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 ($\chi_{\rm{VV}}$) in transition metal compounds. A typical crossover behavior is found for the correlation effect on $\chi_{\rm{VV}}$ as sweeping spin-orbit interaction, $\lambda$. For a small $\lambda$, orbital fluctuation plays a dominant role in the correlation enhancement of $\chi_{\rm{VV}}$; however, the enhancement rate is rather small. In contrast, for an intermediate $\lambda$, $\chi_{\rm{VV}}$ shows a substantial increase, accompanied by the development of spin fluctuation. We will discuss the behavior of $\chi_{\rm{VV}}$ 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.