# Two-dimensional nodal-loop half metal in monolayer MnN

## TL;DR

This paper predicts that monolayer MnN is a robust 2D nodal-loop half metal with fully spin-polarized loops protected by mirror symmetry, which can be tuned by strain, advancing magnetic topological materials.

## Contribution

First-principles calculations reveal monolayer MnN as a new 2D nodal-loop half metal with robust spin-polarized loops protected by symmetry, and demonstrate strain-induced loop transformation.

## Key findings

- Monolayer MnN exhibits ferromagnetism with out-of-plane magnetization.
- It hosts two concentric, fully spin-polarized nodal loops near the Fermi level.
- Nodal loops are protected against SOC by mirror symmetry.

## Abstract

Two-dimensional (2D) materials with nodal-loop band crossing have been attracting great research interest. However, it remains a challenge to find 2D nodal loops that are robust against spin-orbit coupling (SOC) and realized in magnetic states. Here, based on first-principles calculations and theoretical analysis, we predict that monolayer MnN is a 2D nodal-loop half metal with fully spin polarized nodal loops. We show that monolayer MnN has a ferromagnetic ground state with out-of-plane magnetization. Its band structure shows half metallicity with three low-energy bands belonging to the same spin channel. The crossing between these bands forms two concentric nodal loops centered around the $\Gamma$ point near the Fermi level. Remarkably, the nodal loops and their spin polarization are robust under SOC, due to the protection of a mirror symmetry. We construct an effective model to characterize the fully polarized emergent nodal-loop fermions. We also find that a uniaxial strain can induce a loop transformation from a localized single loop circling around $\Gamma$ to a pair of extended loops penetrating the Brillouin zone.