Pressure induced quantum phase transitions in d- and f-electron systems

Vladimir A. Sidorov

Institute for High Pressure Physics of Russian Academy of Sciences

Troitsk - Moscow

Workshop “Heavy Fermions and Quantum Phase Transitions”, November 10-12, 2012, IOP CAS, Beijing

Outline

Three compounds CePt2In7, CeCoSi and CoS2 which exhibit quantum

phase transition under pressure will be discussed in the presentation.

• CePt2In7 - a very close analog of CeRhIn5 , where 4f-electrons of Ce play the main role in magnetism, QPT and superconductivity.

• CeCoSi - a layered antiferromagnet in which Co 3d-electrons become important at high pressure along with Ce 4f-electrons.

• CoS2 - a ferromagnet and nearly a half-metal with a high degree of spin polarization. Co 3d-electrons are responsible for magnetism and QPT.

• A brief review of the experimental technique used in high pressure experiments will be presented.

Collaboration:

Los Alamos National Laboratory, USAE. Bauer, P. Tobash, M.Torrez, R.Baumbach, H. Lee, Xin Lu, F. Ronning, J.D. Thompson

Sungkyunkwan University, KoreaTuson Park

Institute for High Pressure Physics RAS, RussiaS.M. Stishov, A.E. Petrova, V.N. Krasnorussky, A.N. Utyuzh

Ames Laboratory, USAW. M. Yuhasz, T. A. Lograsso

High pressure apparatus and methods Toroid-type anvil pressure cell6 GPa at 27 ton, 8 GPa at 34 tonT = 1.2 – 300 K, no magnetic field

Before high pressure

After 6 GPa

The electrical resistivity, magnetic ac-susceptibility and ac-calorimetry measurements can be organized in a single experiment

Cylinder-piston (up to 2.2 GPa) and indenter-type (up to 3.2 GPa) cells also were used for some experiments down to 0.1 K and in the magnetic field up to 9 Tesla.

CePt2In7 - pressure induced heavy-fermion superconductivity near QCP Our first measurements on CePt2In7 poly-crystals reveal that it is a close analog of famous CeRhIn5. Pressure above 3 GPa suppresses magnetism and a broad dome of the heavy-fermion superconductivity appears around quantum critical point. Indium contamination prevents from detailed resistivity measurements in zero magnetic field. The main method was ac-calorimetry.

Now In-free single crystals of CePt2In7 became available and we present thenew data obtained at high pressure. We constructed P-T diagram based on resistivity and ac-specific heat of single crystals of CePt2In7 and determined some parameters of this heavy-fermion superconductor near QCP.

0 50 100 150 200 250 300 3500

10

20

30

40

50

60

CePt2In

7

ab (

-cm

)

T(K)

P(GPa) 0 0.67 1.54 2.19 2.47 2.66 2.97 3.08 3.29 3.51 3.85 4.33 5.30

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

CePt2In

7

ab (

-cm

)

T(K)

P(GPa) 0 0.67 1.54 2.19 2.47 2.66 2.97 3.08 3.29 3.51 3.85 4.33 5.30

0 1 2 3 4 5 6 7 80

5

10

15

20

25

TC

TN

CePt2In

7

P(GPa) 2.66 2.97 3.08

(

-cm

)T(K)

0 1 2 3 4 5 6

0

5

10

A (

-cm

/Kn )

P(GPa)

0

1

2

3

4

n

-5

0

5

10

2.5 K

0(

-cm

)

Resistivity of CePt2In7 single crystals at high pressure

The kink on (T) dependence at TN shift first to higher temperatures And then above ~ 1.5 GPa it shifts to lower temperatures. At 2.47 GPa a signature of a very broad superconducting transition appears at ~2K. At higher pressures it becomes sharp. At 5.3 GPa one can see the onset of a very broad superconducting transition at ~1.7K.. Fits of the low temperature reistivity by the relation (T) = 0 + ATn give the values of A, 0 and n, which are anomalous near 3.2 GPa. Remarkably, the exponent n is close to 0.5 at this pressure. Similar sublinear behavior of the resistivity was found in CeRhIn5 (T. Park et al., Nature 456(2008) 366).

