Exchange interactions from a nonorthogonal basis set: from bulk ferromagnets to the magnetism in low-dimensional graphene systems

TL;DR

This paper introduces a computational method using nonorthogonal basis sets to determine exchange interactions in magnetic materials, successfully applying it to bulk ferromagnets and graphene nanostructures, revealing new insights into low-dimensional magnetism.

Contribution

The paper presents a novel computational approach for calculating exchange constants from density functional theory using nonorthogonal basis sets, applicable to complex nano-structures.

Findings

Reproduces Heisenberg interactions in bulk ferromagnets

Finds good agreement with previous calculations for fluorinated graphene

Discovers unconventional decay of exchange interactions in zigzag graphene nanoribbons

Abstract

We present a computational method to determine the exchange constants in isotropic spin models. The method uses the Hamiltonian and overlap matrices computed from density functional schemes that are based on nonorthogonal basis sets. We demonstrate that the new method as implemented in the SIESTA code reproduces the Heisenberg interactions of simple metallic bulk ferromagnets as obtained from former well--established computational approaches. Then we address $sp$ magnetism in graphene nanostructures. For fluorinated graphene we obtain exchange interactions in fairly good agreement with previous calculations using maximally localized Wannier functions and we confirm the theoretical prediction of a 120$^\circ$ N\'eel state. Associated with the magnetic edge-states of a zigzag graphene nanoribbon we find rapidly decaying exchange interactions, however, with an unconventional distance dependence of $\exp(-\sqrt{r/\delta})$. We show that the stiffness constant derived from the exchange interactions is consistent with previous estimate based on total energy differences of twisted spin configurations. We highlight that our method is an efficient tool for the analysis of novel hybrid nano-structures where metallic and organic components are integrated to form exotic magnetic patterns.