Antiferromagnetism in MnO and MnF2

MnO:

Manganese oxide is a prototypical antiferromagnetic material. It has the NaCl structure consisting of two interpenetrating face-centered cubic structures, one occupied by the Mn2+  ions and the other by the O2-  ions. The Mn2+  ions carry magnetic moments whose directions lie in (111) planes, and in the fully ordered state all moments in a given (111) plane are lined up in the same direction while the moments in adjacent (111) planes are in the opposite direction.

The interaction between a moment of one Mn2+  ion and the nearest Mn2+  neighbors on adjacent Mn2+  planes is such as to give a lower energy for antiparallel alignment. Note that this interaction is equivalent to a negative exchange energy that acts through the Mn  nearest neighbor O  ions. The existence of the O2- ions can be ignored when visualizing the geometry of the magnetic interactions.
An Mn2+  ion on a given (111) plane in the Mn2+  face-centered cubic structure has six Mn2+  neighbors in its own plane and six more on neighboring Mn2+  planes.


MnF2:

In MnF2, the Mn2+  ions are at the sites of a body-centered cubic structure embedded in the rutile structure of the salt. The body-centered cubic structure consists of two interpenetrating simple cubic sublattices, each of which is ferromagnetic when fully ordered. The ordering on these sublattices is opposite to each other, so the crystal is antiferromagnetic. In this case, the interactions of the ions that are nearest neighbors are antiferromagnetic, and the ferromagnetic ordering is the result of next nearest neighbor interactions.

Within each of the two equivalent sublattices, labeled A and B, there are ferromagnetic interactions between each ion and za neighbors, while across sublattices there are antiferromagnetic interactions between an ion and zb neighbors. In the mean field approach, the magnetic moment on each ion is
subject to an internal field that has two components, one arising from interactions with moments on its own sublattice and the other from interactions on the other sublattice.

Reference:  Statistical Mechanics of Solids

http://book4you.org/dl/495262/d745b4