Abstract
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) and GGA plus the one-site Coulomb interaction $(\text{GGA}+\text{U})$ are considered for the exchange-correlation energy functional. The interactions up to third neighbors are found to be all antiferromagnetic for both materials, regardless of which approximation scheme (GGA or $\text{GGA}+\text{U}$) is used. Surprisingly, the third-neighbor interactions are estimated to be much stronger than the second-neighbor interactions and on the same order in magnitude as the first-neighbor interactions.
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