(T) = 0 + ATn

0,0 0,5 1,0 1,5 2,0 2,5 3,00,000

0,001

0,002

0,003

0.5 mAJ//ab, H//c

3.1 GPa

CePt2In

7

R(

)

T(K)

H (T) 0 0.2 0.5 1 1.5 2 3 4 5 6 7 8 9

0,0 0,5 1,0 1,5 2,0 2,50

5

10

15

20

J // ab, H//c

3.1 GPa

CePt2In

7

TC onset

TC (50% R

N)

TC (5% R

N)

-12.4 T/K

0H (

T)

T(K)

The upper critical field of CePt2In7 superconductor

Resistivity measurements in the indenter cell down to 0.3 K and up to 9 Tesla at 3.1 GPa allow to estimate Hc2(0) and the initial slope dHc2/dT at Tc. The initial slope -12.4 T/K is close to that -15 T/K observed by Muramatsu et al. (J. Phys. Soc. Japan, 70 (2001) 3362) for CeRhIn5 heavy-fermion superconductor near pressure-tuned QCP and in the same orientation of the magnetic field. The estimated Hc2(0) ~15 Tesla is lower, than that (~20 Tesla), estimated by Werthamer-Helfand-Hohenberg formula for orbital pair-breaking. So the upper critical field may be limited by Pauli paramagnetic pair breaking as was suggested for CeRhIn5 by T. Park and J.D. Thompson (New J. Phys. 11 (2009) 055062).

0 1 2 3 4 5 6 7 8 9 100,0

0,1

0,2

0,3

0,4

0,5

0,6 CePt2In

7 + GW 60/40

P(GPa) 0.67 1.54 2.19 2.47 2.66 2.97 3.08 3.29 3.51 3.85 4.33 5.3

C

/T (J

/K2 )

T(K)

0 1 2 3 4 5 6 7 8 9 100,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,0

0,5

1,0

1,5

CePt2In

7

C/T

(J

/K2 )

T(K)

P(GPa) 0 1.54 2.19 2.66 2.97 3.08 3.29 3.85 4.33

C/T

(J/

mol

e-K

2 )

0 5 10 15 20 25 30 350,0

0,1

0,2

0,3

3.29 GPa

CePt2In

7

0~ 0.5-0.8 J/mole-K2

C/T

(J

/K2 )

T2 (K2)

0 1 2 3 4 50,00

0,05

0,10

0,15

0,20

0,25

0,30

0,350 1 2 3 4 5

0

5

10

15

C/T

(J

/K2 )

T(K)

3.29 GPa

CePt2In

7

(

-cm

)

Specific heat of CePt2In7 single crystals at high pressure

The specific heat measurements correlates well with the resistivity measurements. The Neel temperature increases first and then rapidly decreases at high pressure. Above 3.08 GPa the resistive and bulk transitions to the superconducting state take place at the same temperature. But at 2.97 GPa where the resistance of CePt2In7 becomes zero below 2 K, the upturn of the specific heat preceding a peak at the superconducting transition takes place at 1.4 K. This is very similar to CeRhIn5 (T. Park and J.D. Thompson, New J. Phys. 11 (2009) 055062). Superconductivity in CePt2In7 emerges from the heave electron normal state, which is due to strong magnetic fluctuations near QCP.

0 1 2 3 4 5 60

1

2

3

4

5

6

7

SC

AFM

P(GPa)

CePt2In

7

T(K

)

TN, peak C

TN, kink

TC onset

TC = 0

TC peak C

0 1 2 3 4 50

1

2

3 CePt2In

7

Ent

ropy

(J/

mol

e-K

)

P(GPa)

entropy at TN

entropy at TC

0 1 2 3 4 51

10

100

Te

mp

era

ture

(K

)

Pressure (GPa)

0

2

3

4

5

6

7

8

AFM

SC

CePt2In

7

Close analogy between CePt2In7 and CeRhIn5

P-T diagram Entropy Colossal scattering near QCP

(P)/(5 G

Pa)

T. Park and J.D. Thompson, New J. Phys. 11 (2009) 055062 T. Park et al., Nature 456 (2008) 366

CeCoSi: multiple transitions and quantum criticality at high pressure

First synthesis and report of crystal structure: Bodak et al., Zhurnal Struct. Khimii, 11 (1970) 305

Specific heat measurementsB. Chevalier et al., Physica B, 378-380 (2006) 795

AFM transition at 9.2 K (μeff = 2.8 μB, Θp =- 53 K), DOS calculations: B. Chevalier and S.F. Matar,Phys. Rev. B, 70 (2004) 174408

Literature data:

X-ray absorption spectroscopy: O. Isnard et al., J. Synchrotron Rad., 6 (1999) 701

Single crystals are not available. All experiments were performed on polycrystalline samples.

