Electric toroidal octupolar symmetry in pyrite FeS$_2$ probed by Raman optical activity

TL;DR

This study demonstrates that Raman optical activity can detect electric toroidal octupolar symmetry in pyrite FeS$_2$, revealing a sign reversal in circular intensity difference linked to specific phonon modes, supported by first-principles calculations.

Contribution

It introduces Raman optical activity as a novel method to probe higher-rank axial multipolar symmetry in materials, specifically in pyrite FeS$_2$.

Findings

Sign reversal of circular intensity difference between neighboring faces.

Signal only for the doubly degenerate Eg phonon mode.

First-principles calculations confirm experimental observations.

Abstract

We report Raman optical activity in pyrite FeS$_2$, which hosts an electric toroidal octupolar symmetry. A clear and reproducible sign reversal of the circular intensity difference is observed between neighboring $\{111\}$ faces under cross-circular polarization. The signal appears only for the doubly degenerate $E_g$ phonon mode and is absent for other modes, consistent with symmetry analysis. First-principles calculations reproduce these features, establishing Raman optical activity as a probe of higher-rank axial multipolar symmetry.