Does antiferromagnetism become ferrimagnetism in an external field?

[fluidistic]

At first I was wondering whether antiferromagnetic materials exhibit magnetic hysteresis. From what I could read on wikipedia, I think they should, but for a very strange reason. Indeed, in the absence of any external $\vec B$ field, the magnetization of the 2 different sublattices have the same magnitude but opposite direction and so the net magnetization vanishes. However, when an external magnetic field is applied, the net magnetization stops to vanish because the 2 sublattices have different magnitude. So that, if I understand well, we fall into the case of ferrimagnetism. In other words antiferromagnetism would be a magnetic order valid when no external $\vec B$ field is applied. As soon as an external $\vec B$ field exists, the material will turn into a ferrimagnetic ordering.
I do not understand why this would be the case. My intuition tells me it's due to the coupling between the external $\vec B$ field and the magnetization of the 2 sublattices. Can someone give me a reference or quick mathematical exhibition to point me out how the magnetization of each sublattice changes with respect to the external applied $\vec B$ field?

 

[DrDu]

In an antiferromagnet, the sub-lattices will return to having the same magnetisation as before applying the magnetic field once it is switched off. In an antiferromagnet, the ions having anti-parallel spins are equivalent, whence their magnetism compensates. In a ferrimagnet, the sub-lattices correspond to ions on non-equivalent sites in a lattice, hence the magnetic moment will not vanish even if no field is applied.

 

[fluidistic]

In an antiferromagnet, the sub-lattices will return to having the same magnetisation as before applying the magnetic field once it is switched off.

Ok, so far so good. This is basically what I had understood in that antiferromagnetism has the same behavior than ferrimagnetism except when the external $\vec B$ field vanishes.

So, if I understand well, the hysteresis curve of an antiferromagnet is different than the ones of ferro and ferrimagnetic materials in that the curve passes at the origin (0 magnetization when there is 0 magnetic field applied), but everywhere else, hysteresis occurs. Is this correct?