Spin-orbit coupling driven novel magnetism in <i>d</i>⁵ 6H-perovskite iridates Ba₃IrTi₂O₉ and Ba₃TiIr₂O₉.

In the present paper, we have carried out a comparative first principles as well as model Hamiltonian study to understand novel magnetism in 6H perovskite iridates Ba$_3$IrTi$_2$O$_9$ and Ba$_3$TiIr$_2$O$_9$ resulting from an unusual combination of geometrical as well as exchange frustration owing to their unique crystal geometry. Our model calculations corroborated with multipolar analysis provides a comprehensive understanding of the spin-orbit entangled $j_{\rm eff}$~=~1/2 pseudo-spin states in both the materials. While, the $j_{\rm eff}$~=~1/2 character is quite robust in the former compound, it is found to be directly related to the nature of magnetism in the latter iridate. The identification of the relevant spin model for Ba$_3$IrTi$_2$O$_9$ suggests that the Heisenberg exchange interaction dominates the Kitaev term favoring long range magnetic order in the system in line with the {\it ab initio} study while the other iridate Ba$_3$TiIr$_2$O$_9$ hosts a novel spin-orbital singlet state with no resultant moment.&#13.