = 14.9 µΩcm/K2 ∆C/T = γ + DT 3, γ = 1.5 J/molK2
KWR = A/γ2 = 6.7 (µΩcm/K2)/(J/molK2)2, SWR = 1.9
Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 11
A new cubic material: Ce3Pd20Si6
Temperature-field phase diagram
0 2 4 6 8 100.0
0.2
0.4
0.6
0.8
1.0
1.2
TN
cp
ρl
ρt
ρH
T (K)
B (T)
TQ
Cubic, Fm3m
Ce1: fcc, 4a
Ce2: sc, 8c
Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 12
Ordered phases in Ce3Pd20Si6: Below TQ
Mean field solution of effective pseudospin model (Γ8, sc)
0 1 2 3 4 5
H/Jτ
θ=φ=π/4
O0
2
Oxz+O
yz
(b)
0.0 0.5 1.0 1.50.0
0.1
0.2
0.3
0.4
0.5
θ=φ=0
T/J
τ
H/Jτ
Oxy
O0
2
Oxz/yz
Oxy
(a)
Jτ : quadrupole-quadrupole coupling strength
(SI of Custers et al., Nature Mater. 11 (2012) 189)Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 15
Landau Fermi liquid properties of Ce3Pd20Si6: ρ(T, B)
0.0 0.1 0.2 0.3 0.4
6
9
12
15
18
21
(µ
Ωcm
)
T (K)
1.0 T
0.0 T
0 1 2 30
10
20
30
40
50
60
70
80
A (
µΩ
cm
K-2)
0H (T)
H<Hc : A ~ (H
c-H)
-0.42
H>Hc : A ~ (H-H
c)
-0.38
0 2 4 6 80.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
-
0 (
µΩ
cm
)
T2 (10
-3 K
2)
Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 16
Non-Fermi liquid properties of Ce3Pd20Si6
Specific heat
0.1 0.4 10
2
4
6
8
0.1 10
5
10
15
DC/T (J/mol CeK2)
T (K)
T (K)
DC/T (J/mol CeK2)
0.0 T
0.5 T
1.0 T
1.5 T
2.0 T
∆C/T ∝ − ln T
SDW (AFM, d = 3):
∆C/T = γ − b√
T
Electrical resistivity
0.0 0.5 1.0 1.40
5
10
15
20
25
0 T
1 T
2 T
5 T
ρ -
ρ 0 (
mΩcm)
T (K)
∆ρ ∼ T
SDW (AFM, d = 3): ∆ρ ∼ T 3/2
Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 17
Isotherms crossing phase diagram
Hall effect
0.0 0.5 1.0 1.5 2.0
-5
-4
-3
-2
-1
0
B *
61 mK
98 mK
193 mK
300 mK
B (T)
ρ H (10-9 Ωm)
BN
Magnetoresistance
0 1 2 30
1
2
3
4
5
T = 300 mK
B*
BN
D A/(1+(B/B*)p)
D AN/(1+exp((B-B
N)/w
N))
B (T)
ρ l - ρl,back (
mΩcm)
0 2 4 6 8 100.0
0.2
0.4
0.6
0.8
1.0
1.2
TN
cp
ρl
ρt
ρH
T (K)
B (T)
TQ
Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 18
Phase diagram of Ce3Pd20Si6 with T ∗ scale
0 2 4 6 8 100.0
0.5
1.0
1.5
2.0
TQ
cp
TN T *
ρl
ρt
ρH
T (K)
B (T)Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 19
Crossovers in magnetotransport of Ce3Pd20Si6 at B∗
Longitudinal magnetoresistance
0.0 0.5 1.0 1.5 2.0
0.0
0.2
0.4
0.6
0.8
1.0
5 K
80 mK
B/B*
(ρl - ρl,back- ρN)/
ρ(B=0T)
Differential Hall coefficient
0.0 0.5 1.0 1.5 2.0
0.0
0.2
0.4
0.6
0.8
1.061 mK
3 K
B/B*
(dρ H/dB)/
DA
Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 20
Crossovers at B∗ vs transition at BN
Width of crossover at B∗
0.1 10.1
1
10 ρl
ρt
ρH
FWHM (T)
T (K)
Width of transition at BN
0.0 0.1 0.2 0.3 0.40.00
0.05
0.10
0.15
ρl
ρt
ρH
wN (T)
T (K)
Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 21
Suggested theoretical phase diagram at T = 0
G
JK
PS PL
AFS AFL
CPP
CeIn3/LaIn
3
Dimensionality
CPS CeIn3
YRS CCA
Kondo destruction QCPs
SDW QCPs
(Si, Physica B 378-380 (2006) 23; Phys. Stat. Sol. 247 (2010) 476; also: Coleman et al.)Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 22
Suggested theoretical phase diagram at T = 0
G
JK
PS PL
AFS AFL
CPP
CeIn3/LaIn
3
Dimensionality
CPS CeIn3
YRS CCA
Kondo destruction QCPs
SDW QCPs
(Si, Physica B 378-380 (2006) 23; Phys. Stat. Sol. 247 (2010) 476)Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 23
Suggested theoretical phase diagram at T = 0
G
JK
PS PL
AFS AFL
CPP
CeIn3/LaIn
3
Dimensionality
CPS CeIn3
YRS CCA
Kondo destruction QCPs
SDW QCPs
(Si, Physica B 378-380 (2006) 23; Phys. Status Solidi 247 (2010) 476)Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 24
Materials-based global phase diagram
G
JK
PS PL
AFS AFL
CPP
CeIn3/LaIn
3
Dimensionality
CPS CeIn3
YRS CCA
(Custers et al., Nature Mater. 11 (2012) 189)Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 25
Summary & Outlook
• Ce3Pd20Si6: New cubic quantum critical heavy fermion compound
• Crossover in magnetotransport with similar characteristics as in YbRh2Si2,
at T → 0:
– Crossover position coincides with Bc
– Crossover width extrapolates to zero
• Important difference: QCP within other ordered phase!
– Nature of this phase?
– Nature of transition leaving this phase?
– Can in Kondo breakdown scenario be related to higher dimensionality
(lower G)
– Other theoretical scenarios?
– Extensions of theories to 3D?
Heavy Fermions and Quantum Phase Transitions, IOP, CAS, Nov 10-12, 2012, 28