Optoelectronic and magnetic properties of Mn-doped and Mn–C co-doped Wurtzite ZnS: a first-principles study

To induce a magnetic ground state in pure ZnS, we doped Mn atom at Zn-site as shown in figure 3(a). It is found experimentally that TMs like Co, In, and Pt can be doped in solid material by pulsed laser deposition [46]. If one Zn atom is replaced by Mn atom in the host supercell of 2  ×  2  ×  2, leading to 6.25% Mn concentration. After relaxation, the calculated the average bond length Mn–S is 2.38Å, which is smaller than that of Zn–S because of the difference in the atomic size of Mn and Zn.

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In order to check the stability of the Mn-doped ZnS, first we performed magnetic and non-magnetic ground state calculations, and we find that the magnetic ground state is more favorable than the non-magnetic ground state of the doped system. The formation energy for Mn-doped ZnS can be calculated by the following relation

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{E}_{{\rm f}}}={{E}_{{\rm doped}}}-{{E}_{{\rm ZnS}}}+{{\mu }_{{\rm Zn}}}-{{\mu }_{{\rm Mn}}}.\nonumber \end{align} \tag{ 1 }$$

Where ${{E}_{{\rm doped}}}$, and ${{E}_{{\rm ZnS}}}$ are the total energies of Mn-doped ZnS and pure ZnS respectively. The chemical potential ${{\mu }_{{\rm Mn}}}$ of Mn dopant is equal to the total energy per Mn atom in bulk structure while chemical potential ${{\mu }_{{\rm Zn}}}$ depend on the growth conditions, Zn-rich and S-rich conditions. In order to estimate the chemical potential ${{\mu }_{{\rm Zn}}}$, we use the relation ${{\mu }_{{\rm ZnS}}}={{\mu }_{{\rm Zn}}}+{{\mu }_{{\rm S}}}$. For Zn-rich condition, ${{\mu }_{{\rm Zn}}}$ is equal to the total energy of Zn per atom in the hexagonal crystal structure and for S-rich condition, ${{\mu }_{{\rm Zn}}}$ is equal to ${{\mu }_{{\rm ZnS}}}-{{\mu }_{{\rm S}}}$ where ${{\mu }_{{\rm S}}}={{E}_{{\rm S}}}$ (total energy of S per atom in the S8 structure) and ${{\mu }_{{\rm ZnS}}}={{E}_{{\rm ZnS}}}$ (total energy of pure ZnS per formula unit). Therefore, the formation energy of Mn-doped ZnS is  +1.74 eV under Zn-rich condition while that is  −6.65 eV under S-rich condition. The negative formation energy means that under S-rich condition Mn-doped ZnS is easier to fabricate than that in Zn-rich condition.

To see the effects of Mn doping on the electronic and magnetic properties, we have calculated spin-polarized BS and density of state (DOS). In figure 5(a), we have shown spin-polarized BS, which is calculated along high symmetry direction (Г-M-K-H-L-A-Г) of the first BZ. The calculated band gaps are 2.82 eV and 3.34 eV for up-spin and down-spin channels, respectively.