Properties of arc-melted CeCoSi

0 50 100 150 200 250 300 3500.0

1.0x10-5

2.0x10-5

3.0x10-5

4.0x10-5

5.0x10-5

6.0x10-5

7.0x10-5

0 50 100 150 200 250 300 3500

20000

40000

60000

80000

CeCoSi / MT124 annealed 800C/2wkH=0.1T2/14/11

(em

u/gm

)

T(K)

P= -93K

eff

= 3.18 B

T(K)

1/ (

gm/e

mu)

Single phase material, tetragonal P4/nmm, a = 0.4046 nm, c = 0.6969 nm

0 100 200 300 400 5000

500

1000

1500

C/T

(m

J/m

ol-

K2 )

T2 (K)

MT124CeCoSi800 C 2 wks

0 50 100 150 200 250 3000

50

100

150

200

250

300

350

0 2 4 6 8 10 120

20

40

60

RRR = 42

CeCoSi MT124, annealed 2 wk at 800 C

(

cm

)

T(K)

T(K)

(

cm

)

0 5 10 15 20 25 30 35 40 45 50 55 600

5

10

15

20

CeCoSi MT124, annealed 2 wk at 800 C

d/d

T (

cm

/K)

T(K)

Resistivity: pressures up to ~1 GPa. Transformation of the AFM transition related with Ce-sublattice.

0 10 20 30 40 500

50

100

150

200

250

300

P

P(GPa) 0 0.31 0.69 0.91 1.21

CeCoSi MT124, annealed 2 wk at 800 C

(

cm

)

T(K)

0 10 20 30 40 50 60 700

5

10

15

20

P(GPa) 0 0.31 0.69 0.91 1.21

CeCoSi MT124, annealed 2 wk at 800 C sample 1

d/d

T (

cm

/K)

T(K)

2 4 6 8 10 12 140

5

10

15

20

P(GPa) 0 0.31 0.69 0.91 1.21

CeCoSi MT124, annealed 2 wk at 800 C sample 1

d/d

T (

cm

/K)

T(K)

Resistivity: pressures up to ~2 GPa. New SDW-like transition.

0 10 20 30 40 500

50

100

150

200

250

300

P P(GPa) 1.47 1.71 1.83 1.89 1.92 2.02

sample 1CeCoSi MT124, annealed 2 wk at 800 C

(

cm

)

T(K)0 10 20 30 40 50 60 70

-2

0

2

4

6

8

10

12

14

16

P(GPa) 1.47 1.71 1.83 1.89 1.92 2.02

CeCoSi MT124, annealed 2 wk at 800 C sample 1

d/d

T (

cm

/K)

T(K)

Resistivity: pressures ~3-4 GPa. Valence transition.

0 50 100 150 200 250 3000

50

100

150

200

250

300

350

sample 1CeCoSi MT124, annealed 2 wk at 800 C

(

cm

)

T(K)

P(GPa) 0 2.77 3.25 3.63 3.63 3.95 3.95 4.67 5.41 5.77

0 50 100 150 200 250 3000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Valence transition region

P(GPa) 3.0 3.25 3.63 3.95

CeCoSi MT124, annealed 2 wk at 800 C

d/d

T (

cm

/K)

T(K)

Resistivity: P-T diagram

0 1 2 3 40

10

20

30

40

50

CEP

QCP

dTV /dP ~ 400 K/GPa

CeCoSi

T (

K)

P(GPa)

Tn (K) Tm (K) Tv (K) cooling Tv(K) warming T(K) broad peak1 of drho/dT T(K) broad peak2 of drho/dT

0 1 2 3 4 5 60.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

CeCoSi

A (

cm

/Kn )

P(GPa)

0 1 2 3 4 5 61.0

1.5

2.0

2.5

3.0

III

III

CeCoSi

n

P(GPa)

1E-4

1E-3

0.01

0.1

1

A (

-cm

/Kn )

0

5

10

15

20

IV 0 (

cm)

Resistivity measurements at 2 GPa down to 0.1 KShow no signature of superconducrivity near QCP

(T) = 0+ ATn

AC-calorimetry and strain gauge: Possible structural transformation at P ~ 1 GPa. Valence transition at 4.5 GPa.

