quantum criticality in Ce(Co , Rh)In 5 studied by low-temperature - - PowerPoint PPT Presentation

qk

• exp. setup

Motiv ation results Concl.

quantum criticality in Ce(Co, Rh)In5 studied by low-temperature thermal expansion

• J. G. Donath1
• F. Steglich1
• E. D. Bauer2
• J. L. Sarrao2
• P. Gegenwart3

1Max-Planck-Institute for Chemical Physics of Solids,  Dresden, Germany 2Los Alamos National Laboratory, Los Alamos, New Mexico , USA

• 3I. Physikalisches Institut, Universität Göttingen,  Göttingen, Germany

Hvar – September th, 

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl.

Contents

quantum criticality experimental setup motivation: materials results

CeCoIn5−xSnx CeRhIn5−xSnx

conclusion

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl.

specific heat and thermal expansion

LFL δ temperature MO NFL

thermodynamic properties

◮ specific heat Cp = T

∂S

∂T

• p

◮ thermal expansion

α =

1 V

∂V

∂T

• p = − 1

V

• ∂S

∂p

• T

! α = α(T), (∂S/∂p)T pointwise!

◮ Grüneisen ratio Γ ∼ α/C = − 1 V E∗

• ∂E∗

∂p

• if single energy scale E∗ dominates

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl.

specific heat and thermal expansion

LFL δ temperature MO NFL

“nature” of qcp

• i. SDW type (“conventional QCP”)

[Zhu et al. PRL ,  ()]

AFM-QCP 3D 2D (C/T)cr ∼ − √ T − log T (α/T)cr ∼

1/ √ T 1/T

αcr ∼ √ T const Γcr ∼

1/T

• ii. local type (“unconventional QCP”)

no T-dep. for α and C Γcr ∼ 1/T ǫ, ǫ < 1

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl.

specific heat and thermal expansion

LFL δ temperature MO NFL

“nature” of qcp

• i. SDW type (“conventional QCP”)

[Zhu et al. PRL ,  ()]

AFM-QCP 3D 2D (C/T)cr ∼ − √ T − log T (α/T)cr ∼

1/ √ T 1/T

αcr ∼ √ T const Γcr ∼

1/T

• ii. local type (“unconventional QCP”)

no T-dep. for α and C Γcr ∼ 1/T ǫ, ǫ < 1

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl.

quantum criticality experimental setup motivation: materials results

CeCoIn5−xSnx CeRhIn5−xSnx

conclusion

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl.

thermal expansion measuring cell

[Pott and Schefzyk, JPSI ,  ()]

◮ capacitive method ◮ circular springs

parallel capacitor plates

◮ thermally decoupled with

graphite elements cell thermally stabilized

◮ relative resolution up to ∆l/l = 10−11 ◮ dilution fridge: 0.02 T 6 K ◮ SC magnet: 0 B 20 T

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl.

thermal expansion measuring cell

[Pott and Schefzyk, JPSI ,  ()]

6cm

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl.

quantum criticality experimental setup motivation: materials results

CeCoIn5−xSnx CeRhIn5−xSnx

conclusion

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl.

115 systems

◮ tetragonal structure ◮ alternating layers of

CeIn3 and MIn2 Fermi surface: 2 dimensional (cylindrical sheets along c)

◮ large family of compounds

rich physics (SC, MO, NFL, . . .)

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl.

115 systems

p, B = 0

0.5 Ir 0.5 Rh 0.5 Co

T (K)

AFM SC ? SC Tc TN

4 3 2 1

Co

[Pagliuso et al. Physica B -,  ()]

CeCoIn5

◮ HF SC with highest

Tc = 2.3 K

◮ NFL at Bc2

CeRhIn5

◮ AFM at Tc = 3.7 K ◮ SC for p > 1.6 GPa ◮ NFL at pc

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

quantum criticality experimental setup motivation: materials results

CeCoIn5−xSnx CeRhIn5−xSnx

conclusion

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

CeCoIn5: phase diagram

p, x = 0

[Paglione et al. PRL ,  ()]

◮ complex SC phase for

0 < T 2.3 K and 0 Bc2 5 T

◮ around 5 T: NFL - behavior in

C, ρ, α, ... reason for QCP still unclear “hidden order (AFM)”, (SC QCP), ...

