How does applying a critical magnetic field force ferromagnetic order in an anti-ferromagnetic material?

With antiferromagnetic materials, what happens when you apply an external magnetic field depends upon the direction the field is applied relative to the spin axis.

The response of a material to an external magnetic field is the magnetic susceptibility, $chi$. It is the proportionality constant between magnetization, M, the magnetic moment per unit volume, and the applied magnetic field. $$M=chi B$$ For an antiferromagnetic material, there are two fundamental directions to study: perpendicular to the spin axis and parallel to the spin axis.

Here is what $chi$ looks like for $MnF_2$ in both of these directions:

Kittel, in Introduction to Solid State Physics, reports that with a strong magnetic field applied in the parallel direction, the spin system will turn from the parallel orientation to the perpendicular orientation because that lowers the energy. This change happens discontinuously, not continuously. If the magnetic field is already pointing perpendicular to the spin axis, there is no lower energy configuration. NOTE: This is not a change to a ferromagnetic state!

But this paper: How to manipulate magnetic states of antiferromagnets DOES report on page 11 on the change from an AFM state to a FM state in FeRh films at 350K. This is called a Metamagnetic transition. (This term it seems generally refers any sudden change in magnetization with a small change in applied magnetic field.)

Here too is a report on single crystals of $UAu_{0.8}Sb_2$ also on a similar transition, but at much colder temperatures (34K). The metamagnetic transitions can also be induced by the application of a magnetic field. They see two transitions at 0.9 and 1.9T. A chart here gives relative strengths of magnets.

Sorry, I can't find a general reference on Metamagnetic transitions.