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The magnetic, structural and optical properties of  CoX 2 O 4( X  =  Cr ,  Mn  and  Fe ) spinels are calculated using GGA + U approximation. The effect of the octahedral cation  X  on the properties of these spinels are analyzed. In order to better understand the electronic aspect of these compounds we studied the issue between the relative forces of the exchange effect and the crystal field effect through a complete analysis of the densities of electronic states. Obtaining the correct ground state is only possible if the electron–electron interactions between magnetic cations are introduced. When the  X  cations are changed, the crystalline structure changes totally from cubic normal spinel for  CoFe 2 O 4to tetragonal normal spinel one for  CoMn 2 O 4to inverse spinel for  CoCr 2 O 4. The electronic properties of our spinels are significantly different, an increase in the band gap from  Fe  to  Mn  to  Cr  compounds is obtained. Magnetic exchange interactions are strongly affected by sub-lattices occupation in the inverse phase of  CoFe 2 O 4and significant structural distortion of the  CoMn 2 O 4compound. The analysis of structural parameters and electronic structures plays a role on the trends of magnetic exchange interactions. We have noticed that the iron states in  CoFe 2 O 4are extremely localised making this spinel very different from the  X  cation states in the other two spinels. So the variation in  X  cations allows us to confirm the trend in the properties of  CoX 2 O 4 .  The prediction of optical properties is possible and it allowed us to calculate different optical parameters. We have noticed thatdecreases with increasing band gap.

Effect of octahedral cation on electronic, magnetic and optic properties of CoX 2 O 4 ( X = Cr , Mn and Fe ) spinel compound