The ferromagnetic exchange stiffness constant A is one of the most important parameters in micromagnetics. I know it can be measured in FMR experiments but is it possible to determine it from magnetisation or magnetic susceptibility data?
As a bonus, it would be great if the temperature dependence of A could be measured.
You can calculate by temperature dependent saturated magnetization
The realtion of Bloch's law (Js(T,0) = Js0(1-(T/T0)3/2)
here, T0 = ((Ms0/0.117muB)2/3Dsp/kB
and A(T) = Ms(T,0)Dsp/(2gmuB)
With these relations A(t) can be obtained.
A(T)=MS(T,0)Dsp/(2gmuB) = MS(T,0)T0/(2gmuB)*(0.117muB/Ms0)2/3
It is explained well in Book of Micromagnetism and the Microstructure of Ferromagnetic Solids by Helmut Kronmueller and Manfred Faehnle and Journal of applied physics 108, 113910 (2010).
Indeed, the constant A can be determined from the measurements of spontaneous magnetization (under very weak field) and by applying the Bloch's law :
M(T)/Ms(0) =1-f (Qs)1/2 (kBT/2aA)3/2
where
f =0.0587 (*)
C. Kittel, Introduction to Solid State Physics, 6th ed. Wiley, New York, 1986
Q is the number of lattice points per unit cell ( Q = 4 for fcc lattices) and a the lattice
parameter,
and s is spin quantum number which is given by s= Ms(0)a3/Qg mB (**)
** R. Kimura and H. Nose , J. Phys. Soc. Jpn. 17 , 604 , 1962
By plotting the normalized spontaneous magnetization M(T)/Ms(0) vs T3/2, you can easily deduce A from the curve's slope.
example : for Ni films :A=0.82 10-6 erg/cm
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