Design of ac susceptometer using closed cycle

helium cryostat

N. Alzayed

Department of Physics and AstronomyKing Saud UniversityRiyadh, Saudi Arabia

Parts of this presentation were written by Sue KilcoyneDepartment of Physics and Astronomy,

University of Leeds, Leeds LS2 9JT

Why use AC susceptibility?

…..and it is cheap!

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

Non-linear complex AC susceptibility)MH(B Vo

Flux density(Tesla)

Magnetic fieldA.m-1

Volume magnetisationA.m-1

)1(Ho

HMVwhere 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

nnn igiving

)e(H)t(M tinn

1nacv

Im

1nnnac )tncos()tnsin(H

Non-linear complex AC susceptibility

The real and imaginary components of the susceptibility and are determined directly from Mv(t) through the relationships

n n

)t(d)tnsin()t(MH1 2

0v

acn

)t(d)tncos()t(MH1 2

0v

acn

1n is the fundamental ‘real’ component associated with the dispersive magnetic response

1n is the fundamental ‘imaginary’ component associated with absorptive or irreversible components which arise from energy dissipation within the sample.

1nnnacv )tncos()tnsin(H)t(M

Here n=1 denotes the fundamental susceptibility, while n=2,3,4...etc are the higher order harmonics associated with non-linear terms in

Measuring the AC susceptibilityAC susceptibility is most conveniently measured using the mutual inductance principle

dual phase lock-in amplifier

reference

prim

ary

coil

seco

ndar

y co

ils

s1

s2

sample

A sample is subject to a small alternating field (10-100 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

Any background signal is nulled by an identical secondary, s2, connected in series opposition.

Primary And Secondary Coiles

Primary & Secondary

Fig. 3 Schematic diagram of (1) primary and (2) secondary coils. Dimensions in mm

1 2

18

14 9

14

Sample Holder

Heater wire

Steal tube

Hylum tube

Sapphire plate

Thermocouple

Sample

Heater Element

Fig. 4 Sample holder

Sample tubeWilson seal

Quartz tube

Gate valve

Vacuum pump

Vacuum Sealing

Vacuum pump

Gate valve

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

Photos

Photos

Design Advantages

•No Eddy CurrentHigher Freq. LimitMetal can disturbe Uniformity of Field

Design Disadvantages

•Space LimitHeat can increase Temp.Applied Field Limitation

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