# Topological Weyl and Node-Line Semimetals in Ferromagnetic Vanadium-Phosphorous-Oxide $\beta$-V$_2$OPO$_4$ Compound

## TL;DR

This paper predicts that the ferromagnetic vanadium-phosphorous-oxide compound $eta$-V$_2$OPO$_4$ hosts topological semimetal phases, with magnetization direction controlling the transition between node-line and Weyl semimetals, confirmed by first-principles calculations.

## Contribution

It demonstrates that $eta$-V$_2$OPO$_4$ can exhibit tunable topological semimetal phases with magnetic control, a novel finding in magnetic topological materials.

## Key findings

- Magnetization direction switches between node-line and Weyl phases.
- Weyl points are protected by rotational symmetry and are well separated.
- Surface states confirm non-trivial topological properties.

## Abstract

We propose that the topological semimetal features can co-exist with ferromagnetic ground state in vanadium-phosphorous-oxide $\beta$-V$_2$OPO$_4$ compound from first-principles calculations. In this magnetic system with inversion symmetry, the direction of magnetization is able to manipulate the symmetric protected band structures from a node-line type to a Weyl one in the presence of spin-orbital-coupling. The node-line semimetal phase is protected by the mirror symmetry with the reflection-invariant plane perpendicular to magnetic order. Within mirror symmetry breaking due to the magnetization along other directions, the gapless node-line loop will degenerate to only one pair of Weyl points protected by the rotational symmetry along the magnetic axis, which are largely separated in momentum space. Such Weyl semimetal phase provides a nice candidate with the minimum number of Weyl points in a condensed matter system. The results of surface band calculations confirm the non-trivial topology of this proposed compound. This findings provide a realistic candidate for the investigation of topological semimetals with time-reversal symmetry breaking, particularly towards the realization of quantum anomalous Hall effect in Weyl semimetals.