Magnetism and Electronic Structure in ZnFe$_2$O$_4$ and MnFe$_2$O$_4$

Density functional calculations are used to study magnetic and electronic properties of the spinel ferrites, ZnFe$_2$O$_4$ and MnFe$_2$O$_4$. Correct magnetic orderings are obtained. ZnFe$_2$O$_4$ is predicted to be a small gap insulator in agreement with experiment. MnFe$_2$O$_4$ is found to be a low carrier density half-metal in the fully ordered state. However, strong effects on the electronic structure are found upon partial interchange of Fe and Mn atoms. This indicates that the insulating character may be due to Anderson localization associated with the intersite Mn-Fe disorder.