Role of direct exchange and Dzyaloshinskii-Moriya interactions in magnetic properties of graphene derivatives: C$_2$F and C$_2$H

TL;DR

This paper investigates how direct exchange and Dzyaloshinskii-Moriya interactions influence the magnetic properties of functionalized graphene derivatives, revealing mechanisms for ferromagnetism and potential skyrmion formation.

Contribution

It demonstrates that direct exchange interactions can significantly alter magnetic behavior in graphene derivatives, highlighting their role alongside indirect interactions and spin-orbit effects.

Findings

C$_2$H exhibits isotropic ferromagnetism with negligible anisotropy.

C$_2$F is near a magnetic instability, potentially leading to skyrmions.

Direct exchange interactions can counteract antiferromagnetic tendencies.

Abstract

According to the Lieb's theorem the ferromagnetic interaction in graphene-based materials with bipartite lattice is a result of disbalance between the number of sites available for $p_z$ electrons in different sublattices. Here, we report on another mechanism of the ferromagnetism in functionalized graphene that is the direct exchange interaction between spin orbitals. By the example of the single-side semihydrogenated (C$_2$H) and semifluorinated (C$_2$F) graphene we show that such a coupling can partially or even fully compensate antiferromagnetic character of indirect exchange interactions reported earlier [Phys. Rev. B {\bf 88}, 081405(R) (2013)]. As a result, C$_2$H is found to be a two-dimensional material with the isotropic ferromagnetic interaction and negligibly small magnetic anisotropy, which prevents the formation of the long-range magnetic order at finite temperature in accordance with the Mermin-Wagner theorem. This gives a rare example of a system where direct exchange interactions play a crucial role in determining a magnetic structure. In turn, C$_2$F is found to be at the threshold of the antiferromagnetic-ferromagnetic instability, which in combination with the Dzyaloshinskii-Moriya interaction can lead to a skyrmion state.