  We have carried out a detailed first-principles study of a d$^{4.5}$
quaternary iridate Ba$_3$YIr$_2$O$_9$ both in its 6H-perovskite-type ambient
pressure (AP) phase and also for the high pressure (HP) cubic phase. Our
analysis reveals that the AP phase belongs to the intermediate spin-orbit
coupling (SOC) regime. This is further supported by the identification of the
spin moment as the primary order parameter (POP) obtained from a magnetic
multipolar analysis. The large $t_{2g}$ band width renormalizes the strength of
SOC and the Ir intersite exchange interaction dominates resulting in long range
magnetic order in the AP phase. In addition to SOC and Hubbard $U$, strong
intradimer coupling is found to be crucial for the realization of the
insulating state. At high pressure (HP) the system undergoes a structural
transformation to the disordered cubic phase. In sharp contrast to the AP
phase, the calculated exchange interactions in the HP phase are found to be
much weaker and SOC dominates leading to a quantum spin orbital liquid (SOL)
state.
