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

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 proposed method as implemented on top of 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 ${120}^{\ensuremath{\circ}}$ 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 $exp(\ensuremath{-}\sqrt{r/\ensuremath{\delta}})$. We show that the stiffness constant derived from the exchange interactions is consistent with a 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 nanostructures where metallic and organic components are integrated to form exotic magnetic patterns.