Microscopic origin of Heisenberg and non-Heisenberg exchange interactions in ferromagnetic bcc Fe

TL;DR

This study uses first principles calculations to uncover the microscopic origins of Heisenberg and non-Heisenberg exchange interactions in ferromagnetic bcc Fe, highlighting the roles of different 3d orbitals and Fermi surface nesting.

Contribution

It reveals the distinct roles of $E_g$ and $T_{2g}$ orbitals in exchange interactions, showing $T_{2g}$ interactions are Heisenberg-like and driven by Fermi surface nesting, while $E_g$ interactions are non-Heisenberg and linked to double-exchange.

Findings

$T_{2g}$ orbitals participate in Fermi surface nesting-driven exchange interactions.

$E_g$ orbitals exhibit non-Heisenberg behavior dependent on the reference state.

Nearest-neighbor $E_g$ interactions are mainly proportional to hopping integrals.

Abstract

By means of first principles calculations we investigate the nature of exchange coupling in ferromagnetic bcc Fe on a microscopic level. Analyzing the basic electronic structure reveals a drastic difference between the $3d$ orbitals of $E_g$ and $T_{2g}$ symmetries. The latter ones define the shape of the Fermi surface, while the former ones form weakly-interacting impurity levels. We demonstrate that, as a result of this, in Fe the $T_{2g}$ orbitals participate in exchange interactions, which are only weakly dependent on the configuration of the spin moments and thus can be classified as Heisenberg-like. These couplings are shown to be driven by Fermi surface nesting. In contrast, for the $E_g$ states the Heisenberg picture breaks down, since the corresponding contribution to the exchange interactions is shown to strongly depend on the reference state they are extracted from. Our analysis of the nearest-neighbour coupling indicates that the interactions among $E_g$ states are mainly proportional to the corresponding hopping integral and thus can be attributed to be of double-exchange origin.