The exchange bias requires the presence of antiferromagnetic interface magnetization. In this sense the pinning layer (antiferromagnet) contributes with a small magnetic moment that adds to the moment of the exchange coupled ferromagnet and thus shifts the loop also along the magnetization axis in addition to the usually considered shift along the field axis. The higher the interface magnetization the larger the exchange bias field and the shift along the magnetization axis. Often, when the pinning layer is a true antiferromagnet, the latter shift is hard to observe. Check out A. Hochstrat, Ch. Binek, W. Kleemann, Phys. Rev. B 66, 092409 (2002).

thank you very much to both of you.

Binek  Sir, you told that for true AFM this effect is not observed. What does this true AFM means, the ideal AFM or what?

If we observe this exchange bias phenomenon and such vertical shift in bulk systems where no distinct FM/AFM interface is there but it contains both FM and AFM ordering, then how can we understand this phenomenon?

You probably have a disordered FM/AFM structure. Nevertheless, you have interfaces all over the sample, with a disordered geometry.

True AFM means that the pinning layer moments are never reversed during the loop and their contribution to the overall magnetization is always zero. Otherwise, there can be unbalanced magnetic moments which provide the vertical shift.

However, be carefull to Petracic comment

These hysteresis loop is from alloy containing several phases like NiAl and FeCor, CrFe and Cu rich phase. the hysteresis loop shows narrowing at the center followed by anomalous hysterisis loop at 300C. I am not able to find reason for this. could you please help me