Different origins of the ferromagnetic order in (Ga,Mn)As and (Ga,Mn)<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">N</mml:mi></mml:math>

Abstract

The mechanism for the ferromagnetic order of (Ga,Mn)As and (Ga,Mn)$\mathrm{N}$ is extensively studied over a vast range of Mn concentrations. We calculate the electronic structures of these materials using density functional theory in both the local spin density approximation (LSDA) and the local density approximation $(\mathrm{LDA})+U$ scheme, that we have now implemented in the code SIESTA. For (Ga,Mn)As, the $\mathrm{LDA}+U$ approach leads to a hole mediated picture of the ferromagnetism, with an exchange constant $N\ensuremath{\beta}=\ensuremath{-}2.8\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. This is smaller than that obtained with LSDA, which overestimates the exchange coupling between Mn ions and the As $p$ holes. In contrast, the ferromagnetism in wurtzite (Ga,Mn)$\mathrm{N}$ is caused by the double-exchange mechanism, since a hole of strong $d$ character is found at the Fermi level in both the LSDA and the $\mathrm{LDA}+U$ approaches. In this case the coupling between the Mn ions decays rapidly with the Mn-Mn separation. This suggests a two phases picture of the ferromagnetic order in (Ga, Mn)$\mathrm{N}$, with a robust ferromagnetic phase at large Mn concentration coexisting with a diluted weak ferromagnetic phase.