1. Design of ac susceptometer using closed cycle helium cryostat
N. Alzayed
Department of Physics and Astronomy
King Saud University
Riyadh, Saudi Arabia
Parts of this presentation were written by Sue Kilcoyne
Department of Physics and Astronomy,
University of Leeds, Leeds LS2 9JT

2. Why use AC susceptibility ?
ac susceptibility was originally developed for thermometry at sub-K temperatures
It is now used extensively to study spin glass phenomena, superconducting transitions, vortex dynamics and critical current densities and to map magnetic phase diagrams:
it is a very simple technique
Susceptibility is measured directly
The applied field is very small, so it can be easily established
Dynamic magnetic and superconducting phenomena can be measured directly
usually over a frequency range of
10Hz to 100kHz
…..and it is cheap!

3. Non-linear complex AC susceptibility
Flux density
(Tesla)
Magnetic field
A.m-1
Volume magnetisation
A.m-1
where is the susceptibility
However in a sinusoidally modulated magnetic excitation field H(t) the volume magnetisation Mv will also be time dependent
So, if H(t) =HacIm(eiwt) = Hacsin(wt)
the time dependent volume magnetisation Mv(t) can be expanded as a Fourier series of the non-linear complex AC susceptibility
giving

4. Non-linear complex AC susceptibility
Here n=1 denotes the fundamental susceptibility, while n=2,3,4...etc are the higher order harmonics associated with non-linear terms in
The real and imaginary components of the susceptibility and are determined directly from Mv(t) through the relationships
is the fundamental ‘real’ component associated with the dispersive magnetic response
is the fundamental ‘imaginary’ component associated with absorptive or irreversible components which arise from energy dissipation within the sample.

5. Measuring the AC susceptibility
AC susceptibility is most conveniently measured using the mutual inductance principle
primary coil
dual phase lock-in amplifier
reference
secondary coils s1 s2
A sample is subject to a small alternating field ( A.m-1) produced by the primary coil 

The resulting emf induced in a secondary coil, s1, wound around the sample is detected and analysed
sample
Any background signal is nulled by an identical secondary, s2, connected in series opposition.

6. Primary And Secondary Coiles

7. Primary & Secondary
Fig. 3 Schematic diagram of (1) primary and (2) secondary coils. Dimensions in mm 1 2 18 14 9

8. Sample Holder Heater wire Steal tube Hylum Element Sapphire plate
Thermocouple
Sample
Element
Fig. 4 Sample holder
Sample Holder

9. suceptometer Sample tube Wilson seal Quartz tube Gate valve
Vacuum pump
Vacuum Sealing
Secondary
Primary
sample
Secondary coil
Double walled sample well
To the Cold Head and vac-uum syst-em
19 mm
32 mm
Fig. 2 Schematic diagram of ac susceptometer inside the sample well of cryocooler.
He gas
Sample holder
suceptometer

10. Photos

11. Photos

12. Design Advantages
No Eddy Current Higher Freq. Limit Metal can disturbe Uniformity of Field

13. Space Limit Heat can increase Temp. Applied Field Limitation
Design Disadvantages
Space Limit Heat can increase Temp. Applied Field Limitation

14. Conclusion
We have discussed the design aspect of the low cost ac susceptometer using closed cycle helium cryostat. The limitation of measurement of χ at higher frequency due to eddy current problem has been solved in placing the coils assembly inside the sample well. The main feature is that the coils are kept at 10 K and sample's temperature is varied independently