Comparison of the energies of the AFM and FiM runs are presented in Figure with relative energies defined relative to FiM normal MnFe 2 O 4 and FM normal ZnFe 2 O 4 . For all compositions except N Zn = 7 or 8 the ground state structure is most stable in the FiM runs than the AFM runs. This shows a collapse of the AFM magnetic structure upon addition of a small amount of Mn to the unit cell. Looking at the whole collection of sampled structures shows that when any inversion is introduced, even for N Zn = 7 or 8, structures have a lower energy in the FiM state than the AFM state.