Heat capacity measurements in high magnetic fields

1. Heat capacity measurements in high magnetic fields J. B. Betts, A. Migliori, S. Riggs, F.F.Balakirev National High Magnetic Field laboratory @ Tallahassee & Los Alamos National Laboratory

2. Outline • Heat capacity measurement methods • Cryogenics and probes • Taking the data • High magnetic field issues • Some results • Future work

3. Methods we use to measure heat capacity. • Classic Relaxation Calorimetry • Dual Slope relaxation Calorimetery • AC Calorimetry We use the same calorimeter setup for all three methods Weak thermal link Temperature controlled block Thermometer (Cernox) Sample NiCr Heater Heater Sapphire platform Thermometer NiCr leads Silver epoxy contacts Sample platform With integral heater and thermometer

4. Classic relaxation method • Measure platform temperature with zero heat applied. • Turn on platform heater. • Allow platform temperature to relax exponentially to new stable temperature. • Turn off platform heater • Allow platform temperature to relax exponentially to initial stable temperature. Cp = Tau * kappa Pros. • Simple method • Reasonable results • Easy to impliment Cons. • High temperature stability of block required • Needs exponential fit causing scatter in results • Stable magnetic field during measurement • Long time to take measurement

5. Dual slope relaxation method • Measure platform temperature with zero heat applied. • Turn on platform heater. • Allow platform temperature to relax exponentially to new temperature. • Turn off platform heater • Allow platform temperature to relax exponentially to initial temperature. Cp = Heater Power/(slope(W) – slope(C)) Pros. • Simple fitting routines to determine slopes • Excellent results • Relatively fast measurement • No need to wait for temperature stabilization • External influences cancel at slope(W) = slope(C) Cons. • High temperature stability of block required • Stable magnetic field during measurement • Both warming & cooling curves needed

6. AC method • Measure platform temperature with zero heat applied. • Turn on AC platform heater at f. • Allow platform temperature to relax exponentially to new temperature. • Measure AC temperature swing at 2f Cp = AC Heater Power/(2f(T[ac]) Cons. • High temperature stability of block required • Needs large DR/DT thermometer • Complicated measuring system • Suspect accuracy • Thermometer magneto resistance causes problems during field sweeps • Penetration depth issues Pros. • No fitting routines needed • Fast measurement (1Hz – 10Hz ) • Once temperature is stable magnetic filed can be swept

7. Cryogenics • To measure heat capacity with small errors using any of the three methods requires excellent block temperature stability. • Great care must be taken with wiring and grounding of all measurement leads • Sample is in a vacuum • Good heat sinking of leads is required to reach lowest temperatures • 100K – 300mk temperature range • Materials selected for maximum thermal conductivity and minimum eddy current heating

8. Temperature control & taking the data • Conventional hardware temperature control. • LabView software temperature control Lockin Amplifier Heat capacity platform + - 1KHz – 5KHz Current resistor Platform Thermometer Transformer V Platform Heater I • Lockin limited to 512Hz measurement • Internal time constants cause problems with fitting data • Noise from large GPIB data transfers

9. Taking the data AC Method + - 1KHz – 5KHz Current resistor Platform Thermometer Transformer + Platform Heater - 1Hz – 10Hz Current resistor • Lockin circuit produces RMS voltage needs to be converted to Pk – PK to give AC temperature fluctuation. • Problems with grounding issues and noise from GPIB transfers • Lockin time constants and averaging data issues

10. Taking the data with the digital lockin The hardware • Three independent synchronously locked outputs • Variable voltage sine wave • fixed voltage sine wave • Clock • Frequency of all three outputs can be varied in multiples of each other. • Onboard USB digitizer 8 channels • Data streams to computer continuously • Onboard Preamplifier with configurable settings

11. Taking the data with the digital lockin The software • Raw sine wave data streamed to computer • Raw data can be saved and operated on later • No fixed time constants • “On the fly” lockin processing implemented in LabView (2.5KHz max data rate 2 channels) • Labview modules can be used to meet individual circumstances.

12. Taking the data with the digital lockin Second channel used to record heater voltage

13. Digital lockin setup for AC calorimetry Variable sine out 5KHz Current resistor Platform Thermometer Transformer + Digitizer 50 Points/sine wave Clock 250KHz Thermometer RMS voltage Digital lockin Platform Heater - 5Hz 500 Points/sine wave Current resistor Thermometer 10Hz Pk–Pk voltage Digital lockin Fixed sine out

14. High magnetic field issues • Vibration of the platform in the magnetic field causes heating. • Open loop area of platform leads causes Bdot pickup on the measuring circuit. 8 small Manganin leads, large open loop area Good vibrational stability 4 small NiCr leads smaller open loop area Very good vibrational stability

15. Results Quantum oscillations in AC component of temperature for Bismuth at 3K Betts October 2008

16. Results YBCO Quantum oscillations in heat capacity Betts, Riggs, Harrison, Sebastian, Bonn

17. Future work and conclusions • Heat capacity can be measured with good accuracy and repeatability in very high magnetic fields, but great care is needed with the initial setup to avoid large scatter in the measurements. • Dual slope method is faster and has less scatter than the classic exponential fit relaxation method • Digital lockin techniques greatly enhance the capability. • AC method using the digital lockin looks promising but needs more work. • The development of the next generation thermometers with little or no magnetic field dependence will greatly improve our ability to measure heat capacity especially in sweeping magnetic fields. • Development of top loading sorbtion pumped cryogenics will allow faster sample turn around and lower base temperatures.