# Faraday effects emerging from the optical magnetic field

## TL;DR

This paper shows that the magnetic component of light contributes to the Faraday effect and its inverse, challenging previous assumptions about light-matter interactions.

## Contribution

The study demonstrates that the optical magnetic field contributes to both the Faraday effect and its inverse, with quantifiable impact on the Verdet constant.

## Key findings

- The magnetic component of light accounts for ~17% of the Verdet constant in Terbium-Gallium-Garnet at 800 mm.
- The Verdet constants for the Faraday effect and inverse Faraday effect are found to be different.
- The optical magnetic field plays a significant role in light-spin interactions beyond the electrical field.

## Abstract

The Faraday effect (FE) is commonly attributed to the electrical component of optical radiation. Recently, we reported on an inverse-FE (IFE) that emerges from the Zeeman energy arising from the optical magnetic field. Here, we show that the magnetic component of light reproduces additional signatures observed experimentally in the IFE. Consequently, we show that the magnetic component of light also contributes to the reciprocal, direct FE. Calculating the Verdet constant for the well-studied Terbium-Gallium-Garnet, we find that it accounts for \documentclass[12pt]{minimal}
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\begin{document}$$\sim 17\%$$\end{document} of the measured value at 800 mm. The Verdet constants derived for the FE and IFE are found to be different, consistent with the breakdown of reciprocity between the two effects in the nonequilibrium ultrafast timescales as reported previously. Our findings highlight the role of the optical magnetic field in the interaction between light and spins, in addition to the primary effects that stem from the electrical field.

The online version contains supplementary material available at 10.1038/s41598-025-24492-9.