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**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

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**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!

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**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

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**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.

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**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.

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**Primary And Secondary Coiles**

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

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**Sample Holder Heater wire Steal tube Hylum Element Sapphire plate**

Thermocouple Sample Element Fig. 4 Sample holder Sample Holder

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**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

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Photos

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Photos

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

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**Space Limit Heat can increase Temp. Applied Field Limitation**

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

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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

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