Role of orbital degrees of freedom in investigating the magnetic properties of geometrically frustrated vanadium spinels

The inconsistency about the degree of geometrical frustration has been a long issue in AV2O4 (A ≡ Zn, Cd and Mg) compounds, which arises from the two experimental results: (i) frustration indices and (ii) magnetic moments. In the present study, we try to understand such inconsistency by using ab initio electronic structure calculations. The orbital degrees of freedom are found to play an important role in understanding the geometrically frustrated magnetic behavior of these compounds. The magnitude of the maximum calculated values of orbital magnetic moment per formula unit for ZnV2O4, MgV2O4 and CdV2O4 compounds are found to be ∼1.54 μB, ∼0.92 μB and ∼1.74 μB, respectively. The inclusion of the orbital and spin angular momenta for calculating the frustration indices improves the understanding about the degree of geometrical frustration in these compounds. The calculated values of the frustration indices (fJ) are largest for MgV2O4 and smallest for CdV2O4 for 3.3 ⩽ U⩽ 5.3 eV. In this range of U, the calculated values of ΔM2 = Mtotal-Mexp (where, Mtotal=Mspin-|Morbital|) are also found to be largest for MgV2O4 and smallest for CdV2O4. Hence, the consistency about the degree of geometrical frustration, which arises from the fJ as well as from the ΔM2 is achieved and improves the understanding about the degree of geometrical frustration in these compounds. Calculated values of band gap in this range of U are found to be closer to that of experimentally observed values for all three compounds. The absolute values of the nearest neighbor exchange coupling constant (Jnn) between V spins are found to be largest for MgV2O4 and smallest for CdV2O4, which indicate that the calculated absolute values of the Curie-Weiss temperature (ΘCW)J are highest for MgV2O4 and smallest for CdV2O4 for 3.3 ⩽ U⩽ 5.3 eV. In this range of U, the magnetic transition temperature(TN)J is found to be ∼150 K, ∼60 K and ∼22 K for MgV2O4, ZnV2O4 and CdV2O4, respectively, which shows that the order of (TN)J is similar to that of (TN)exp for these compounds. Hence, all the magnetic properties studied in the present work are well explained in these spinels for 3.3 ⩽ U⩽ 5.3 eV. This work is expected to provide a valuable input in understanding the geometrically frustrated magnetic behavior for those systems for which the orbital part of the angular momenta are not quenched.