The interplay between various competing parameters, for example covalency, non-cubic crystal field, and spin-orbit coupling (SOC) leads to fascinating electronic and magnetic phases of matter. In the present work, the effect of these competing parameters on the ground state properties of the systems with d(5), d(4), and d(3) electronic configurations are studied using atomic and two-site full multi-orbital man-body electronic Hamiltonian. In order to connect with the real world materials, explicit density functional calculations are employed to study the electronic and the magnetic properties of a series of double perovskite iridates Sr2MIrO6 (M = Ce, Sc, Ca) with formal valences of Ir: Ir4+ (d(5)), Ir5+ (d(4)), and Ir6+ (d(3)). All these iridates facilitate a finite noncubic crystal field and strong Ir-O covalency along with large SOC, thereby offering an excellent platform for the present study. Using the symmetry allowed magnetic structures, the magnetic properties of these materials are studied and compared with the available experimental results. The results of the present work are pertinent to describe the electronic properties of a broad family of spin-orbit coupled materials.
