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Universal excitonic superexchange in spin-orbit-coupled Mott insulators

We point out the universal presence of the excitonic superexchange in spin-orbit-coupled Mott insulators. It is observed that, the restriction to the lowest spin-orbit-entangled "$J$" states may sometimes be insufficient to characterize the microscopic physics, and the virtual excitonic processes via the upper "$J$" states provide an important correction to the superexchange. We illustrate this excitonic superexchange from a two-dimensional $5d$ iridate Sr$_2$IrO$_4$ and explain its physical consequences such as the orbital-like coupling to the external magnetic flux and the nonlinear magnetic susceptibility. The universal presence of the excitonic superexchange in other spin-orbit-coupled Mott insulators such as $3d$ Co-based Kitaev magnets and even $f$ electron rare-earth magnets is further discussed.