In order to understand the electronic properties of Mn-doped ZnS system in more detail, we computed the total density of state (TDOS) of Mn-doped ZnS and partial density of states (PDOS) of 3d-states of Mn atom and 3p-states of the nearest-neighboring S atoms as a function of energy as shown in figure 5(b). The calculated TDOS shows asymmetric distribution between up-spin and down-spin channels, which demonstrates the spin polarization for Mn-doped ZnS system. According to crystal field theory 'the 3d-state of Mn is decomposed into two sub-states' one is doubly degenerate states ${{e}_{{\rm g}}}$ (${{d}_{{{x}^{2}}}}$, ${{d}_{{{z}^{2}}}}$) and other is triply degenerate state ${{t}_{2{\rm g}}}$(${{d}_{xy}}$, ${{d}_{yz}}$, ${{d}_{xz}}$) under the action of the tetrahedral field formed by S-atoms around Mn ion'. But for the hexagonal structure, the d-state is divided into three states e₁ (${{d}_{yz}}$, ${{d}_{xz}}$), e₂ (${{d}_{xy}}$, ${{d}_{{{x}^{2}}}}$) and a (${{d}_{{{z}^{2}}}}$). Since Mn dopant has five electrons in 3d-state. According to Hund's rule, these sub-states are filled with the five up-spin electrons, so these states located below the Fermi energy level are shown in the PDOS of Mn-3d state. These five up-spin electrons in 3d-states are responsible to induce the spin polarization in the system with the total magnetic moment of 5 µ_B. The spin-down channel of these sub-states are empty, and therefore located the above the Fermi energy level. Near the Fermi level, the 3d-states of Mn play an important role in the magnetic properties. We see that near the Fermi-level, Mn-3d states hybridize with S-3p  states. Due to this p -d hybridization, the up-spin and down-spin channels at the valence band are unbalanced and the spin-polarization induces in the system. In figure 4(b), we plot 3D iso-surface of spin density for a single Mn doped ZnS system. It can be seen clearly that the spin density distribution is largely localized on Mn dopant and distributed over the nearest neighboring S atoms which indicates that the wave function of the Mn-3d states is spatially extended to the nearest neighboring S atom and interact to the 3p  states of S atoms. We can also see that Mn doping polarizes the neighboring S atoms in the same direction. It can be seen that a large portion of magnetization is localized around Mn and little localized around non-magnetic sites Zn and S due to p-d hybridization. Due to this p-d hybridization, the local magnetic moment of Mn is reduced to 4.30 µ_B. Xie [44] obtained similar results for a local and total magnetic moment in his first principle study of magnetic properties of the Mn doped wurtzite-ZnS. The magnetic moment on each atom in Mn doped ZnS supercell is tabulated in table 1. The small magnetizations induced at non-magnetic sites Zn and S (nearest neighboring S and Zn atoms of Mn) are due to the sharing of electronic charge through hybridization between Mn-3d states and the bands of the host semiconductor [47].

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Table 1. The total magnetic moment of supercell $M{{M}_{{\rm tot}}}$ (${{\mu }_{{\rm B}}}$) and local magnetic moments $M{{M}_{{\rm loc}}}$ (${{\mu }_{{\rm B}}}$) on each atoms Mn and its nearest Zn, and S atoms and, C in Mn-doped and Mn–C co-doped and pure ZnS configurations.

Systems	$M{{M}_{{\rm zn}}}$	$M{{M}_{{\rm S}}}$	$M{{M}_{{\rm Mn}}}$	$M{{M}_{{\rm C}}}$	$M{{M}_{{\rm tot}}}$
Pure ZnS	0.00	0.00	—	—	0.00
Mn-doped ZnS	0.012	0.02	4.30		5.00
Mn–C co-doped ZnS	−0.026	−0.024	3.64	−0.43	3.00
C doped ZnS	0.066	0.046	—	0.85	2.00

In order to study the interaction between Mn ion and bands of the host semiconductor, we calculated the exchange constants Noβ and Noα. The Noβ shows the interaction of valence band of the host with magnetic ion (p-d-coupling) and Noα indicates the interaction of conduction band with magnetic ion (s-d coupling). These two parameters are very important for the analysis of band edge splitting and p-d hybridization. The band edge splitting depends upon the value of exchange constants and depends on the concentration of magnetic impurities (n). On the basis of mean field theory, these two exchanges constants can be determined by using the following relations

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{N}_{0}}\beta =\frac{\Delta {{E}_{{\rm v}}}}{\left\langle S \right\rangle n}\nonumber \end{align} \tag{ 2 }$$

and

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{N}_{0}}\alpha =\frac{\Delta {{E}_{{\rm c}}}}{\left\langle S \right\rangle n}.\nonumber \end{align} \tag{ 3 }$$

