Calorimetric Investigation under High Pressure

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 • CeRu2Ge2 (heavy fermion compound) • Specific Heat of Heavy Fermion Compounds • Motivation • Experimental Method • Results & Discussion • Summary • My Study

3. Specific Heat • heat capacity [C(J/K)] ※ Heat capacity per unit mass is ‘specific heat’. C = dQ/dT dQ sample thermometer T T +dT • Specific heat shows characteristic behavior for various phase transitions ! • observe phase transitions clearly

4. Under pressure, specific heat measurement with adiabatic state is very difficult. ac-calorimetric method P = I2R, I = I0[1 + cos (wt/2)] K T0 Bath C, T Sample Vth AC-Calorimetric Method • give ac power Pto the sample,T = T0 + |TAC|cos(wt + f) • Thermal amplitude : TAC = P0/(K + iwC) ∝ Vth • w w1 (cut off frequency : w1 = K/C) • TAC = P0/wC

5. CeRu2Ge2 (heavy fermion compound) • Previous work Fig.2. (T, P) phase diagram of the transition temperatures in CeRu2Ge2. Fig.1. Temperature dependence of the electrical resistivity of CeRu2Ge2at selected pressures. 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)

6. Specific Heat of Heavy Fermion Compounds • Specific Heat • Heavy fermion compounds • Normal metal A. Sumiyama et al., J. Phys. Soc. Jpn. 55 (1986) 129411 W. H. Lien et al., PHYSICAL REVIEW A-GENERAL PHYSICS 133 (1964) 1370 CexLa1-xCu6 CeRu2Ge2 K C/T (J/K2・mol) C/T (mJ/K2・mol) T2(K2) log10T g : Electronic specific heat coefficient AT2 : Lattice specific heat In heavy fermion compounds, g is much larger than normal metals. Specific heat is a powerful tool to investigate physical properties of these compounds.

7. 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.

8. Experimental Method • Bridgman anvil I(w/2) （圧力計） Pressure transmitting medium (steatite : 3MgO・4SiO2・H2O) VPb Lock-in amplifier V(w) H. Wilhelm, arXiv:cond-mat/0303457 1 21 (2003) Thermal properties of the pressure transmitting medium determine the working conditions. (Tac=│P0/(K+iCw)│)

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. ~ 450 Hz Results & Discussion 1 use frequencies between 500 and 4000 Hz. At 0.7 GPa, cut-off frequency w1 is ~ 450 Hz. Changing the temperature and pressure influences the cut-off frequencies! Tac = P0/(Cw) (w  w1) Fig.3. Low pressure specific heat measurement compared with that at ambient pressure. 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 (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.) A B Fig.4. C/T vs. T and (T, P) phase diagram of CeRu2Ge2

12. 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.

13. 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.

14. My Study(V3Si [A15 Compound]) A : V B : Si • A lattice distortion (Martensitic transition) (cubic-to-tetragonal lattice transformation) • At atmospheric pressure, Tc= 16.7 K TM = 20.5 K L. R. Testardi, Reviews of Modern Physics, 47, 637 (1975)

15. V3Si My Study TM From previous work, TMdecreases while Tcincreases with applying pressure. Tc Investigate the relationship between TM and Tc C.W.Chu, Physical Review Letters,32,766 (1974)

16. diamond anvil 100 mm My Study Pt foil Insulation layer (c-BN + epoxy) Au AuFe (0.07 % at.) Gasket (SUS310Si) Sample (V3Si) Pressure transmitting medium (NaCl) Manometer (ruby) Lock-in-amplifier I (w/2) Measure martensitic transition (at TM) and superconducting transition (at Tc) by AC-calorimetric method. V(w)