In case of paramagnetic impurities (e.g. in an insulating substrate such as MgO) the paramagnetic contribution to the signal will be temperature dependent. In case you have to chose certain temperatures, you will need to measure that contribution at every temperature. In case you are free to choose, you may choose the temperature to have paramagnetic and diamagnetic contributions compensate each other. This may give you enhanced sensitivity for small sample magnetizations.

Measure the magnetic properties of the blank substrate first and then subtract such contributions from your film-substrate structure.

In case of paramagnetic impurities (e.g. in an insulating substrate such as MgO) the paramagnetic contribution to the signal will be temperature dependent. In case you have to chose certain temperatures, you will need to measure that contribution at every temperature. In case you are free to choose, you may choose the temperature to have paramagnetic and diamagnetic contributions compensate each other. This may give you enhanced sensitivity for small sample magnetizations.

thank you @ S.N. Piramanayagam....I know about these way to subtract substrate contribution. However, just eliminating the slope from the slope of blank substrate leads many times unrealistic output. Sometimes just subtracting slope of substrate leads to saturation even though system has property of non-saturation and sometimes even the contribution not eliminates completely as the slope remains negative. I have faced these problems many times. May anyone suggest relevant papers which describes substrate contribution and its elimination in detail.

thank you @Kai Fauth: I agree with you .this is the nice way. However, Many times we need to measure magnetization at low temperature where contribution from paramagnetic impurities enhances and in such scenario it become difficult to extract actual signal from film. Sometimes I faced trouble even to eliminate diamagnetic contribution from M-H loop. If I subtract slope of the film (film+substrate) from the M-H loop it gets saturation (will be alwayz for all sample without caring of the nature of the system whether it is saturating or non-saturating) and if I subtarct substrate slope then the diamagnetic contribution not eliminate completely as slope of the loop still remains somewhat negative.

@S.N. Piramanayagam: thank you again for your reply. If the sample saturates then there is no need to subtract substrate contribution as there is no need to go beyond the field where sample gets saturate. Possibly your second suggestion may work. thanks.

@SNP: if your 'unawareness' refers to my mentioning of paramagn/diamagn compensation, it was used, e.g., here: DOI:10.3762/bjnano.2.51.

@Pankaj P.: maybe you have done it all the right way. Just to recall: it's not about using some seemingly similar substrate of (nominally) same dimensions but THE same substrate. If that is impossible, measure many similar ones to gt an impression on the repeatability of the results. IMHO, stakes are high that you find considerable variations (depending on substrate materials, of course).

Are you sure to always use appropriate tools (made of appropriate materials, think of tweezers, e.g.) to handle your specimens. Are all people using the magnetometer dedicated to doing that? (I have learned about more than one spoiled magnetometer due to "misconduct" of some collaborators).

Otherwise it could also be that you have more or less serious problems with sample homogeneity and/or quality. In this case you will have to cross-check by other means, I guess.

@kai Fauth: thank you for your valuable informations. Possibly 'unawareness' mentioned by @SNP refers to my query quoted as "May anyone suggest relevant papers which describes substrate contribution and its elimination in detail".

@Pankaj Pandey (your second last comment): you possibly miss the point SNP is making: if you have the slope at saturation (where there should be none) then you have it everywhere (taking for granted that the substrate susceptibility is independent of field, i.e. given by a straight. this is not necessarily so with paramagnetic contribs. at low temperature!). This enables you correcting those parts in your M(H) curves where you have finite slopes.

It will depend, though on the feasability of knowing well the expected approach to saturation. Depending on what specimens you study, you never really saturate (i.e. Stoner-Wohlfarth - M(H) neither along nor perpendicular to uniaxial axis). In such cases you have to do some modelling on top, which usually comes along with new uncertainties. It may nevertheless prove better than doing nothing.

@PP again: oops, I missed an answer of yours: if you have to measure at low temperature, and have paramagnetic, field dependent (differential) susceptibility (i.e. not a straight line M(H) for the substrate) then I understand you feel being in trouble.

And there's not much you can do. The magnetometer can't tell the origin of the moment it's measuring.

(i) characterize each blank substrate down to lowest temperature befor using it for film growth

(ii) seek for better substrates (you may run into limitations here)

(iii) use different method for magnetic characterization, which does not measure the substrate contribution. Possibilities include

-a) magneto-optics (polar, longitudinal and transverse Kerr effects)

-b) X-ray magnetic circular dichroism (requires you to obtain beam time at a synchrotron radiation facility)

-c) Mößbauer effect in applied fields (works particularly well for iron)

Maybe others want to suggest yet other alternatives.

thank you @ Kai Fauth..I really missed that point by @S.N. Piramanayagam.So even after saturation if slope is negative we have to correct that contribution rather ignoring the field higher than saturation field.

I would say so, yes. It doesn't resolve the possible problem of nonlinear paramagnetic contribution(s), though!

Also, if the magnetic measurement at room temperature, we can subtract the blank substrate contribution from the film-substrate structure

A way ca be substracting substrate contribution by measuring first the substrate and then deposit the films, an then measure the substrate with the thin film. Take care of any contamination from sample handling. I hope it can be useful.

Some people prefer the procedure in the reverse order: first you measure the sample on substrate, then you remove the sample, say by etching or ion bombardment. This may require few attempts until the investigated material is really gone, nevertheless you are sure to record exactly the same substrate. However, one must be aware that magnetic properties of the sample under investigation may significantly depend on the presence of the substrate: lattice mismatch --> strains --> magnetostriction. Similarly, the chemical properties of the interface, as well as the disorder ther may be non-neglible. Not ideally flat substrate may also create the magnetic anisotropy in otherwise isotropic sample. Conclusion: the procedure makes sense for samples thick enough.