  For the first time, the Fe-Fe interactions in the geometrically frustrated
antiferromagnetic systems of zinc and cadmium ferrites are determined
quantitatively by the first-principles methods of density functional theory.
Both the generalized gradient approximation (GGA) as well as GGA plus the
onesite Coulomb interaction (GGA+U) are considered for the exchange-correlation
energy functional. The interactions up to third neighbours are found to be all
antiferromagnetic for both materials, regardless of which approximation scheme
(GGA or GGA+U) is used. Surprisingly, the thirdneighbour interactions are
estimated to be much stronger than the second-neighbour interactions and on the
same order in magnitude as the first-neighbour interactions.
