Artificially fabricated 3$d$/5$d$ superlattices (SLs) involve both strong electron correlation and spin-orbit coupling in one material by means of interfacial 3$d$-5$d$ coupling, whose mechanism remains mostly unexplored. In this work we investigated the mechanism of interfacial coupling in LaMnO$_3$/SrIrO$_3$ SLs by several spectroscopic approaches. Hard x-ray absorption, magnetic circular dichroism and photoemission spectra evidence the systematic change of the Ir ferromagnetism and the electronic structure with the change of the SL repetition period. First-principles calculations further reveal the mechanism of the SL-period dependence of the interfacial electronic structure and the local properties of the Ir moments, confirming that the formation of Ir-Mn molecular orbital is responsible for the interfacial coupling effects. The SL-period dependence of the ratio between spin and orbital components of the Ir magnetic moments can be attributed to the realignment of electron spin during the formation of the interfacial molecular orbital. Our results clarify the nature of interfacial coupling in this prototypical 3$d$/5$d$ SL system and the conclusion will shed light on the study of other strongly correlated and spin-orbit coupled oxide hetero-interfaces.
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