0 1 2 3 4 5 620

25

30

35

40

45

50

55

CeCoSi

R (

m)

30

0 K

P(GPa) LT

0 1 2 3 4 5 6

12.6

12.7

12.8

12.9

13.0

13.1

L/L0 ~0.7%

L/L0 ~1.8%

300 K

CeCoSi

Rhe

ater ()

P(GPa)

AC-calorimetry: data.

0 10 20 30 40 500

1

2

3

4

5

P(GPa) 0.35 0.65 1.02 1.16 1.24

CeCoSi + GW60/40

C/T

(J

/K2 )

T(K)

0 10 20 30 40 500

1

2

3

4

5

P(GPa) 1.51 1.71 1.82 2.0 2.04 2.14 2.56 3.0 3.62 5.0

CeCoSi + GW60/40

C/T

(J

/K2 )

T(K)

0 1 2 3 4 50

5

10

15

20

CeCoSi

(ar

b. u

nits

)

P(GPa)

The temperature of AFM transition related with Ce-sublattice does not change much at high pressure, but it splits into two transitions at modest pressure. At ~1.2 GPa the new magnetic transition appear at ~35 K probably related with Co-sublattice and Ce-related transition becomes very broad and is shifted to ~14 K. These big changes in magnetism of CeCoSi are most probably related with a structural transformation at 1.2 GPa. Magnetism is quencehed at ~2 Gpa in the manner of a QCP. The A coefficient of the T2 term in resistivity and the electronic specific heat coefficient diverges at 2 GPa. But the enhanced specific heat at 2-3 GPa shows the importance of critical magnetic fluctuations in this pressure range.

AC-calorimetry: P-T diagram.

0 1 20

10

20

30

40

broad C(T)anomaly

broad C(T) anomalywith small entropyshort rande correlations ?

structuralreconstruction

P-T diagram of CeCoSi by calorimetry

peaks of and A sharp drop of

= 0 + ATn

SDW ?

AFM

CeCoSi

T(K

)

P(GPa)

1 2 3 4 50

50

100

150

200

250

300

CeCoSi

T(K

)P(GPa)

Tn(K) peak1 Tn(K) peak2 Tsrc(K) broad peak Tm(K) Tv(K) Tv(K) rho

Very complex P-T diagram was found in CeCoSi - structural and valence transitions, two different magnetic transitions, quantum critical point for magnetism and critical end point for valence transition.The structural, valence and magnetic instabilities are probably originate from the effects of hybridization and interplay of Ce 4f and Co 3d-electrons.

First-order-like quantum phase transition in the itinerant ferromagnet CoS2

C. Utfeld et al., PRL 103 (2009) 226403

Below TC = 122 K CoS2 becomes a ferromagnet with high degree of spin polarization.

T. Goto et al., PRB 56 (1997) 14019

Magnetic measurements under pressure reveal metamagnetism and a transformation of a second-order transition to a wekly first-order one at P ~ 0.3-0.4 GPa.

Resistivity measurements of CoS2 are controversial: in a liquid pressure medium TC decreases faster at high pressure than in a solid medium and the resistive anomaly becomes sharper, whereas it broadens and disappear in a solid pressure medium. S. Yomo, J. Phys. Soc. Japan, 47 (1979) 1486

110 115 120 125

0.0

0.5

1.0

1.5

2.0

2.5

b)

ac(a

.u.)

Temperature (K)

110 115 120 125100

105

110

115

120

a)

(

cm

)

0 50 100 150 200

0

2

4

6

8

10

0 10 20 300

5

10

b)

ac (

a.u.

