# Ferromagnetic Dirac-Nodal Semimetal Phase of Stretched Chromium Dioxide

## TL;DR

This study predicts that chromium dioxide can host a ferromagnetic Dirac nodal-line semimetal phase at room temperature under small tensile strains, with topological protection by mirror symmetry, opening avenues for novel magnetic and topological physics.

## Contribution

First-principles calculations reveal a stable ferromagnetic Dirac nodal-line phase in chromium dioxide under strain, highlighting symmetry-protected topological features in a widely used magnetic material.

## Key findings

- Dirac nodal ring near Fermi energy in CrO₂ under strain
- Topological protection by mirror symmetry $D_{4h}(C_{4h})$
- Persistence of the nodal ring under small anisotropic strains

## Abstract

We show by first-principles calculations that the Dirac nodal-line semimetal phase can co-exist with the ferromagnetic order at room temperature in chromium dioxide, a widely used material in magnetic tape applications, under small tensile hydrostatic strains. An ideally flat Dirac nodal ring close to the Fermi energy is placed in the reflection-invariant boundary of the Brillouin zone perpendicular to the magnetic order, and is topologically protected by the unitary mirror symmetry of the magnetic group $D_{4h}(C_{4h})$, which quantizes the corresponding Berry phase into integer multiples of $\pi$. The symmetry-dependent topological stability is demonstrated through showing that only the topologically protected nodal ring can persistently exist under small anisotropic stains preservingthe symmetry $D_{4h}(C_{4h})$, while the other seeming band touching points are generically gapped. Our work provides a practical platform for the investigation of novel physics and potential applications of the Dirac nodal-line and drumhead fermions, in particular those related to ferromagnetic properties