1. Calorimetric Investigation under High Pressure Shimizu-Group M1 Shigeki TANAKA F. Bouquet et al., Solid State Communications 113 (2000) 367-371

2. Contents Introduction  Specific Heat  AC-Calorimetric Method  CeRu 2 Ge 2 (heavy fermion compound)  Specific Heat of Heavy Fermion Compounds  Motivation Experimental Method Results & Discussion Summary My Study

3. 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 + dT thermometer sample dQdQ ※ Heat capacity per unit mass is ‘specific heat’.

4. AC-Calorimetric Method Under pressure, specific heat measurement with adiabatic state is very difficult. ac-calorimetric method 1. give ac power P to the sample, T = T 0 + |T AC |cos(  t +  ) 2. Thermal amplitude : T AC = P 0 /(K + i  C) ∝ V th 3.    1 (cut off frequency :  1 = K/C) T AC = P 0 /  C C, T Sample P = I 2 R, I = I 0 [1 + cos (  t/2)] T 0 Bath V th K

5. CeRu 2 Ge 2 (heavy fermion compound)  Previous work Fig.1. Temperature dependence of the electrical resistivity of CeRu 2 Ge 2 at selected pressures. Fig.2. (T, P) phase diagram of the transition temperatures in CeRu 2 Ge 2. From electrical resistivity measurement, it’s known that CeRu 2 Ge 2 shows two magnetic phase transitions (T C, T N ) and an unclear phase transition (T L ). H. Wilhelm et al., Physical Review B 59, 3651 (1999)

6. Specific Heat of Heavy Fermion Compounds  Specific Heat Normal metal  : Electronic specific heat coefficient AT 2 : Lattice specific heat Heavy fermion compounds T 2 (K 2 ) C/T (mJ/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. CeRu 2 Ge 2 Ce x La 1-x Cu 6 log 10 T C/T (J/K 2 ・ 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

7. Motivation The purpose of this work is to measure the magnetic phase transitions of CeRu 2 Ge 2 under pressure by AC-calorimetric measurement. CeRu 2 Ge 2 is a good candidate for testing the AC-calorimetric technique under high pressure. Fig.2. (T, P) phase diagram of the transition temperatures in CeRu 2 Ge 2.

8. Experimental Method  Bridgman anvil Thermal properties of the pressure transmitting medium determine the working conditions. ( T ac =│P 0 /(K+iC  )│ ) H. Wilhelm, arXiv:cond-mat/0303457 1 21 (2003) Lock-in amplifier Pressure transmitting medium (steatite : 3MgO ・ 4SiO 2 ・ H 2 O) （圧力 計） I (  /2) V ()V () V Pb

9. Experimental Method In 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

10. 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. T ac = P 0 /(C  ) (  1 ) relaxation technique AC-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).

11. Results & Discussion 2 Anomalies in C/T can be followed up to ~8 GPa for the first time! Two magnetic phase transitions (T C, T N ) and T L 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.) B A Fig.4. C/T vs. T and (T, P) phase diagram of CeRu 2 Ge 2

12. Results & Discussion 3 T L is maximum at 5.0 GPa. (T L ~ 3.5 K) The specific heat data confirms that this transition (at T L ), 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 CeRu 2 Ge 2 (sample B) at high pressure.

13. Summary The specific heat of CeRu 2 Ge 2 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.

14. My Study (V 3 Si [A15 Compound]) A : V B : Si A lattice distortion (Martensitic transition) (cubic-to-tetragonal lattice transformation) At atmospheric pressure, T c = 16.7 K T M = 20.5 K L. R. Testardi, Reviews of Modern Physics, 47, 637 (1975)

15. My Study From previous work, T M decreases while T c increases with applying pressure. C.W.Chu, Physical Review Letters,32,766 (1974) TMTM TcTc V 3 Si Investigate the relationship between T M and T c

16. My Study  m I (  /2) Lock-in- amplifier V(  ) Manometer (ruby) Pressure transmitting medium (NaCl) Sample (V 3 Si) AuFe (0.07 % at.) Pt foil Insulation layer (c-BN + epoxy) Au diamond anvil Gasket (SUS310Si) Measure martensitic transition (at T M ) and superconducting transition (at T c ) by AC-calorimetric method.