Optical Hall response in spin-orbit coupled metals: Comparative study of magnetic cluster monopole, quadrupole, and toroidal orders

TL;DR

This paper theoretically investigates how different magnetic multipole orders in spin-orbit coupled metals influence the optical Hall response, revealing distinct spectral features that can help identify these orders experimentally.

Contribution

It provides a comparative analysis of optical Hall spectra for monopole, quadrupole, and toroidal magnetic orders, highlighting their unique spectral signatures and underlying selection rules.

Findings

Monopole and quadrupole orders produce distinct high- and low-energy optical Hall responses.

Toroidal order results in a dispersed and weak optical Hall response.

Optical Hall measurements can effectively detect and distinguish magnetic multipole orders.

Abstract

The optical Hall response is theoretically studied for spin-orbit coupled metals with ferroic orders of cluster-type magnetic multipoles. We find that different magnetic multipoles give rise to distinct spectra in the optical Hall conductivity. In the cases of monopole and quadrupole orders, the optical Hall response appears predominantly in high- and low-energy regions, which correspond to the energy scales of electron correlation and kinetic energy, respectively, while the response is dispersed and rather weak in the case of toroidal order. By decomposing the spectra into different interband contributions, we reveal selection rules stemming from the interplay between the antisymmetric spin-orbit coupling and the underlying multipoles. Our results suggest that the optical Hall measurement is useful to detect and distinguish the cluster-type magnetic multipole orders.