Thermal Expansion and Grüneisen parameter of

URh0.62Ru0.38Ge

Alessia GaspariniUniversity of Amsterdam

PCFES8, Prague 2006

Outline

• Motivation• Material -> URh0.62Ru0.38Ge• Experimental setup• Experimental results• Outlook

Coworkers• Nguyen Thanh Huy• Anne de Visser• Jacques Klaasse• Huang Yingkai University of Amsterdam

Quantum criticalityQuantum Critical Point (QCP) -> in system tuned to a Quantum Phase Transition (QPT) at T=0

pressure, magnetic field, dopingsystem properties at finite temperature

T exponent of Grüneisenratio in QPT

TSpS

TVc mp ∂∂∂∂−==Γ

//1β

The Grüneisen ratio diverges at the QCPZhu et al, PRL 2003

Theorical prediction for SDW-QCPs in quantum critical regime with d=3

13/2

3/1

)1log(

1log

−∝Γ

∝

∝

TT

TTc

T

cr

cr

crα

z = 3 FM

1

2/3

2/1

−−∝Γ

−∝

∝

T

Tc

T

cr

cr

crαz = 2 AFM CeIn3-xSnx

CeNi2Ge2

…

Grüneisen parameter of CeCu6-xAux

0 1 2 3 40

20

40

60

80

100

x=0.1

x=0

CeCu6-xAux

Grü

neis

en ra

tio

T (K)de Visser

Theorical prediction for SDW-QCPs in quantum critical regime with d=3

13/2

3/1

)1log(

1log

−∝Γ

∝

∝

TT

TTc

T

cr

cr

crα

z = 3 FM

0.2 0.4 0.6 0.8 1T

-15

-10

-5

5

10Γ

Thermal expansion

pp TV

VTV

∂∂=

∂∂= 1lnβ

pTl

l ∂∂= 1α

volume

linear

ααααβ 3321 =++=

for cubic structures or isotropic solids (as polycrystals)

0 ,

,3 →+∝

Θ>>∝

TbTaT

TT D

ββ

URhGe• Orthorhombic structure• Ferromagnetism (TC=9.5 K) and

superconductivity (Ts=0.25 K) at patm (Aoki et al, Nature 413, 2001)

• Sommerfeld coefficient γ=160 mJ/mol K2

0

1

2

3

4

5

a-axis

T (K)

URhGe

α (1

0-6 K

-1)

0

1

2

3

4 TCb-axis

0 5 10 15

0

1

2

3

4c-axis

0.0 0.1 0.2 0.3 0.4 0.50

2

4

6

8

10

12

Magn.Res.

U(Rh1-xRux)Ge

T C (K

)

Ru concentration x

xcr= 0.38 Sakarya etal., 2003

Sample• Polycrystalline button URh0.62Ru0.38Ge

prepared by arc melting• Cut from sample used for specific heat• Plane-parallel shaped using spark erosion• Sample dimensions: 5 x 4 x 4 mm3

z

yx

Experimental setup• OI 3He refrigerator

(Tbase=250mK)

• Three terminal parallel-plate capacitancedilatometer

• Capacitance bridge (sensitivity 10-7 pF)

dAC r 0εε=

Dilatometer

Sample (here Cu l=5.000 mm)

Lower plate

Upper plate

Sample platform

The cell was made in the WZI with OFHC copper

spacers 64 µm

de Visser, PhD thesis 1986

Dilatometer

sample

spring

5 10 15 20THKL

-5×10-8

5×10-8

1×10-7

1.5 ×10-7

2×10-7

2.5 ×10-7

3×10-7

αHK−1L

)(11)( TTd

LTd

LT Cu

Cucellssamplecellss αα +⎟

⎠⎞

⎜⎝⎛

∆∆+⎟

⎠⎞

⎜⎝⎛

∆∆−=

++

~10-7 K-1

Kroeger and Swenson, J. Appl.Phys., Vol 48 (march 1977)

∑>

=0 ,

)(oddn

nnTATα

KTK 20 2 ≤≤

We consider different contributions:

0 5 10 15 20

-14

-12

-10

-8

-6

-4

-2

0

2

∆d/∆

T (Å

/K)

T (K)

Cell calibration curve

0/

2/

121 yeAeA

Td tTtT ++=

∆∆ −−ce

ll ef

fect

bec

omes

big

ger

at lo

w te

mpe

ratu

re

Comparison with measurement

0 5 10 15 20

0

2

4

6

8

10

∆d/∆

T (Å

/K)

T (K)

sample cell

URh0.62Ru0.38Ge

Experimental resultsy

x

z

0 7 14 21

0

5

10

α (1

0-7K-1

)

T (K)

x y z

URh0.62Ru0.38Ge

Experimental results

1 100

1

2

3

4

5

61 10

0.10

0.15

0.20

0.25

0.30

0.35β/

T (1

0-7K-2

)

T (K)

C/T

(J/m

olU K

-2)

URh0.62Ru0.38Ge

Grüneisen ratio

1 100

1

2

3

4

5

6

Γ

T (K)

URh0.62Ru0.38Ge

Summary• We measured the thermal expansion of

polycrystalline URh0.62Ru0.38Ge• We obtained β by averaging over 3 directions• Relatively small thermal expansion for a

correlated metal• β does not follow T1/3 dependence as predicted

by the theory for itinerant FM QCP• Grüneisen ratio is not diverging down to 1 K

Outlook

• Improvement of dilatometer below 1 K (reduce the cell effect)

• Experiment on single crystals(anisotropy)

• Follow the FM contribution as functionof Ru content