Should the law of approach be weighted with the same behavior at the moment of fitting the M-H loop in the case of MNPs?

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A. A. Timopheev

I think that thermal fluctuations of the magnetic moment orientation (superparamagnetism), which will be depedendent also on magnetic field, should be taken into account and it is desirable to have that as a separate term in the Law of approach (it will have not only the field but the temperature also ~ H/T).

Kai Fauth

In order to have expectations for a and b it is useful to go and find equations that are built from models and have 1/H and 1/H^2 terms. I recall that one of Chris Binns (many :-) articles on MNP assemblies provided a nice example.

In the simplest case one of the terms is due to thermal excitations and the other one could be due e.g. to the distribution of easy axes.

A finite high field slope can have various reasons and it is therefore also difficult to provide you with any expected value range for chi.