Calorimetric Investigation under High Pressure

Shimizu-Group

M1 Shigeki TANAKA

F. Bouquet et al., Solid State Communications 113 (2000) 367-371

Contents Introduction

Specific HeatAC-Calorimetric MethodCeRu2Ge2 (heavy fermion compound)Specific Heat of Heavy Fermion CompoundsMotivation

Experimental Method Results & Discussion Summary My Study

Specific Heat

C = dQ/dT

heat capacity [C (J/K)]

• Specific heat shows characteristic behavior for various phase transitions !• observe phase transitions clearly

T T + dTthermometer

sampledQ

※ Heat capacity per unit mass is ‘specific heat’.

AC-Calorimetric MethodUnder pressure, specific heat measurement with adiabatic state is very difficult. ac-calorimetric method

1. give ac power P to the sample, T = T0 + |TAC|cos(t + )

2. Thermal amplitude : TAC = P0/(K + iC) ∝ Vth

3. 1 (cut off frequency : 1 = K/C)

TAC = P0/C

C, T

Sample

P = I2R,

I = I0[1 + cos (t/2)] T0

Bath

Vth

K

CeRu2Ge2 (heavy fermion compound) Previous work

Fig.1. Temperature dependence of the electrical resistivity of CeRu2Ge2 at selected pressures.

Fig.2. (T, P) phase diagram of the transition temperatures in CeRu2Ge2.

From electrical resistivity measurement, it’s known that CeRu2Ge2 shows two magnetic phase transitions (TC, TN) and an unclear phase transition (TL).

H. Wilhelm et al., Physical Review B 59, 3651 (1999)

Specific Heat of Heavy Fermion Compounds Specific Heat

• Normal metal

2/ ATTC : Electronic specific heat coefficientAT2 : Lattice specific heat

• Heavy fermion compounds

T2 (K2)

C/T

(m

J/K

2・

mol

)

K

In heavy fermion compounds, is much larger than normal metals.

Specific heat is a powerful tool to investigate physical properties of these compounds.

CeRu2Ge2

CexLa1-xCu6

log10T

C/T

(J/

K2・

mol

)

W. H. Lien et al., PHYSICAL REVIEW A-GENERAL PHYSICS 133 (1964) 1370

A. Sumiyama et al., J. Phys. Soc. Jpn. 55 (1986) 129411

Motivation

The purpose of this work is to measure the magnetic phase transitions of CeRu2Ge2 under pressure by AC-calorimetric measurement.

CeRu2Ge2 is a good candidate for testing the AC-calorimetric technique under high pressure.

Fig.2. (T, P) phase diagram of the transition temperatures in CeRu2Ge2.

Experimental Method Bridgman anvil

Thermal properties of the pressure transmitting medium determine the working conditions. (Tac=│P0/(K+iC)│)

H. Wilhelm, arXiv:cond-mat/0303457 1 21 (2003)

Lock-in amplifier

Pressure transmitting medium

(steatite : 3MgO ・ 4SiO2 ・H2O)

（圧力計）

I (/2)

V ()

VPb

Experimental MethodIn this work, two different ways of supplying the heat to the samples were tested.

Sample A (for low pressure (P ≤ 5 GPa))

• prevented electrically from the heater

• good thermal contact with the heater

Sample B (for high pressure (P ≥ 5 GPa))

• set apart on a Pb foil, electrically linked to the heater through a Au-wire

• No heating current passes through this sample.

• better hydrostatic pressure conditions than A

Results & Discussion 1~ 450 Hz

use frequencies between 500 and 4000 Hz.

At 0.7 GPa, cut-off frequency 1 is ~ 450 Hz.

Changing the temperature and pressure influences the cut-off frequencies!

Fig.3. Low pressure specific heat measurement compared

with that at ambient pressure.

Tac = P0/(C) (1)

relaxation techniqueAC-technique

The phase transitions are clearly visible and detected by AC-technique.

This technique is not the proper tool to measure a latent heat (first order phase transition).

Results & Discussion 2

Anomalies in C/T can be followed up to ~8 GPa for the first time!

Two magnetic phase transitions (TC, TN) and TL could be measured under pressure.

The anomalies in sample A tend to be broader at high pressure. (the deviation from hydrostatic pressure condition)

The anomalies in sample B tend to be smaller. (The heat capacity of the metallic foil contributes to the measured signal.)

BA

Fig.4. C/T vs. T and (T, P) phase diagram of CeRu2Ge2

Results & Discussion 3

TL is maximum at 5.0 GPa. (TL ~ 3.5 K)

The specific heat data confirms that this transition (at TL), also observed in other measurements, has thermodynamic origin and is a bulk property.

The nature of this transition is still unclear. (2000)

Fig.5. Specific heat of CeRu2Ge2 (sample B) at high pressure.

Summary

The specific heat of CeRu2Ge2 in the temperature range 1.5-11 K was measured up to 8 GPa with an AC-calorimetric method.

The (T, P) phase diagram is in excellent agreement with the previously presented one.

This demonstrates that AC-calorimetric method can be successfully adapted to high pressure experiments in a clamp pressure device, and opens a new route for thermodynamic measurements.

My Study (V3Si [A15 Compound])

A : VB : Si

A lattice distortion (Martensitic transition)

(cubic-to-tetragonal lattice transformation)

At atmospheric pressure,

Tc = 16.7 K

TM = 20.5 KL. R. Testardi, Reviews of Modern Physics, 47, 637 (1975)

My Study

From previous work,

TM decreases while Tc increases with applying pressure.

C.W.Chu, Physical Review Letters,32,766 (1974)

TM

Tc

V3Si

Investigate the relationship between TM and Tc

My Study

m

I (/2)

Lock-in-amplifier

V()

Manometer (ruby)

Pressure transmitting medium (NaCl)

Sample (V3Si)

AuFe (0.07 % at.)

Pt foilInsulation layer (c-BN + epoxy) Au

diamond anvil

Gasket (SUS310Si)

Measure martensitic transition (at TM) and superconducting transition (at Tc) by AC-calorimetric method.