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

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 implemeted 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 • Néel 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(− r/δ). 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.

Systematic determination of a material’s magnetic ground state from first principles

“…This is because the ways of assigning the spins to the atoms are not unique. The usual way is to use atomic-centered basis set functions, as in the case of muffin-tin spheres, Wannier functions 24,48 , or numerical atomic orbitals 24,49 . Here, it is assumed that the magnetic moments within the basis functions of one atom rotate uniformly.…”

Systematic determination of a material's magnetic ground state from first principles

“…This is because the ways of assigning the spins to the atoms are not unique. The usual way is to use atomic-centered basis set functions, as in the case of muffin-tin spheres, Wannier functions [16,36], or numerical atomic orbitals [16,37]. Here, it is assumed that the magnetic moments within the basis functions of one atom rotate uniformly.…”

High-throughput design of magnetic materials

“…As we discussed, there are a few possible solutions for the former question. Regarding the latter, as far as we are aware, there has been no reliable implementation where the exchange parameters can be evaluated in an automated way, where either the DFT part of the codes needs careful adaption for materials with diverse crystal structures or only specific components of the exchange parameters can be evaluated [96].…”