# Multifold nodal points in magnetic materials

## TL;DR

This paper classifies and explores multifold fermions in magnetic materials, revealing new types of degeneracies and providing a framework to identify candidate compounds hosting these exotic quasiparticles.

## Contribution

It introduces a comprehensive classification of multifold fermions in magnetic space groups and discusses their realization in real materials.

## Key findings

- Only 3-, 6-, and 8-fold degeneracies are possible in magnetic materials.
- Identifies specific space groups where these fermions can occur.
- Provides methods to find candidate materials hosting these fermions.

## Abstract

We describe the symmetry protected nodal points that can exist in magnetic space groups and show that only 3-, 6-, and 8-fold degeneracies are possible (in addition to the 2- and 4-fold degeneracies that have already been studied.) The 3- and 6-fold degeneracies are derived from "spin-1" Weyl fermions. The 8-fold degeneracies come in different flavors. In particular, we distinguish between 8-fold fermions that realize non-chiral "Rarita-Schwinger fermions" and those that can be described as four degenerate Weyl fermions. We list the (magnetic and non-magnetic) space groups where these exotic fermions can be found. We further show that in several cases, a magnetic translation symmetry pins the Hamiltonian of the multifold fermion to an idealized exactly solvable point that is not achievable in non-magnetic crystals without fine-tuning. Finally, we present known compounds that may host these fermions and methods for systematically finding more candidate materials.