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The electronic and magnetic properties of Ba$_5$AlIr$_2$O$_{11}$ containingIr-Ir dimers are investigated using the GGA and GGA+SOC calculations. We foundthat strong suppression of the magnetic moment in this compound recently foundin [J. Terzic {\it et al.}, Phys. Rev. B {\bf 91}, 235147 (2015)] is not due tocharge-ordering, but is related to the joint effect of the spin-orbitinteraction and strong covalency, resulting in the formation of metal-metalbonds. They conspire and act against the intra-atomic Hund's rule exchangeinteraction to reduce total magnetic moment of the dimer. We argue that thesame mechanism could be relevant for other $4d$ and $5d$ dimerized transitionmetal compounds.

Suppression of magnetism in Ba5AlIr2O11: interplay of Hund's coupling, molecular orbitals and spin-orbit interaction