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

Sn doping: CeCoIn5−xSnx

why Sn-doping?

◮ separate BQCP from Bc2

study origin of NFL

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

Sn doping: CeCoIn5−xSnx

p, B = 0

[Daniel et al. PRL ,  ()]

◮ Sn (electron)-doping

suppresses SC

◮ for x = 0.18: Tc = 0,

but no AFM order

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

CeCoIn5−xSnx qc behavior: α and C

p, x = 0

0.1 1

1

0.1 1 7 5 10 15 20 ~T

−1/2

∆C/T (J/K

2mol)

~(const −T

1/2)

~ log T a CeCoIn5 5 T // c α / T (10

−6 K −2)

T (K)

~ T

−1

T * b

C/T:

[A. Bianchi et al. PRL ,  ()]

◮ 2D or 3D α/T:

[JGD et al. PRL ,  ()]

◮ 2D: T >T∗, 3D: T <T∗

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

CeCoIn5−xSnx qc behavior: α and C

p = 0, B = Bc2

[Bauer et al. PRL ,  ()]

◮ diverging C for all concentrations

at the upper critical field Bc2

◮ (α/T)cr ∼ 1/T for T > T ∗ 2D ◮ αcr ∼

√ T for T < T ∗ 3D

◮ crossover temperature T ∗

increases with increasing x

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

CeCoIn5−xSnx qc behavior: α and C

p = 0, B = Bc2

0.1 1 5 10 15 20 25 30 35 40 45 50 55 60

x 0.00 0.03 0.06 0.09 0.12 0.18 / T (10

• 6K
• 2)

T (K) CeCoIn5-xSnx

[JGD et al. PRL ,  ()]

◮ diverging C for all concentrations

at the upper critical field Bc2

◮ (α/T)cr ∼ 1/T for T > T ∗ 2D ◮ αcr ∼

√ T for T < T ∗ 3D

◮ crossover temperature T ∗

increases with increasing x

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

CeCoIn5−xSnx qc behavior: α and C

p = 0, B = Bc2

1 2 3 4 5 6 1 2 3 4 5 6

x 0.00 0.18 (10

• 6K
• 1)

T (K)

T* T*

CeCoIn5-xSnx

[JGD et al. PRL ,  ()]

◮ diverging C for all concentrations

at the upper critical field Bc2

◮ (α/T)cr ∼ 1/T for T > T ∗ 2D ◮ αcr ∼

√ T for T < T ∗ 3D

◮ crossover temperature T ∗

increases with increasing x

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

CeCoIn5−xSnx qc behavior: α and C

p = 0, B = Bc2

[Bauer et al. PRB ,  ()]

◮ disorder effect? ◮ intrinsic?

layered lattice structure coupled planes α and κ most sensitive

◮ Γ ∼ T −0.65

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

CeCoIn5−xSnx qc behavior: α and C

• FL

FL

• rdered

phase

2d classical 2d quantum critical

T r

3d 2d 3d quantum critical 2d quantum critical 3d classical Tcl Λ2

η

Λ2

η

Tc TG Tx ∼ r

• [Garst et al. arXiv:.v]

◮ disorder effect? ◮ intrinsic?

layered lattice structure coupled planes α and κ most sensitive

◮ Γ ∼ T −0.65

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

CeCoIn5−xSnx qc behavior: α and C

p, x = 0

0.1 1 8 10 100 1000 10 100 1000

YbRh2(Si0.95Ge0.05)2 CeCoIn5 CeCoIn4.82Sn0.18

T

− 0.6

T

− 0.65

Γcr −Γcr

T (K)

[JGD et al. PRL ,  ()]

◮ disorder effect? ◮ intrinsic?

layered lattice structure coupled planes α and κ most sensitive

◮ Γ ∼ T −0.65

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

CeCoIn5−xSnx qc behavior: α and C

p, x = 0

• ✁
• ✁

• ✁

• ✁
• ✁

• ✂

[JGD et al. PRL ,  ()]

◮ disorder effect? ◮ intrinsic?

layered lattice structure coupled planes α and κ most sensitive

◮ Γ ∼ T −0.65

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

Sn doping: CeRhIn5−xSnx

p, B = 0

[Bauer et. al. Physica B -,  ()]

