# Asymmetric splitting of an antiferromagnetic resonance via quartic exchange interactions in multiferroic hexagonal HoMnO$_3$

## TL;DR

This study uncovers asymmetric antiferromagnetic resonance splitting in HoMnO3 caused by quartic exchange interactions, revealed through THz spectroscopy and supported by theoretical modeling, highlighting complex Ho-Mn interactions.

## Contribution

It demonstrates the necessity of including quartic spin interactions in models to explain AFR asymmetry in low-symmetry multiferroic materials.

## Key findings

- Asymmetric AFR splitting observed in HoMnO3
- g-factor difference of approximately 50% between branches
- Quartic exchange interactions are essential for theoretical explanation

## Abstract

The symmetric splitting of two spin-wave branches in an antiferromagnetic resonance (AFR) experiment has been an essential measurement of antiferromagnets for over half a century. In this work, circularly polarized time-domain THz spectroscopy experiments performed on the low symmetry multiferroic h-HoMnO$_3$ reveal an AFR of the Mn sublattice to split asymmetrically in applied magnetic field, with an $\approx$ 50\% difference in $g$-factors between the high and low energy branches of this excitation. The temperature dependence of the $g$-factors, including a drastic renormalization at the Ho spin ordering temperature, reveals this asymmetry to unambiguously stem from Ho-Mn interactions. Theoretical calculations demonstrate the AFR asymmetry is not explained by conventional Ho-Mn exchange mechanisms alone and are only reproduced if quartic spin interactions are also included in the spin Hamiltonian. Our results provide a paradigm for the optical study of such novel interactions in hexagonal manganites and low symmetry antiferromagnets in general.