)

Temperature (K)

P(GPa) 0 1.22 2.34 3.39 3.88 4.24 4.54 4.78 4.92

0 50 100 150 2000

50

100

150

a)

(

cm

)

(

cm

)

Resistivity and magnetic ac-susceptibility of CoS2 at high pressure

Compressed helium pressure cell (pressure up to 0.9 Gpa)

Compressed liquid toroid-typeanvil pressure cell (P up to 6 GPa)

V.A. Sidorov et al., Phys. Rev. B, 83 (2011) 060412(R)

60 70 80 90 100 110 120 1300

1

2

3

4

60 70 80 90 100 110 120 130

-10

-5

0

5

b

a

4.24 3.88

0

1.22 GPa

2.343.39

CoS2

4.24 3.88 3.39

2.34

1.22 GPa

0

Cm

ag/T

(J

/K2 )

T(K)P

ha

se s

hift

(d

eg

)

0 50 100 150 200 250 3000

1

2

3

4

5

6

7

0 1 2 3 4 50,0

0,1

0,2

0,3

0,4

CoS2

1.22 GPa

TC CoS

2 TG GW60/40

C/T

(J

/K2 )

T(K)

S. Ogawa, J.Phys.Soc. Japan, 41 (1976) 462.

Sm

ag /

Rln

2

P(GPa)

Specific heat and magnetic entropy of CoS2 at high pressure

0 1 2 3 4 5 6 70

20

40

60

80

100

120

140

0.0 0.5 1.0 1.5 2.0105

110

115

120

125

CoS2

[7] [10] [15] [16]

Tra

nsiti

on te

mpe

ratu

re T

c (K

)

Pressure (GPa)

Pressure (GPa)

Tc(

K)

0 1 2 3 4 5 61.0

1.5

2.0

2.5

3.0

n

P(GPa)

0 1 2 3 4 5 60.00

0.01

0.02

A (

-cm

/Kn )

0 1 2 3 4 5 60.0

0.5

1.0

loading unloading

CoS2

0 (-

cm)

0 1 2 3 4 5 60.05

0.06

0.07

0.08

1.28 K17.5 mJ/mole-K2

C/T

(J

/K2 )

P-T diagram and nature of the quantum phase transition in CoS2

Three systems with quantum phase transitions were considered in this presentation:

CePt2In7 – a very close analog of CeRhIn5. The evolution of magneticentropy through the quantum critical point where one can see the smooth flow of the spin entropy from the magnetic to the superconducting channel gives evidence of the magnetic origin of superconductivity.

CeCoSi exhibits a diversity of ground states. The magnetic entropy decreases strongly on approaching the critical pressure (2 GPa) at which quantum critical phenomena usually associated with a QCP are observed. However the residual magnetic anomaly with progressively decreasing magnetic entropy is still visible up to much higher pressures (3 GPa) where the critical end point of the valence transition takes place at low tenperature. These complex phenomena are probably related with the development of magnetism in two different (Ce and Co) magnetic sublattices.

CoS2 exhibits a first-order like quantum phase transition from the ferromagnetic to the paramagnetic state. No quantum critical phenomena are observed and the magnetic entropy decreases to the negligibly small values on approaching the critical pressure. These observations indicate on the progressively increasing itinerancy and the delocalization of the magnetic moment in CoS2.

Thank you for your attention !

Basics of AC calorimetry in the ideal case

• If the heater is exited by oscillating power P(t)=P0(1-sint) then the oscillations of the sample temperature are related with the sample heat capacity (Sullivan and Siedel, 1968) by TAC = P0/C[1 + (1)-2 + (2)2]-1/2 = (P0/C)F() where 1 = C/K1 describes the thermal coupling to the bath and 2 describes the thermal coupling sample-heater

if (1)2 >> 1 and (2)2 << 1 then TAC = P0/C and F()≈1

F() has maximum value [1+2(2/ 1)]-1/2 at the optimal frequency 0=(12)-1/2, which is the best for AC calorimetry measurement. Frequency dependence of the product TAC is to be determined to find 0. It may vary with temperature (and pressure).

Appendix

AC calorimetry of Glycerol-water 60/40 at high pressure

• Frequency dependence of AC calorimetry signal at P=10 kbar

• The inverse of temperature oscillations (~C) vs T at P=10kbar

0 50 100 150 200 250 3000

1

2

3

4

9 Hz 15 Hz 31 Hz 51 Hz 102 Hz 205 Hz 835 Hz 1670 Hz

10 kbar

Glycerol-water 60/40

(fR

)-1 (

sec/V

)

T(K)

1 10 100 1000 10000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

T(K)

Glycerol-Water 60/40 at 10 kbar

fR /

fR m

ax

f (Hz)

298 156 75.5 51 25 16.2 9.1 3.95 1.1