Aggregation and magnetism of Cr, Mn, and Fe cations in GaN

A first-principles density functional theory–generalized gradient approximation DFT-GGA$+$$U$ study of the doping of bulk GaN and its surface with Cr, Mn, and Fe confirms a strong tendency of these magnetic ions, occupying Ga sites of the wurtzite and zinc blende phases of GaN, to form embedded clusters. Our study reveals that the tendency for aggregation is larger in the case of Cr and Mn ions than for Fe ions. In contrast to previous DFT-GGA calculations, we predict a ferromagnetic ordering of the Cr and Mn clusters consisting of more than two atoms, whereas it turns out that the Fe clusters are all antiferromagnetic. We have also investigated the magnetic ordering of the nearest-neighbor ionic pairs that substitute gallium atoms at the (0001) wz-GaN surface. We find that Fe ions tend to aggregate, whereas there is a mutual repulsive interaction in the case of Cr and Mn. The nearest neighbor Mn and Fe pairs are coupled antiferromagnetically, whereas the Cr pair is coupled ferromagnetically. Further, the relevance of our findings to recent experimental results is discussed.

Figure 1

Geometries of the TM${}_n$ ($n$ $=$ 2, 3, and 4) clusters in wurtzite and zinc blende GaN, which were studied in the paper. The gray circles represent TM substituting the Ga cations. In the case of the four TMs constituting a tetrahedron, we have used tetrahedrons surrounding an interstitial site (without the N atom in its centers), which have turned out to be a energetically more favorable configuration for Cr and Fe.

Figure 2

Heat of reaction as a function of the number of TM atoms in the Cr, Mn, and Fe clusters in the wz- and zb-GaN.

Figure 3

Heat of reaction as a function of the number of TM atoms in the Cr, Mn, and Fe clusters in the wz- and zb-GaN, calculated without taking into account the spin polarization. This exhibits the pure chemical aspect of the clustering.

Figure 4

Energy difference per TM atom between the FM and AFM configurations as a function of the number of TM atoms in the Cr, Mn, and Fe clusters in the wz- and zb-GaN.

Figure 5

Net magnetic moment (in Bohr magnetons) as a function of the number of TM atoms in the Cr, Mn, and Fe clusters in the wz- and zb-GaN.