Yes it is just as we suspected.  There is plenty of precedence for your system as you likely know

J. Appl. Phys. 96, 3399 (2004); http://dx.doi.org/10.1063/1.1775045

 You have a large diamagnetic mass in your sample (the subtrate), Although there could be some weak metallic paramagnetic component as well.  The proper way to treat this would be to measure the substrate's magnetic response before you deposit your material and then apply (subtract) that data set as a diamagnetic correction to your data.  The lazy way to do this would be to determine the slope of a line that your data is skewed by and subtract that (for instance the slope near the left most part of your data).  That would give you a better idea of what you are looking at for now, but it is not certified advice.

William - More information is needed. What is the sample? is it a thin film? Bulk? Composition?....

Without knowing anything about the sample i see a strong diamagnetism (shown by the negative slope) with some ferromagnetic component (shown by the hysteresis around 0 field). The moment is very small and some drift could account for the splitting in the return field sweep.    Without more information not much more can be said.

I agree with Steven - more information is needed, but with the appropriate diamagnetic correction this would probably look like a typical hysteresis loop.  In that case, I am guessing that it is a low mass sample such as a thin film grown on a diamagnetic substrate.  I have seen data like this before in that context - but you actually know what the sample is!

Steven and Ryan, actually i have spin coated Bismuth Ferrite over Pt/Ti/SiO2/Si substrate and got this result...

Yes it is just as we suspected.  There is plenty of precedence for your system as you likely know

J. Appl. Phys. 96, 3399 (2004); http://dx.doi.org/10.1063/1.1775045

 You have a large diamagnetic mass in your sample (the subtrate), Although there could be some weak metallic paramagnetic component as well.  The proper way to treat this would be to measure the substrate's magnetic response before you deposit your material and then apply (subtract) that data set as a diamagnetic correction to your data.  The lazy way to do this would be to determine the slope of a line that your data is skewed by and subtract that (for instance the slope near the left most part of your data).  That would give you a better idea of what you are looking at for now, but it is not certified advice.

I suspect that the question is about why the curve has two diverging branches.  This will happen when temperature drift occurs during measurements.

Absolutely Marek My another question was that only i.e why the the curve splits into two without continuity?

After you cycle the field few times in a row, you should see the continuous curve, maybe consisting of many non-overlapping branches.  This could indeed be attributed to temperature drifts.  Not necessarily the temperature of the sample, maybe slowly changing temperature of measuring instrument (or magnet).  This should give you an idea of the true uncertainty of your results.

But after a second look I am a bit surprised to see the point (0,0) not located between both branches.  This suggests either some systematical error in your instrument or the presence of a quite hard (magnetically hard, in a sense of high coercivity field, Hc > 12 500 units) material present in the sample.  If the second possibility is at play, then the results will depend on earlier history of a sample, even when temperature stability is perfect.

I have had an similar result in a measurement, when the Gaussian probe was come loose. I recomment to check all components of your device.

First time I've seen such a curve and I do not know if it is well made. If so, then maybe something is wrong with the VSM.

It seems that your sample exhibits diamagnetism with some ferromagnetic component. The moment is very small and some drift could account for the splitting in the return field sweep.  However, the point (0,0) is not located between both branches.  This suggests some systematical error in your instrument. I recommend to check all components of your device.