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Interplay of Spin-Orbit Interaction and Electron Correlation on the Van Vleck Susceptibility in Transition Metal Compounds

We have studied the effects of electron correlation on Van Vleck susceptibility ($χ_{\rm{VV}}$) in transition metal compounds. A typical crossover behavior is found for the correlation effect on $χ_{\rm{VV}}$ as sweeping spin-orbit interaction, $λ$. For a small $λ$, orbital fluctuation plays a dominant role in the correlation enhancement of $χ_{\rm{VV}}$; however, the enhancement rate is rather small. In contrast, for an intermediate $λ$, $χ_{\rm{VV}}$ shows a substantial increase, accompanied by the development of spin fluctuation. We will discuss the behavior of $χ_{\rm{VV}}$ in association with the results of Knight-shift experiments on Sr$_2$RuO$_4$ and an anomalously large magnetic susceptibility observed for $5d$ Ir compounds.