In magnetic materials the demagnetization factor depends on the shape of your magnet, in thin films Nx=Ny=0 and Nz = 1 (S.I) or 4pi (CGS). Experimentally you can find the effective magnetization, which depends on the demagnetization factor, with FMR measurements. By varying the frequency used to promote resonance one can get experimental data for the Kittel equation.
For superconducting materials i am not sure if the same would apply. I am not and expert in the area but at a superconducting phase, the magnetic field would be expelled from inside the material (Meissner effect) thus no demagnetization should be expected.
For objects whose thickness is many times smaller than the dimensions in the other two dimensions of space (very thin films), the demagnetizing factors of the shape are described as respected José said. On the one hand, a superconductor from a formal point of view is an ideal diamagnet having magnetic susceptibility x = -1.
On the other hand, since the true value of the magnetic field inside it is compensated to zero, it makes no sense to talk about its magnetization, which according to the definition is equal to (described by the expression) M = xH.
However, it should be borne in mind that the magnetic field penetrates into superconductors to a fixed depth (so called London penetration depth), which in the case of metals is about 10 nm, which is comparable, but still less than the thickness of your film.
I'm not sure, but maybe some layer of your sample will work as a magnetic material.
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