◮ Sn doping suppresses AFM

Specific heat

• vol. (!) thermal expansion

◮ QCP at x ≈ 0.48

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

Sn doping: CeRhIn5−xSnx

p, B = 0

0.1 1 6

• 20
• 15
• 10
• 5

5

TN,onset TN TN

x 0.30 0.36 0.40 0.48 β / T (10

−6K −2)

T (K) CeRhIn5-xSnx

[JGD et al., to be published]

◮ Sn doping suppresses AFM

Specific heat

• vol. (!) thermal expansion

◮ QCP at x ≈ 0.48

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

comparison CeIn3−xSnx – CeRhIn5−xSnx

B, p = 0

0.0 0.2 0.4 0.6 1 2 3 4 5 0.0 0.5 2 4 6 8 10 b TN CeRhIn5-xSnx TN (K) x a CeIn3-xSnx TI TN TN (K) x [Küchler et al. PRL ,  () ]

◮ CeIn3: cubic

CeRhIn5: tetragonal

◮ similar T − x−phase diagram

(similar x, inflection point in TN(x))

◮ 3D behavior in thermal

expansion (β/T ∼ 1/

√ T)

similar qc behavior in cubic and layered systems

◮ 3D behavior along both

crystallographic axis doping smears out anisotropic qc fluctuations

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

comparison CeIn3−xSnx – CeRhIn5−xSnx

B, p = 0

0.1 1 7 5 10 15 20 lines: T

• 0.5

β/T (10

−6K −2)

T (K)

CeRhIn4.52Sn0.48 CeIn2.35Sn0.65 [CeRh4.52Sn0.48: JGD et al., to be published] [CeIn2.35Sn0.65: Küchler et al. PRL ,  ()]

◮ CeIn3: cubic

CeRhIn5: tetragonal

◮ similar T − x−phase diagram

(similar x, inflection point in TN(x))

◮ 3D behavior in thermal

expansion (β/T ∼ 1/

√ T)

similar qc behavior in cubic and layered systems

◮ 3D behavior along both

crystallographic axis doping smears out anisotropic qc fluctuations

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl. CeCoIn5 CeRhIn5

comparison CeIn3−xSnx – CeRhIn5−xSnx

B, p = 0

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

CeRhIn4.52Sn0.48

α (10

• 6K

−1)

T (K)

// c ⊥ c [JGD et al., to be published]

◮ CeIn3: cubic

CeRhIn5: tetragonal

◮ similar T − x−phase diagram

(similar x, inflection point in TN(x))

◮ 3D behavior in thermal

expansion (β/T ∼ 1/

√ T)

similar qc behavior in cubic and layered systems

◮ 3D behavior along both

crystallographic axis doping smears out anisotropic qc fluctuations

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl.

conclusion

◮ dimensional crossover in qc fluctuations in

CeCoIn5−xSnx for all x

◮ Sn substitution shifts Crossover to higher T

disorder, intrinsic?

◮ 3D SDW scenario for all concentrations x in

CeRhIn5−xSnx similar to CeIn3 disorder? no lattice dependence?

guido donath qc in Ce(Co, Rh)In5

qk

• exp. setup

Motiv ation results Concl.

conclusion

◮ dimensional crossover in qc fluctuations in

CeCoIn5−xSnx for all x

◮ Sn substitution shifts Crossover to higher T

disorder, intrinsic?

◮ 3D SDW scenario for all concentrations x in

CeRhIn5−xSnx similar to CeIn3 disorder? no lattice dependence?

guido donath qc in Ce(Co, Rh)In5

appendix

0.1 1 5 10 15 20 25 30 35 40 45 50 55 60

x 0.00 0.03 0.06 0.09 0.12 0.18

/ T (10

• 6K
• 2)

T (K) CeCoIn5-xSnx

guido donath qc in Ce(Co, Rh)In5

appendix

0.0 0.5 1.0 2 4 6 T * H (T) 5 10

α (10

−6K −1)

T (K)

guido donath qc in Ce(Co, Rh)In5

appendix

guido donath qc in Ce(Co, Rh)In5

appendix

guido donath qc in Ce(Co, Rh)In5

appendix

TABLE I. Physical properties of CeCoIn5−xSnx. Superconducting transition temperature Tc; specific heat jump at Tc, C; parameters 0 and n determined from fits of the data to Eq. 1; residual resistivity 0; temperature maximum of electrical resistivity Tmax. x Tc K C/Tc

