It seems that your sample is paramagnetic and shows non-linear like behavior (hysteresis) at low field. What is your measuring temperature? There is no way to subtract paramagnetic contribution from M-H data. You can show the ferromagnetic contribution by cutting down the field axis range. However, a low temperature M-H or M-T will help in detail understanding the magnetic nature of your sample.

It depends on if your paramagnetic contribution comes from your sample or is external (e.g., substrate, sample holder, any supporting material, etc.). If from external sources, you should measure that material in a pure sample, under the same conditions, and substract the emu/g (or whatever units) from your sample. If intrinsic of your sample, you would need to identify the source (by phase analysis with RXD or TEM, for example).

Hope this helps.

Usually the samples saturated at 1T using Squid. There is no need to apply 5T which will effect the sensitivity of the system. You can subtract the paramagnetic contribution using origin lab software. As you know the paramagnetic contribution is linear, therefore, open Origin lab and from the top -> Analysis -> Data Manipulation ->  subtract straight line. Then click on the straight line on the graph at the beginning of the line and at the end for example at 2T and 5T. this will remove the paramagnetic contribution. This will give you a fast view about your data. More accurate follow G. F. Goya advice.

1. You didn't tell us what is your material.  Majority of magnetic materials are already saturated in fields between 1 and 2T (at room temperature). Some other, certainly not usual ferromagnets (ferrimagntes, helical magnets, etc.),  saturate only above 50T, exhibiting a more or less single line (unique) part of magetic hysteresis between ~2 and ~20T.

2. Maybe what you measure is not M vs. field but rather B vs. field?  If this is the case then advice given by Marzook S. Alshammari is applicable.  In this case the general equation B=\mu_0*H + M applies and what you observe is strictly linear term proportional to the external field.

3. Nothing of the above.  If so, then what you observe is the approach to saturation rather than paramagnetic component.  In this case we would rather talk about the irreversible part of magnetic hysteresis loop, not about paramagnetic component.  This one, in turn, is usually modeled as the Langevin curve, exactly like for paramagnets.  Is it correct?   Nobody knows for sure.  Takacs proves that such a component must exist but presents no formula (anyway, his model deals with hyperbolic tangent-type curves).  Others treat it rather like an "educated guess" (Jiles-Atherton model of magnetic hysteresis).  Unfortunately there are two ways to get this curve experimentally, both time consuming and thus rarely tried, and they produce different results ...

Yes, according to the M-H loop description given, this type of paramagnetic contribution can be subtracted from the samples by linearly fitting the M-H curves at higher fields which will give the paramagnetic susceptibility.

Subtraction of the magnetic moment related to this paramagnetic susceptibility from the total observed magnetic moments will give the saturated ferromagnetic curves.

Here are the equations.

M(Total) = M(PM) + M(FM) = X(PM)*H + X (FM)*H       X is Susceptibility

So M(FM) = X(FM)*H = M(Total) - X(PM)*H

But, this kind of behavior mostly appear in the samples (or nanoparticles) which are either antiferromagnetic or paramagnetic in nature but their uncompensated surface spins can give a net non zero magnetic moment which can align in field and Total magnetism of the sample is a convolution of paramagnetic + weakly ferromagnetic response (loop at lower fields and linear at higher fields). As the samples are weakly ferromagnetic, the paramagnetic contribution dominates at higher fields.

But as already answered, usual ferromagnets should saturate up to 2 Tesla, so you need to further confirm the magnetic nature of your samples. 

More information is needed concerning the range of applied field and in which range of field the linear behavior of the magnetization was observed. If the material contains a significant paramagnetic phase in addition to the ferro- (or ferri-) magnetic component, separation of the two contributions can be achieved by the method proposed by Marzook Alshammary if the ferromagnetic phase is a soft magnetic material (for example, if it saturates well below ~ 5 kOe in measurements carried out in applied fields up to 10 kOe). If the linear behavior was observed at significantly higher fields (> 50 kOe for example), one should be careful that the approach to saturation behavior in that range could contain a linear contribution arising from the forced magnetic magnetization term (the last term in the LAS M = Ms (1 – A/H – B/H2) + χH)). In this case the linear part is due to the increase in the spontaneous magnetization of the magnetic domains of the material rather than due to the presence of a paramagnetic phase, and the four contributions in the LAS (The spontaneous magnetization, the contribution of the inclusions/microstress, the magnetocrystalline anisotropy contribution, and the forced magnetization term, respectively) can be obtained by fitting the magnetization data with a polynomial in accordance with the LAS.  Also, one should know that the inclusion/microstress term is applicable over a limited field range, and other forms of the polynomial were suggested (see Cullity, Introduction to Magnetic Materials, Wiley, Hoboken, NJ, 2009).  

You can use theoretical formula and use it to fit your experimental data. That will show you PM/AFM as well as FM content in you data. Use this link to find the formula

S. Duhalde et al., PHYSICAL REVIEW B 72, 161313R (2005)

Thank you all