The ferromagnetic order in graphene

TL;DR

This paper investigates the conditions under which ferromagnetic order can exist in graphene, demonstrating that intrinsic symmetry prevents spontaneous magnetization at nonzero temperatures unless symmetry-breaking fluctuations occur.

Contribution

It provides a rigorous proof that pristine graphene remains nonmagnetic at finite temperatures due to symmetry, highlighting the role of electronic fluctuations in inducing ferromagnetism.

Findings

Pristine graphene is nonmagnetic at nonzero temperature under symmetry preservation.

Electronic fluctuations breaking pseudospin conservation can induce ferromagnetic order.

The Mermin-Wagner theorem constrains magnetic ordering in two-dimensional materials.

Abstract

The conditions for spontaneous magnetization in a single graphene sheet are discussed in the context of Mermin-Wagner theorem. It is rigorously proved that at any nonzero temperature the graphene monolayer is nonmagnetic as long as its intrinsic symmetry is preserved. Any electronic fluctuations breaking the pseudospin conservation law can be responsible for the existence of ferromagnetic order inside the graphene structure.