N₀β and N₀β are exchanged constants and $\Delta {{E}_{{\rm v}}}=E{{v}^{\downarrow ~}}-E{{v}^{\uparrow }}$ and $\Delta {{E}_{c}}=E{{c}^{\downarrow }}-E{{c}^{\uparrow }}$ are the valence band edge and conduction band edges splitting respectively and $\left\langle {\rm S} \right\rangle$ is one half of the total magnetization. The calculated $\Delta {{E}_{{\rm v}}}$ and $\Delta {{E}_{{\rm c}}}$ are  −0.48eV and 0.12eV respectively. Using these value in the above two equations (2) and (3), the obtained value of ${{N}_{0}}\beta$ and ${{N}_{0}}\alpha$ are  −4.16 eV and 0.51 eV respectively. The negative value of N₀β indicates that coupling between magnetic moment on dopant atom and band electrons is attractive and thus antiferromagnetic. And the positive N₀α shows that s-d interaction is repulsive and ferromagnetic [48].

To investigate magnetic interaction between the spins of Mn ions in Mn-doped ZnS system, two Mn atoms are substituted at the Zn sites in Mn-doped ZnS supercell, leading 12.5% concentrations of Mn in the system. As sketch in figure 3(c), two configurations 'near' and 'far' with substitutional sites (1,2) and (1,3) respectively are considered. The separation between two Mn ions is 3.76 Å in near configuration and 6.16 Å in the far configuration. For each configuration, we calculated the energy difference between AFM (ant-parallel spin orders) and FM (parallel spin orders) states. This energy difference is used to indicate the stabilization of the magnetic ground state. If the FM state energy is lower than AFM state energy, then the stable magnetic ground state is FM state otherwise AFM state. The calculated energy difference (ΔE) between AFM and FM states in near and far configurations are  −187.5 meV and  −6 meV respectively. We see that in both configurations, the energy difference (ΔE) is negative i.e. the AFM energy is smaller than the energy of FM state, which indicates that AFM state in both configurations is stable. Our finding is consistent with the experimental report [29]. From the total energy calculations for AFM states in both near and far configurations, we found that near configuration is lower in energy than far configuration, it demonstrates that near configuration is most stable.

We have performed one calculation for 3  ×  3  ×  2 ZnS supercell doped with two Mn atoms separated by one S atom in order to confirm that our results are consistent and to be close to the concentration of dopants used experimentally. Doping two Mn atoms at Zn sites in the supercell leads to 5.6% Mn concentrations, which are close to the ones used in the experiments [29, 49]. We calculate the energy difference between AFM and FM states and found that ΔE is  −92 meV. It means that the total energy for the AFM state is 92 meV lower than the FM state, showing that the ground state is AFM. Therefore, our analysis remains valid for a wide range of Mn concentration in the system.

Figure 6 depicts the density of states DOSs for 12.5% Mn-doped ZnS in stable configuration (near) with AFM state. One can see that the system shows semiconducting behavior in the AFM state. It is portrayed that unoccupied d-states of Mn atoms are at 2.32 eV above the Fermi level. It means that Mn-doped ZnS system in AFM configuration absorbs 2.32 eV during the optical d-d transition, which is in good agreement with the experimental study of Mn-doped ZnS nanobelts [24]. It is interesting to note that the Mn doping at Zn sites does not produce holes around the Fermi level to mediate long-range FM coupling. Therefore, the interaction between Mn spins is AFM under the super-exchange mechanism [50]. In super-exchange interactions, no electronic hopping is taking place between Mn ions during interactions.

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Before determining electronic and magnetic properties of (Mn C) co-doped ZnS, we first calculate the total energy for (Mn C) co-doped system with C atom at five different positions as shown in figure 4(a). In table 2, the calculated results are listed. We can see that the total energy of (C, Mn) co-doped with C atom position at P1 is lower than that for other positions. This depicts that the C atom prefers to locate near the Mn atom. We also see that the energy difference at P2, P3, P4, and P5 are close to one another. This means that the interaction between C atom and Mn atom in (C, Mn) co-doped ZnS system is insensitive to the distance once the distance exceeds 2.35 Å.

