Ruderman-Kittel-Kasuya-Yosida–like Ferromagnetism in ${\mathrm{M}\mathrm{n}}_x{\mathrm{G}\mathrm{e}}_{1-x}$

The nature and origin of ferromagnetism in magnetic semiconductors is investigated by means of highly precise electronic and magnetic property calculations on ${\mathrm{M}\mathrm{n}}_x{\mathrm{G}\mathrm{e}}_{1-x}$ as a function of the location of Mn sites in a large supercell. Surprisingly, the coupling is not always ferromagnetic (FM), even for large Mn-Mn distances. The exchange interaction between Mn ions oscillates as a function of the distance between them and obeys the Ruderman-Kittel-Kasuya-Yosida analytic formula. The estimated Curie temperature is in good agreement with recent experiments, and the estimated effective magnetic moment is about $1.7{\mu }_B/\mathrm{M}\mathrm{n}$, in excellent agreement with the experimental values, $(1.4–1.9){\mu }_B/\mathrm{M}\mathrm{n}$.

Figure 1

The exchange interaction, $J_n$, for the Mn atoms versus their distance in ${\mathrm{M}\mathrm{n}}_x{\mathrm{G}\mathrm{e}}_{1-x}$, where the $J_n$’s are defined with the convention $|\mathbf{S}|=1$. The solid line is the RKKY model fitted with $k_F=1.02{\AA }^{-1}$.

Figure 2

The total DOS and projected Mn $3d$ and Ge $4p$ DOS of the $N440$ FM case in ${\mathrm{G}\mathrm{e}}_{62}{\mathrm{M}\mathrm{n}}_2$, with Gaussian broadening technique with a parameter of 0.05 eV. Spin up and spin down are represented with positive and negative images, respectively. The distance of the nearest Ge to Mn is 2.45 Å while it is 6.93 Å for the furthest Ge atom.

Figure 3

The spin density of the $N440$ case in ${\mathrm{G}\mathrm{e}}_{62}{\mathrm{M}\mathrm{n}}_2$ for both FM (left) and AFM (right) configurations. The solid (dashed) lines represent spin up (down) density with $\rho =0.0005\times 2^{(n-1)/2}e/{\mathrm{b}\mathrm{o}\mathrm{h}\mathrm{r}}^3$. Here $n$ represents the $n\mathrm{t}\mathrm{h}$ contour line from the lowest density zone.