Diluted magnetic semiconductors with narrow band gaps

We propose a method to realize diluted magnetic semiconductors (DMSs) with $p$- and $n$-type carriers by choosing host semiconductors with a narrow band gap. By employing a combination of the density function theory and quantum Monte Carlo simulation, we demonstrate such semiconductors using Mn-doped ${\mathrm{BaZn}}_2{\mathrm{As}}_2$, which has a band gap of 0.2 eV. In addition, we found a nontoxic DMS Mn-doped ${\mathrm{BaZn}}_2{\mathrm{Sb}}_2$, of which the Curie temperature $T_c$ is predicted to be higher than that of Mn-doped ${\mathrm{BaZn}}_2{\mathrm{As}}_2$, the $T_c$ of which was up to 230 K in a recent experiment.

Figure 1

Schematic pictures of an impurity bound state (IBS) and ferromagnetic (FM) coupling in diluted magnetic semiconductors (DMSs). (a) Host bands $\epsilon \left(k\right)$ with a wide band gap ${\mathrm{\Delta }}_{\text{g}}$ between the valence band (VB) and the conduction band (CB). The position of the IBS ${\omega }_{\text{IBS}}$ (arrow) is close to the top of the VB owing to strong mixing between the impurity and the VB, and usually no IBS appears below the bottom of the CB because of weak mixing between the impurity and the CB [13, 14, 15]. We have $0\lesssim {\omega }_{\text{IBS}}\ll {\mathrm{\Delta }}_{\text{g}}$. (b) Magnetic correlation $\langle M_1^z{M}_2^z\rangle$ between two impurities as a function of the chemical potential $\mu$ for case (a). Positive $\langle M_1^z{M}_2^z\rangle$ denotes FM coupling, which can be developed when $\mu \sim {\omega }_{\text{IBS}}$ [16, 17, 18]. Hence, for $p$-type carriers $\left(\mu \sim 0\right)$, FM coupling can be obtained as $\mu \sim {\omega }_{\text{IBS}}$, and for $n$-type carriers $\left(\mu \sim {\mathrm{\Delta }}_{\text{g}}\right)$, no magnetic coupling is obtained between impurities because $\mu \gg {\omega }_{\text{IBS}}$ [13, 14, 15]. (c) Similar to case (a), except for a narrow ${\mathrm{\Delta }}_{\text{g}}$. By choosing suitable host semiconductors and impurities, the condition $0\lesssim {\omega }_{\text{IBS}}\lesssim {\mathrm{\Delta }}_{\text{g}}$ is obtained. (d) Similar to case (b), except for a narrow ${\mathrm{\Delta }}_{\text{g}}$. FM coupling can be achieved for both $p$-type and $n$-type carriers when $\mu \sim {\omega }_{\text{IBS}}$. In this study, we describe cases (c) and (d).

Figure 2

Host band and mixing parameters of Mn-doped ${\mathrm{BaZn}}_2{\mathrm{As}}_2$. (a) Energy bands ${\epsilon }_{\alpha }$ of host ${\mathrm{BaZn}}_2{\mathrm{As}}_2$, which has space group $I4/mmm$. An indirect band gap of 0.2 eV was obtained by DFT calculations, which agrees well with the experimental value [7]. The mixing function between the $\xi$ orbitals of an Mn impurity and ${\mathrm{BaZn}}_2{\mathrm{As}}_2$ hosts (b) valence bands and (c) conduction bands.

Figure 3

For Mn-doped ${\mathrm{BaZn}}_2{\mathrm{As}}_2$, chemical potential $\mu$ dependence of (a) occupation number $\langle n_{\xi }\rangle$ of $\xi$ orbital of an Mn impurity, (b) partial density of state $d\langle n_{\xi }\rangle /d\mu$, and (c) magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between the $\xi$ orbitals of two Mn impurities with fixed distance $R_{12}$ of the first-nearest neighbor, where the temperature is 360 K. The top of the VB is 0 and the bottom of the CB is 0.2 eV.

Figure 4

For Mn-doped ${\mathrm{BaZn}}_2{\mathrm{As}}_2$, the distance $R_{12}$ dependence of magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between the $\xi$ orbitals of two Mn impurities for the (a) $p$-type case with chemical potential $\mu =-0.3$ eV and (b) $n$-type case with $\mu =0.15$ eV, where temperature is 360 K. The first-, second-, and third-nearest neighbors of $R_{12}$ are noted.

Figure 5

For Mn-doped ${\mathrm{BaZn}}_2{\mathrm{As}}_2$, the distance $r$ dependence of magnetic correlation $\langle M_{\xi }^z{m}^z\left(r\right)\rangle$ between the $\xi$ orbitals of Mn impurity at site origin and the host electron at site $\mathbf{r}$ for the (a) $p$-type case with chemical potential $\mu =-0.3$ eV and (b) $n$-type case with $\mu =0.15$ eV, where temperature is 360 K.

Figure 6

Similar to Fig. 2, with the exception that ${\mathrm{BaZn}}_2{\mathrm{As}}_2$ is replaced by ${\mathrm{BaZn}}_2{\mathrm{Sb}}_2$, which has a different space group $Pnma$. A direct band gap of 0.2 eV is obtained by DFT calculations, which is in good agreement with the experimental value [29].

Figure 7

Similar to Fig. 3, except ${\mathrm{BaZn}}_2{\mathrm{As}}_2$ is replaced by ${\mathrm{BaZn}}_2{\mathrm{Sb}}_2$.

Figure 8

Similar to Fig. 4, except ${\mathrm{BaZn}}_2{\mathrm{As}}_2$ is replaced with ${\mathrm{BaZn}}_2{\mathrm{Sb}}_2$.

Figure 9

Similar to Fig. 3, except Coulomb repulsion parameter $U=4$ eV is replaced by a larger value $U=5$ eV.

Figure 10

Similar to Fig. 3, except impurity level parameter ${\epsilon }_d=-1.5$ eV is replaced by a deeper value ${\epsilon }_d=-2$ eV.

Figure 11

Similar to Fig. 7, except Coulomb repulsion parameter $U=4$ eV is replaced by a larger value $U=5$ eV.

Figure 12

Similar to Fig. 7, except impurity level parameter ${\epsilon }_d=-1.5$ eV is replaced by a deeper value ${\epsilon }_d=-2$ eV.