When C atom is substituted at S site at the P1 position, then we optimize the structure of C, Mn co-doped ZnS. The optimized structure is shown in figure 3(b). After optimization, the bond length between C–Zn and C–Mn are 2.09 Å and 1.92 Å respectively.

For structure stability of C, Mn co-doped ZnS, we calculate the formation energy using the following equation

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{E}_{{\rm f}}}={{E}_{{\rm co{{\text -}}doped}}}-{{E}_{{\rm ZnS}}}+{{\mu }_{{\rm Zn}}}+{{\mu }_{{\rm S}}}-{{\mu }_{{\rm Mn}}}-{{\mu }_{{\rm C}}}.\nonumber \end{align} \tag{ 4 }$$

Where ${{E}_{{\rm co{{\text -}}doped}}}$, and ${{E}_{{\rm ZnS}}}$ are the total energy of (C, Mn) co-doped ZnS,and pure ZnS respectively. ${{\mu }_{{\rm Zn}}}$, ${{\mu }_{{\rm S}}}$, ${{\mu }_{{\rm Mn}}}$ and ${{\mu }_{{\rm C}}}$ are the chemical potentials of Zn, S, Mn, and C respectively. The calculated formation energies for (Mn C) co-doped ZnS in Zn-rich and S-rich conditions are 7.25 eV and  −1.17 eV respectively. The formation energy under S-rich condition is negative, which indicates that C, Mn co-doped ZnS can be easily fabricated experimentally under S-rich condition. Thus, the ferromagnetism in Mn doped ZnS can be induced by co-doping with C atom in S-rich condition.

For the investigation of the electronic structure for (Mn, C) co-doped ZnS with C atom at position P1, we calculated the energy BS along high symmetry direction as shown in figure 7(a). We can see that (Mn–C) co-doped ZnS is half-metallic material since the up-spin channel crosses the Fermi level and therefore, the material can be used in a spintronic device for producing spin-polarized current [51]. In co-doped ZnS system, the band edges splitting ΔE_v and ΔE_c are  +0.16 eV and  +0.11 eV respectively. Therefore, the calculated N₀α and N₀β are  +0.70 eV and1.02 eV, respectively.

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In order to shed light on the electronic structure of (C, Mn) co-doped ZnS in detail, the total density of state (TDOS) and partial density of state (PDOS) for (Mn, C) co-doped system are calculated and shown in figure 7(b). Compared to ZnS doped with Mn, ZnS co-doped with (C, Mn) is half metallic. The defects level appears at the Fermi-level, mostly contributed by the 3p -states of S and C and 3d-states of Mn ion.

In an ionic picture, when the C atom is doped at the site of S atom, it provides two holes to the system because the C-2p  state carries two less electrons than S-3p  state. Thus C-atom behaves as acceptor. The Fermi level, as a result, moves downward and up-spin Mn-3d orbitals are now partially filled rather than fully filled orbitals for ZnS doped with Mn. The C-2p  state in Mn–C co-doped ZnS are also partially occupied and strongly hybridized with Mn-3d (e2) orbitals. The total magnetization per supercell containing one Mn atom and one C atom is 3.00 ${{\mu }_{{\rm B}}}$. In order to calculate magnetization on each atom, we calculate the spherical integration of the spin density using VASP default atomic radii of Zn (1.27 Å), S (1.164Å), C (0.863Å), and Mn (1.323Å). The local magnetic moment of Mn, C, S and Zn atoms are listed in the table 1. We can see that the magnetic moment of S and C are negative and that of Mn is positive. It means that the interactions of S and C with Mn are antiferromagnetic. In figure 4(c), the spin distribution for (Mn, C) co-doped ZnS is displayed. It is clearly seen that the spin density is largely localized at the Mn and C atoms and little localized at nearest neighboring S and Zn atoms. Hence, the magnetism comes from the C and Mn atoms in Mn–C co-doped system.

