The role of ionic sizes in inducing the cubic to tetragonal distortion in A V₂O₄ and A Cr₂O₄ ( A  = Zn, Mg and Cd) compounds

Cubic to tetragonal distortion in A V₂O₄ and A Cr₂O₄ ( A  = Zn, Mg and Cd) compounds have been a contentious issue for last two decades. Different groups have proposed different mechanisms to understand such a distortion in these spinels, which are: (i) spin lattice coupling mechanism known as the spin driven Jahn–Teller (JT) effect, (ii) the strong relativistic spin–orbit coupling, a moderate JT distortion and weak V–V interactions and (iii) the JT effect. Now, in order to know the possible cause for such a distortion, we have avoided these complexities (various interactions among spin, electronic, orbital and lattice degrees of freedom) by carrying out spin unpolarized calculations. The calculated values of bulk moduli for ZnV₂O₄ (ZnCr₂O₄), MgV₂O₄ (MgCr₂O₄) and CdV₂O₄ (CdCr₂O₄) are found to be ∼289 (∼254), ∼244 (∼243) and ∼230 (∼233) GPa, respectively which suggest that CdV₂O₄ (among vanadates) and CdCr₂O₄ (among chromates) are more compressible. For vanadates and chromates, the order of calculated values of lattice parameter a are found to CdV₂O₄ > MgV₂O₄ > ZnV₂O₄ and CdCr₂O₄ > MgCr₂O₄ > ZnCr₂O₄, respectively and are consistent with the experimental results. The calculated values of cubic to tetragonal distortion ( c / a ), with c / a  < 1 for ZnV₂O₄ (ZnCr₂O₄), MgV₂O₄ (MgCr₂O₄) and CdV₂O₄ (CdCr₂O₄) are ∼0.996 (∼0.997), ∼0.995 (∼0.994) and ∼0.997 (∼0.998), respectively. These values are in good agreement with the experimental data for ZnV₂O₄, MgV₂O₄, ZnCr₂O₄ and MgCr₂O₄ compounds. The present study clearly shows the role of ionic sizes in inducing the cubic to tetragonal distortion in these spinels. However, the discrepancies between the calculated and experimental data for CdV₂O₄ and CdCr₂O₄ are expected to improve by considering the above mentioned mechanisms. These mechanisms also appear to be responsible for deciding the other physical properties of these compounds. (paper)