# Topological Semimetal features in the Multiferroic Hexagonal Manganites

## TL;DR

This paper uses first-principles calculations to explore topological features in the band structures of multiferroic hexagonal manganites, revealing nodal rings and drumhead surface states, and discusses phase transitions relevant for topological and multiferroic properties.

## Contribution

It identifies topological nodal rings and surface states in YVO3 and YCrO3, and analyzes phase transitions between different crystal symmetries, linking topology with multiferroicity in hexagonal manganites.

## Key findings

- Nodal rings near the Fermi energy in YVO3 and YCrO3.
- Existence of topological drumhead surface states.
- Potential for phase transitions affecting topological properties.

## Abstract

Using first-principles calculations we examine the band structures of ferromagnetic hexagonal manganites $\mathrm{YXO_3}$ (X=V, Cr, Mn, Fe and Co) in the nonpolar nonsymmorphic $P6_3/mmc$ space group. For $\mathrm{YVO_3}$ and $\mathrm{YCrO_3}$ we find a band inversion near the Fermi energy that generates a nodal ring in the $k_z=0$ mirror plane. We perform a more detailed analysis for these compounds and predict the existence of the topological "drumhead" surface states. Finally, we briefly discuss the low-symmetry polar phases (space group $P6_3cm$) of these systems, and show they can undergo a $P6_3/mmc \rightarrow P6_3cm$ transition by condensation of soft $K_3$ and $\Gamma_2^-$ phonons. Based on our findings, stabilizing these compounds in the hexagonal phase could offer a promising platform for studying the interplay of topology and multiferroicity, and the coexistence of real-space and reciprocal-space topological protection in the same phase.