# Comparing the anomalous Hall effect and the magneto-optical Kerr effect through antiferromagnetic phase transitions in Mn$_3$Sn

## TL;DR

This study compares the anomalous Hall effect and magneto-optical Kerr effect in Mn$_3$Sn across magnetic phase transitions, revealing differences in transition temperatures and magnetic reversal fields that suggest surface-bulk magnetic property disparities.

## Contribution

It provides the first direct comparison of AHE and MOKE measurements in Mn$_3$Sn across phase transitions, highlighting discrepancies and surface-bulk magnetic property differences.

## Key findings

- AHE and MOKE detect the same magnetic transitions but at different temperatures.
- Magnetic reversal fields are larger in MOKE measurements than in AHE.
- Results suggest surface and bulk magnetic properties differ in Mn$_3$Sn.

## Abstract

In the non-collinear antiferromagnet Mn$_3$Sn, we compare simultaneous measurements of the anomalous Hall effect (AHE) and the magneto-optical Kerr effect (MOKE) through two magnetic phase transitions: the high-temperature paramagnetic/antiferromagnetic phase transition at the N\'eel temperature ($T_N \approx$420~K), and a lower-temperature incommensurate magnetic ordering at $T_1 \approx$270~K. While both the AHE and MOKE are sensitive to the same underlying symmetries of the antiferromagnetic non-collinear spin order, we find that the transition temperatures measured by these two techniques unexpectedly differ by approximately 10~K. Moreover, the applied magnetic field at which the antiferromagnetic order reverses is significantly larger when measured by MOKE than when measured by AHE. These results point to a difference between the bulk and surface magnetic properties of Mn$_3$Sn.