If you are not familiar with it, I think you want to check out the Goodenough-Kanamori rule, see e.g.
http://www.scholarpedia.org/article/Goodenough-Kanamori_rule
Some can undergo Antiferromagnetic while the the others may undergo Ferromagnetic superexchange. This depends upon the type of interaction between the orbitals of two paramagnetic cations and the intervening diamagnetic anion.
So both Antiferromagnetic and Ferromagnetic Superexchange need separate discussion
[I] Superexchange describes the interaction between moments on ions too far apart to be connected by direct exchange, but coupled over a relatively long distance through a non-magnetic material( generally O^-2).
[II] Consider the interacting cations A&B and the intermediate O. It is generally assumed that the nature and the strength of interaction for a given pair of cations is a function primarily of the distance between AO and OB and the angle AOB. The closer the angle AOB to 180 degrees, the stronger will be the superexchange interaction. { in other cases, sp hybridof anions may be considered}
Both Antiferromagnetic and ferromagnetic superexchange are briefly explained as:
[III] ANTIFERROMAGNETIC SUPEREXCHANGE:{ See attached file ;Figure-I; MnO; Zoom-150-200 }
The idea can be illustrated by two Mn^2 ions[ t2g^3eg^2] and one intervening O^2-. The Mn^2 -- O2- —Mn^2 are arranged along the one axis, forming a 180 degree position[both eg orbitals undergo sigma interaction with pz]. There are two spins in the O^2- site (the up-spin state + and down-spin state − ). Because of the overlap of wave function , one of p electrons (with down-spin state − ) from the O^2- HOPS OVER to one of Mn^2 ions {LHS}. [We assume that a part of one electron hops]. Note that only the down-state electron of p-electrons can move to the Mn^2 site {LHS}. The remaining unpaired p electron on the O^2- site then enters into a DIRECT EXCHANGE with the other Mn^2+ ion {RHS}. Such interaction between Mn^2 ions coupled through O^2- is called antiferromagnetic superexhange.
It is a strong interaction . The magnetic moment decreases and becomes less than even the normal paramagnetic substance.Its experimental magnetic moment is 4.58 BM.
[IV]FERROMAGNETIC SUPEREXCHANGE See 2nd and 3rd Figures:
Consider two Fe^4 ions[ t2g^3eg^1] and one intervening O2-.
One overlapping half filled 3d orbital belongs to eg set and the other to the half filled t^2g set.There can be two types of interactions called 180 degree and 90 degree interactions represented separately as:
[i]180 degree interaction
The eg set of orbital of Fe^4{RHS} can undergo sigma interaction with pz to enter into a DIRECT EXCHANGE while the other from the O^2- HOPS OVER to the t2g set of orbital of the other Fe^4{LHS} to undergo week pi interaction with px orbital of the anion.
[ii] 90 degree interaction
It is the reverse of 180 degree interaction.
Such ferromagnetic superexchange interaction is much weaker .Such substances still have enough ferromagnetic character{ Experimental magnetic moment of this oxide of iron(IV)=3.5BM/ Fe .
Angewandte Chemie International Edition . 50(52):12547-50[2011].
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