• J

mol K2

• m,J

mol K2 n T range cm Tmax K 2.25 1.686 40 1 0.09–0.4 2.5 38 0.015 2.08 1.497 0.03 1.89 1.488 135 2.1 0.06–0.4 7.5 51 0.06 1.56 1.279 272 2.5 0.2–0.5 9.4 45 0.09 1.14 0.907 14.9 49 0.12 0.79 0.535 515 1.6 0.06–0.4 11.6 59 0.15 0.44 0.1 14.2 55 0.18 17.1 61 guido donath qc in Ce(Co, Rh)In5

appendix

1 10 2 4 6 8 10 12 14 16 18 20 5 10 15 20 25 30 35 40 0.48 0.24 0.08 x=0 CeRhIn5-xSnx ρmag (µΩcm) T (K)

guido donath qc in Ce(Co, Rh)In5

appendix

• FIG. 3 (color online).

Evolution of characteristic energy scales in CeCoIn5 vs magnetic field. The Fermi-liquid temperature TFL is the end of the T2 regime in wT (squares). The quasiparticle temperature TQP is the onset of the low-T upturn in LT (diamonds). The spin-fluctuation temperature TSF is reached when T 0 at high T (circles). Error bars for TQP and TFL are smaller than the size of symbols. Note that TQP TFL at H 10 T and above. To the right, we also show TSF and TFL for CeRhIn5 (at H 0).

guido donath qc in Ce(Co, Rh)In5

appendix

• Fig. 2. Violation of the WF law. Residual re-

sistivities (extrapolated to T = 0) as a function of magnetic field, for heat (solid symbols) and charge (open symbols) transport. For in-plane transport (bottom), the two resistivities track each other as a function of field, thereby obeying the WF law at all fields. For inter-plane transport (top), the electrical resistivity rc is flat as H→Hc, whereas the thermal resistivity increases, thereby causing a violation of the WF law at the QCP, with a Lorenz number L < L0.

guido donath qc in Ce(Co, Rh)In5

appendix

]. rate). normal . . at

0.1 1 10 20 30

0.0 0.1 0.2

6 8 0.0 0.2

2 4 6 8 µ0H (T) µ0Hmin (T) T (K) ~ T

0.76

c) b) T (K) CeCoIn5 H || c SC a) Hd H

Hall c2

µ0H (T) T (K)

• FIG. 4 (color online).

(a) Phase diagram resulting from Hall effect measurements. The hatched area marks the H range within which SC influences the slope of xyH [ mark onset of nonzero xyH]. HdT values for which a minimum in jRd

Hj

can directly be observed are marked by . A power law fit extrapolates to 4.1 T at T 0 (dashed line). (b) T dependence of

• Hmin. A fit (dashed line) again extrapolates to 4.0 Tat T 0. MR

data (*) taken from Ref. [3]. (c) Our results compared to those from resistivity and specific heat measurements in Refs. [6] (+, ) and [3] (*). Lines are guides to the eye.

guido donath qc in Ce(Co, Rh)In5

appendix

, s- he

• GPa

d A l efficient iquid ely s

• l

fer- her

• f
• n
• heat

for . h e

P* P

c

b

PG FL NFL AFM SC T P

1 2 3 4 5 1 2 3 TFL Tpg

a

CeCoIn5 SC

n = 1.5 ± 0.1 n ≈ 1 n = 2

T(K) P(GPa)

• FIG. 4.

(a) Temperature-pressure phase diagram for CeCoIn5 constructed from data shown in Figs. 2 and 3 . (b) Schematic T–P phase diagram. AFM: Ne ´el state; PG: pseudogap state; SC: unconventional superconducting state; FL: Fermi-liquid; NFL: non-Fermi-liquid. See text for details. guido donath qc in Ce(Co, Rh)In5

appendix

0.1 1 10 100 0.2 0.4 0.6 0.8 1

T * T * T *

Ce1-xLaxCoIn5

TSC Tcoh

T (K) x(La)

TFL Tlinear

s ab ab c

guido donath qc in Ce(Co, Rh)In5