How many times have you reproduced your finding?

This behavior was seen in 1000 and 10 kOe measurements of the sample. the two curves are pretty close by. Yet, i can zoom in and see that the ZFC curve is above the FC curve. While in all other graphs, i find the reverse.

By all the other graphs, i meant the graphs of other materials I looked up on the internet.

I would think you have to reveal more details about your specimens, before an educated answer can be given. So, you field cooled once in 1kOe, once in 10kOe, if I get you right. For both, there is a temperature regime in which M(ZFC,T)>M(FC,T) during warm-up. What is the field of warm-up?

How many times did you repeat each of the FC,ZFC cycles, is the level of reproduceability of each of the curves such that you can be certain to safely resolve the "minimal" difference between the different cases? How many independent samples of this type did show the same behavior?   (sorry for insisting...)

By ZFC and FC i mean the following_ 

ZFC - sample cooled to 2 K without the application of any field and then measurements were taken while heating from 2K to 300K with the application of a field of 1 kOe. 

FC - sample was cooled from 300 K to 2K with the application of a field of 1 kOe.

This is what was done to the sample i mentioned. I have attached the susceptibility graph for the same. I am not aware of FCW. Can you kindly elaborate on how it is performed?

This is the only set of data I possess. I could not repeat the measurements, hence, not sure about the reproducibility of the finding. 

Dear Kavya Mukundan,

in doing the experiment as you described it, you did not adhere to the standard protocols of FC/ZFC measurements (which advise you to do the warm-up run in a small applied field, 50 Oe or maybe 100 Oe, after either field or zero field cooling). Of course this only makes really sense if you specimen has significant remanence after field cooling. [One reason behind this is the following: especially for soft magnetic materials, applying as high a field as you did may place you way into the nonlinear part of the magnetization curve M(H). Then, your magnetometer output is no longer proportional to the (zero field) susceptibility, the quantity normally considered.]

And since you cannot make a statement on reproduceability (several measurements on one sample, and measurements on several samples) it is hard to tell whether your effect is really worth discussing. In our lab, reproducability and error analysis figure among the top priorities.

This said, what you see at low temperature does indeed look like a significant difference between the measurements. Repeating them would be necessary to exclude that the specimen has changed with time (making it only seem that the difference between the data originates from the cooling protocol).

This is all I can say at this time.

just to put another spanner in the works!. If your samples are rocks ( superpara etc) , spin glasses or softish ferromagnets you have to take Time eg magnetic viscosity into acount ... can be minutes to hours. So if you prepare in one way say  ZFC then apply a field  , even keeping H, T constant  M will creep in time.  If you change H and T after a particular prep.  you can , within reason ,get any result you wish  with time as an added variable.

So Take care with the temp. sweep rate . Better sit at one temp ( assumed constant to 0.1K !!! and record any variation of M with time . Fairly obviously the rate constants( they are not exp decays  rather log aprprox) diminish rapidly  towards the magnetic freezing temp.

Finally if sample is 2+ phases then again lots of weird things can happen..... and of course obey sod's law

Have you tried to measure ZFC and FC magnetization in low applied field?  for example 1 mT or 10 mT? Please do that and I believe you will get normal result.