Microscopic mechanism of high-temperature ferromagnetism in Fe, Mn, and Cr-doped InSb, InAs, and GaSb magnetic semiconductors

In recent experiments, high Curie temperatures $T_c$ above room temperature were reported in ferromagnetic semiconductors Fe-doped GaSb and InSb, while low $T_c$ between 20 K to 90 K were observed in some other semiconductors with the same crystal structure, including Fe-doped InAs and Mn-doped GaSb, InSb, and InAs. Here we study systematically the origin of high temperature ferromagnetism in Fe, Mn, Cr-doped GaSb, InSb, and InAs magnetic semiconductors by combining the methods of density functional theory and quantum Monte Carlo. In the diluted impurity limit, the calculations show that the impurities Fe, Mn, and Cr have similar magnetic correlations in the same semiconductors. Our results suggest that high (low) $T_c$ obtained in these experiments mainly comes from high (low) impurity concentrations. In addition, our calculations predict the ferromagnetic semiconductors of Cr-doped InSb, InAs, and GaSb that may have possibly high $T_c$. Our results show that the origin of high $T_c$ in (Ga,Fe)Sb and (In,Fe)Sb is not due to the carrier induced mechanism because ${\mathrm{Fe}}^{3+}$ does not introduce carriers.

Figure 1

(a) The crystal structure of InSb and (b) its first Brillouin zone with high symmetry paths indicated. (c) Energy bands ${\epsilon }_{\alpha }$ of host semiconductor InSb. A direct band gap of 0.17 eV was obtained by DFT calculations with the modified Becke-Johnsom (mBJ) exchange potential, which agrees well with the experimental value.

Figure 2

The mixing function between $\xi$ orbitals of an Fe impurity ($3d$ electrons) and InSb host for (a) valence bands and (b) conduction bands.

Figure 3

For Fe-doped InSb, chemical potential $\mu$ dependent (a) occupation number $\langle n_{\xi }\rangle$ of $\xi$ orbital of an Fe impurity, and (b) magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between the $\xi$ orbitals of two Fe impurities with fixed distance $R_{12}$ of the first-nearest neighbor at temperature of 360 K with ${\varepsilon }_d=-2$ eV. (c) and (d) are the same physical quantities as (a) and (b) with ${\varepsilon }_d=-1$ eV.

Figure 4

For Fe-doped InSb, the distance $R_{12}$ dependent magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between the $\xi$ orbitals of two Fe impurities for (a) $p$-type case with chemical potential $\mu =0$ eV and (b) $n$-type case with $\mu =0.2$ eV, where temperature is 360 K.

Figure 5

The mixing function between $\xi$ orbitals of a Mn impurity and InSb host for (a) valence bands and (b) conduction bands.

Figure 6

For Mn-doped InSb, chemical potential $\mu$ dependent (a) occupation number $\langle n_{\xi }\rangle$ of $\xi$ orbital of a Mn impurity, and (b) 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 at temperature 360 K with ${\varepsilon }_d=-1$ eV.

Figure 7

For Mn-doped InSb, the distance $R_{12}$ dependent magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between the $\xi$ orbitals of two Mn impurities for (a) $p$-type case with chemical potential $\mu =0$ eV and (b) $n$-type case with $\mu =0.15$ eV, where temperature is 360 K.

Figure 8

The mixing function between $\xi$ orbitals of a Cr impurity and InSb host for (a) valence bands and (b) conduction bands.

Figure 9

For Cr-doped InSb, chemical potential $\mu$ dependent (a) occupation number $\langle n_{\xi }\rangle$ of $\xi$ orbital of a Cr impurity, and (b) magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between $\xi$ orbitals of two Cr impurities with fixed distance $R_{12}$ of the first-nearest neighbor at temperature 360 K with ${\varepsilon }_d=-1$ eV.

Figure 10

For Cr-doped InSb, the distance $R_{12}$ dependent magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between $\xi$ orbitals of two Cr impurities for (a) $p$-type case with chemical potential $\mu =0$ eV and (b) $n$-type case with $\mu =0.15$ eV, where temperature is 360 K.

Figure 11

Energy bands ${\epsilon }_{\alpha }$ of host InAs, which has the same space group as InSb. A direct band gap of 0.42 eV was obtained by DFT calculations, which agrees well with the experimental value.

