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