Heat capacity measurements in high magnetic fields

Scott C. Riggs, J. B. Betts, A. Migliori, F.F.Balakirev National High Magnetic Field laboratory @ Tallahassee & Los Alamos National Laboratory

C (H=0) = γ T + βT3

Specific heat – why?

Most fundamental thermodynamic quantity.

Gives the density of states:

Electronic component:

In a metal:

Outline

• Heat capacity measurement methods • Cryogenics and probes • Making a measurement/taking the data • High magnetic field issues • Some results • Future work

Methods we use to measure heat capacity. • Classic Relaxation Calorimetry • Dual Slope relaxation Calorimetery • AC Calorimetry • Differential Scanning Calorimetry

The same calorimeter setup can be used for 3 methods

Heater

Thermometer

Weak thermal link Temperature controlled block

Sample platform

With integral heater and thermometer

Sample Thermometer (Cernox) NiCr Heater

NiCr leads Silver epoxy contacts

Sapphire platform

1. Measure platform temperature with zero heat applied.

2. Turn on platform heater.

3. Allow platform temperature to relax exponentially to new stable temperature.

4. Turn off platform heater

5. Allow platform temperature to relax exponentially to initial stable temperature.

Cp = κ * τ = P/ΔT * τ = IV/ΔT * τ

Classic relaxation method

Cons. • High temperature stability of block required • Needs exponential fit • Stable magnetic field during measurement • Long time to take measurement

Pros. • Simple method • Real units of heat capacity • Easy to implement

Classic relaxation method – tau 2 issues

Heater

Thermometer

Weak thermal link Temperature controlled block

Sample platform

With integral heater and thermometer

Sample

Strong or comparable thermal link

1. Measure platform temperature with zero heat applied.

2. Turn on platform heater.

3. Allow platform temperature to relax exponentially to new temperature.

4. Turn off platform heater

5. 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)

Dual slope relaxation method

Cons. • High temperature stability of block required • Stable magnetic field during measurement • Both warming & cooling curves needed

Cryogenics

• To measure heat capacity with small errors using any 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

Temperature control & taking the data

• Conventional hardware temperature control.

• LabView software temperature control

Current resistor

Platform

Thermometer Transformer

Platform

Heater

I

V

Heat capacity platform

Lockin Amplifier

+

- 1KHz – 5KHz

• Lockin limited to 512Hz measurement • Internal time constants cause problems with fitting data • Noise from large GPIB data transfers

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

Real experimental set-up – with experimenter

In Cell 12 – 36T Resistive magnet

In Office – Second Floor

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.

Taking the data with the digital lockin

Second channel used to record heater voltage

Taking the data with the digital lockin

Addenda Measurements.

0 10 20 30 40 500

50

100

150

200

250

300

350

400

450

500

C (µ

J/K)

Temperature (K)

Addenda Comparison between PPMS and NHMFL Calorimeter

PPMS

NHMFL

• Area of NHMFL platform is 4 times larger than PPMS

• Large-area, insulating nano material samples easily mounted

• At 50K addenda are < ½ of a typical PPMS setup

• Only useful up to 50K because of small thermometer dR/dT

Heat capacity in high magnetic fields.

• Calorimeter Design • Calibration • Cryogenics • Electronics and software • Calorimeter Comparisons

Old School Calorimeter

• Basic Calorimeter o Thermometer o Heater o Platform

• Sapphire platform • Cernox™ Thermometer

evaporated directly onto the platform

• NiCr Heater evaporated directly onto the platform

• Manganin leads used also for thermal contact to the block

2nd generation design of the calorimeter.

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

• Sapphire platform cut down to reduce addenda

• Cernox™ Thermometer contact traces changed to reduce loop area

• Twisted pair leads used to reduce loop area

2nd generation design of the calorimeter.

Magnetic Field Calibrations

0 10 20 30 40 50

-0.20

-0.15

-0.10

-0.05

0.00

∆R/R

Magnetic Field (T)

Magnetoresistance of platform thermometer

500mK

4K

17K Magnetoresistance of the platform thermometer was measured in a 50T pulsed magnet at the NHMFL Los Alamos.

Classic relaxation method…. RESISTANCE IS TEMPERATURE!

R

Cp = IV/ΔT * τ = IV/ΔR * τ

Pulsing the magnet

Process • Get data at fixed

temperature

• Build a temperature array

• That’s it.

0 10 20 30 40 50150

200

250

300

350

400

450

500

550

600

650

R (O

hms)

Field (T)

20K

7.5K

4K5K

3.2K

1K0.7K

*Important* - Know your temperature ranges

• Log-log scale

• Polynomial fit

o More weight on low temp data

1 10 100

100

1000

10000

B=20T 4th order fit

R (Ω

)

Temp (K)

What we’ve been able to achieve

• New calorimeter design – low addenda, good thermal contact

• Properly calibrate for high magnetic fields • Cryogenics • Grounding • Vibration isolation • New electronics

0 1 2 3 4

Tem

pera

ture

Time (s)

6T (SC magnet Hmax=16 T) 45T (Hybrid magnet)

YBCO x=6.55

28 30 32 34 36 38 40 42 44 4616

18

20

22

24

26

28

30

Magnet sweep up (T=1K) Magnet sweep down

C (m

J m

ol-1

K-1)

Magnetic Field (tesla)

Each point in the field sweeps below is determined over one cycle

High Magnetic Fields - YBCO

Sm1111 heat capacity data

C = Celectronic + Cphonon + Cmag + Cnuclear + Cd-wave + Cosc + Cvortex

C (H=0) = γ T + βT3

C = Celectronic + Cphonon + Cmag + Cnuclear + Cd-wave + Cosc

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 lock-in techniques greatly enhance the capability.

• 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.

Dive right in!