Figure 12

For Fe-doped InAs, chemical potential $\mu$ dependent (a) occupation number $\langle n_{\xi }\rangle$ of $\xi$ orbital of an Fe impurity, and (b) magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between $\xi$ orbitals of two Fe impurities with fixed distance $R_{12}$ of the first-nearest neighbor at temperature of 360 K with ${\varepsilon }_d=-1$ eV.

Figure 13

For Fe-doped InAs, the distance $R_{12}$ dependent magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between $\xi$ orbitals of two Fe impurities for the $p$-type case with chemical potential $\mu =0.1$ eV, where temperature is 360 K.

Figure 14

For Mn-doped InAs, chemical potential $\mu$ dependent (a) occupation number $\langle n_{\xi }\rangle$ of $\xi$ orbital of a Mn impurity, and (b) magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between $\xi$ orbitals of two Mn impurities with fixed distance $R_{12}$ of the first-nearest neighbor at temperature of 360 K with ${\varepsilon }_d=-1$ eV.

Figure 15

For Mn-doped InAs, the distance $R_{12}$ dependent magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between $\xi$ orbitals of two Mn impurities for the $p$-type case with chemical potential $\mu =0$ eV, where temperature is 360 K.

Figure 16

For Cr-doped InAs, chemical potential $\mu$ dependent (a) occupation number $\langle n_{\xi }\rangle$ of $\xi$ orbital of a Cr impurity, and (b) magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between $\xi$ orbitals of two Cr impurities with fixed distance $R_{12}$ of the first-nearest neighbor at temperature 360 K with ${\varepsilon }_d=-1$ eV.

Figure 17

For Cr-doped InAs, the distance $R_{12}$ dependent magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between $\xi$ orbitals of two Cr impurities for the $p$-type case with chemical potential $\mu =0.1$ eV, where temperature is 360 K.

Figure 18

Energy bands ${\epsilon }_{\alpha }$ of host GaSb, which has the same space group as InSb. A direct band gap of 0.75 eV was obtained by DFT calculations, which agrees well with the experimental value.

Figure 19

For Fe-doped GaSb, chemical potential $\mu$ dependent (a) occupation number $\langle n_{\xi }\rangle$ of $\xi$ orbital of an Fe impurity, and (b) magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between $\xi$ orbitals of two Fe impurities with fixed distance $R_{12}$ of the first-nearest neighbor at temperature of 360 K with ${\varepsilon }_d=-1$ eV.

Figure 20

For Fe-doped GaSb, the distance $R_{12}$ dependent magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between $\xi$ orbitals of two Fe impurities for the $p$-type case with chemical potential $\mu =0.1$ eV, where temperature is 360 K.

Figure 21

For Mn-doped GaSb, chemical potential $\mu$ dependent (a) occupation number $\langle n_{\xi }\rangle$ of $\xi$ orbital of an Mn impurity, and (b) magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between $\xi$ orbitals of two Mn impurities with fixed distance $R_{12}$ of the first-nearest neighbor at temperature of 360 K with ${\varepsilon }_d=-1$ eV.

Figure 22

For Mn-doped GaSb, the distance $R_{12}$ dependent magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between $\xi$ orbitals of two Mn impurities for the $p$-type case with chemical potential $\mu =0.1$ eV, where temperature is 360 K.

Figure 23

For Cr-doped GaSb, chemical potential $\mu$ dependent (a) occupation number $\langle n_{\xi }\rangle$ of $\xi$ orbital of a Cr impurity, and (b) magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between $\xi$ orbitals of two Cr impurities with fixed distance $R_{12}$ of the first-nearest neighbor at temperature of 360 K with ${\varepsilon }_d=-1$ eV.

Figure 24

For Cr-doped GaSb, the distance $R_{12}$ dependent magnetic correlation $\langle M_{1\xi }^z{M}_{2\xi }^z\rangle$ between $\xi$ orbitals of two Cr impurities for the $p$-type case with chemical potential $\mu =0.2$ eV, where temperature is 360 K.

Figure 25

(a) $12.5\%$ doping concentration for Fe-doped InSb in a supercell of InSb containing eight In atoms and the views from (b) [100] and (c) [001] directions, where we have only plotted the magnetic atoms (Fe atoms) and the supercell is indicated.