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

TL;DR

This study investigates how electron correlation and spin-orbit interaction jointly influence Van Vleck susceptibility in transition metal compounds, revealing a crossover behavior with implications for experimental observations.

Contribution

It provides a detailed analysis of the interplay between spin-orbit interaction and electron correlation effects on magnetic susceptibility in transition metal materials.

Findings

Orbital fluctuation enhances susceptibility at small spin-orbit coupling.

Significant increase in susceptibility occurs at intermediate spin-orbit coupling.

Results relate to experimental data on Sr$_2$RuO$_4$ and Ir compounds.

Abstract

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.