Additionally, we investigate the properties of C doped ZnS. One S atom in the 2  ×  2  ×  2 supercell is replaced by C atom, leading to 6.25% concentration. After the structure relaxation, the local structure around the C-atom is suppressed slightly with Zn-atoms drawn closer to the C-dopant, the average bond length between C–Zn (2.08 Å) is smaller than that of S–Zn (2.31 Å). Then we calculate the total energy for spin-polarized and non-spin polarized states. We find that the total energy of spin-polarized state is 86 meV lower than the non-spin polarized state, indicating that spin-polarized state is favorable in C doped ZnS with total magnetization (2 µ_B) which is in good agreement with the previous report [52].

In order to show the extended spin-polarized defect states produced by C in 2  ×  2  ×  2 supercell of ZnS, we calculate the spatial spin distribution, as shown in figure 4(d). We can see that a large portion of the total magnetization come from the C atom. It can be seen that along with C, it is neighboring S, Zn, and next to neighboring S are also polarized with same spin direction and the spin moment is largely extended. Therefore, it can be expected that extended spin density destribution caused by C doping may play an important role to mediate the long range FM coupling between magnetic impurities in the magnetic semiconductor. Table 1 tabulates the results for the local magnetic moment of C and its nearest Zn and S atoms, which are in line with the calculated the spatial spin distribution, as shown in figure 4(d).

In order to study the magnetic coupling between Mn ions in Mn–C co-doped ZnS. We considered five different configurations C-1(1, 2, x), C-2 (1, 2, y ), C-3 (1, 2, z), D-1 (1, 3, y ) and D-2 (1, 3, z) as shown in figure 3(c). In C Configurations the distance between two Mn atoms is 3.824 Å while in D configurations, the two Mn atoms are separated by 5.25 Å. We calculated the energy difference between FM and AFM state for all configurations. The calculated energy difference between AFM and FM state for each configuration and magnetic moments of both Mn ions in (C, Mn) co-doped ZnS are listed in table 3. We found that the energy difference between AFM and FM states is positive, showing that FM states are stable in all configurations, except C-2 configuration. The total energy of C-1 is lower than that of all configurations. It means that stable ground state configuration is C-1.

Table 3. The calculated the energy difference ΔE (meV) between AFM and FM states, favorable magnetic state (MS) and local magnetic moment $M{{M}_{{\rm lol}}}$ (${{\mu }_{{\rm B}}}$) of two Mn atoms replace the Zn atoms in Mn–C co-doped supercell with the mentioned configurations. C-1, C-2, C-3, D-1,and D-2 indicate different configurations in (C, Mn) co-doped ZnS, as shown in figure 3(c).

Configurations	ΔE	MS	$M{{M}_{{\rm lol}}}$
C-1 (1, 2, x)	720	FM	4.03/4.03
C-2 (1, 2, y )	−36.00	AFM	3.67/4.39
C-3 (1, 2, z)	98.00	FM	4.36/4.36
D-1 (1, 3, y )	20.00	FM	3.66/4.36
D-2 (1, 3, z)	10.00	FM	3.71/4.40

In order to study ferromagnetism in C-1 for (Mn, C) co-doped ZnS, we plot TDOS and PDOS of S-3p , C-2p , Mn1-3d, and Mn2-3d, as shown in figure 8(a). After C co-doping in between two Mn atoms in configuration C-1, the material reveals a half-metallic nature with the spin up channel being metallic and the spin down channel being semiconducting. The 100% spin polarization at the Fermi level suggests that (C, Mn) co-doped ZnS may play an important role in spin injection where spin polarized current is highly desired [53]. It is found that 3d states of both Mn atoms exists at the Fermi level due to the symmetric position of Mn1 and Mn2 relative to the position of C-atom as shown in PDOS of Mn1 and Mn2 ions. We can also see that besides Mn1-3d and Mn2-3d states, C-2p, and S-3p  states are also spin polarized with partial occupied states. Therefore, Zener double exchange mechanism [54] is responsible for ferromagnetic interaction between Mn spins in (Mn, C) co-doped ZnS. During the ferromagnetic coupling, the hoping of an electron from one Mn1-3d states to another Mn2-3d states is possible, provided the neighboring Mn atoms have parallel spins. Thus, the kinetic energy of the system in the FM state is lowered.

