Structural and magnetic properties of (Ga,Mn)N from first principles

The structure of Mn clusters in (Ga,Mn)N and the interactions of the magnetic Mn ions and clusters are studied using first-principles calculations. Curie temperatures are calculated using mean-field and Monte Carlo methods. It is found that joining substitutional Mn ions to clusters is energetically favorable and especially the structures of two to four Mn ions formed around a single N ion are most stable. These clusters are always found to have a ferromagnetic ground state, and ferromagnetic intercluster interactions are also present even at relatively long distances. For randomly distributed Mn impurities, high Curie temperatures are obtained at high Mn concentrations (above room temperature for $x\gtrsim 0.14$).

Figure 1

A schematic illustration of the used scales. (a) Accurate first-principles calculations are restricted to small supercells, (b) while Monte Carlo simulation enables analysis of mesoscopic behavior using large cells (with only Mn clusters visible). In (b), the shades of gray denote cluster sizes (the size grows from one to four Mn as the color changes from white to black).

Figure 2

Wurtzite structure from isometric and top-down perspectives.

Figure 3

(Color online) (a)–(c) Structurally optimized geometries for the energetically most stable complexes (clusters) of two to four Mn ions. The Mn sites are numbered according to Fig. 2. Bond lengths are shown both as numbers (in Å) and using different colors, black corresponds to bonds in GaN. In (a) and (b), the first structure is lowest in energy and the $\delta E$’s give the energies with respect to them.

Figure 4

Binding energies $E_b$ of Mn ions in ${\mathrm{Mn}}_n$ complexes. The cases $n⩽4$ (squares) are calculated in a 72 atom ${\mathrm{Ga}}_{36-n}{\mathrm{N}}_{36}{\mathrm{Mn}}_n$ supercell with structural optimization, while for $n⩾4$ a 108 atom ${\mathrm{Ga}}_{54-n}{\mathrm{N}}_{54}{\mathrm{Mn}}_n$ supercell is used without optimization (diamonds). The unconnected diamond at $n=4$ is calculated in a 72 atom supercell without structural optimization. GGA values for $n=2$, 3, and 4 (72 atom supercell) are from Ref. 13.

Figure 5

Spin-flip energies $\Delta E$ for ${\mathrm{Mn}}_{n_1}\text{−}{\mathrm{Mn}}_{n_2}$ cluster pairs as a function of separation of the cluster centers of mass, $r$. The small squares represent values obtained using supercells of 48 and 72 atoms, while the large squares are calculated in 96 and 108 atom cells. Some of the values are from Ref. 12.

Figure 6

The spin-flip energies $\Delta E$ given by DFT versus the same energies calculated from the effective Hamiltonian. The filled squares have been used in the fitting of the exchange function, while the open squares are additional points calculated in order to test consistency.

Figure 7

Calculated Curie temperatures as a function of Mn concentration $x$. Solid and dashed lines represent $T_C^{\mathrm{MC}}$’s for random and $1000\mathrm{K}$ clustered states, respectively (Ref. 13). $T_C^{\mathrm{MFA}}$ and $T_C^{\Delta E}$ values for ordered lattices are given as diamonds and triangles, respectively. $T_C^{\Delta E_{\mathrm{DFT}}}$ and $T_C^{\Delta E_H}$ are calculated from $\Delta E_{\mathrm{DFT}}$ and $\Delta E_H$, respectively. The cluster sizes in each lattice are given by the numbers in parentheses. Some of the $T_C^{\Delta E_{\mathrm{DFT}}}$ values are taken from Ref. 12.