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It is also found that the magnetic moment of Mn in free space (5.00 $\mu {\rm s}$) is greater than that of Mn ions (4.03/4.03 ${{\mu }_{{\rm B}}}$) in the co-doped system. The decrease in the magnetic moment of Mn ions in the co-doped system is because of the strong interaction between Mn-3d and C-2p  orbitals. From the table, we can see that both Mn ions in C-1 configuration have nearly the same magnetic moments. This is due to the fact that the C atom is located between two Mn atoms at the same distance. So the interaction of C atom with both Mn atoms are equal. The C atom, on another hand, contributes about  −0.42 ${{\mu }_{{\rm B}}}$ magnetic moments to the system. Consequently, in C-1, the ferromagnetic state with total the magnetic moment of 8.00 ${{\mu }_{{\rm B}}}$ is favorable than the AFM state by 710 meV. This energy difference 710 meV is greater than that of C Mn co-doped ZnO (656.7 meV) [22].

Next, we study the long-range ferromagnetic interaction between Mn spins; we study the configuration D-1 where –C–Zn–S– along (0 0 0 1) direction separates two Mn atoms, and C-atom is bounded to one of Mn atoms. From the table 3, it can be seen that in configuration D-1, the energy difference between AFM and FM state is 20 meV. Therefore, we predict that C co-doping can induce long-range ferromagnetism in (C, Mn) co-doped system.

To discuss the cause of long-range magnetism in (C, Mn) co-doped ZnS, we plot total density of states (TDOS) of (C, Mn) co-doped ZnS and partial density of states (PDOS) of Mn1-3d and Mn3-3d states, C-2p  state, and S-3p  state in D-1 configuration as shown in figure 8(b). We see that the Fermi level exists around the Fermi level, showing that the system with FM state in configuration D-1 also shows half-metallic semiconducting. The Mn1-3d state in the up-spin channel is partially filled while 3d-state of Mn3 are completely filled because, with respect to the position of C-atom, both Mn1 and Mn3 have asymmetric coordination. As depicted in figure 8(b), Mn1-3d, C-2p , and S-3p  states are spin polarized states with partial occupied states. Therefore, the interaction of those partially filled up-spin orbitals makes them ferromagnetic coupling, forming the configuration D-1 ferromagnetic. Due to asymmetry coordination of both Mn atoms with respect to C atom, the magnetic moment of Mn1 atom (which is bonded to C-atom) is smaller than that of another Mn3 atom (which is not bonded to C atom). Thus, the interaction of Mn1 with C atom is stronger than that of Mn3 with C-atom. This fact can be seen from PDOS that Mn1 has partial 3d-state due to strong interaction with C atom and during the interaction, electrons from 3d-state of Mn1 transfer to 2p  state of C atom, so 3d-state of Mn1 atom become partial occupied and cross the Fermi energy level. We can see also that Mn3 has half-filled 3d-state. It means that no electron transfers from 3d-state of Mn3 to the 2p  state of C-atom, indicating negligible interaction of Mn3 with C-atom.

In order to investigate the magnetic coupling in (C, Mn) co-doped ZnS with 5.6% Mn and 2.8% C concentrations, we have performed the additional calculation for the total energy of AFM and FM state in 3  ×  3  ×  2 ZnS supercell with two Mn atoms at Zn sites and one C atom at S site. We found that ground state of (C, Mn) co-doped ZnS is still FM and its energy is 738 meV lower than that of AFM state. Thus, for a wide range of concentration of Mn impurity, (Mn, C) co-doped ZnS should be ferromagnetic.