Diluted magnetic semiconductors (DMSs), which are semiconductors doped with magnetic impurities, have attracted extensive attention due to their potential applications in spintronic devices as well as their fundamental scientific values.^[1–7] Experimentally, the synthesis of materials combining the semiconducting behavior with the robust ferromagnetism has long been a dream of material physicists and much effort has actually been devoted to searching for such materials with Curie temperature (T_c) above room temperature.^[8–13] Theoretically, the focus is placed on understanding the magnetic mechanism in order to provide suggestions for exploring high-T_c materials.^[14–18] However, despite several decades of intensive work, the preparation of materials with practical feasibility is still a challenge and the complexity of real materials often hinders a clear theoretical understanding.

The exploration of DMS materials mainly involves the semiconductors doped with an Mn atom due to its large local magnetic moment. In the early days, the Mn-doped compounds were often chosen as prototypical systems,^[14] as the isovalent (Mn²⁺, A^II) substitution would make them easy to achieve a high solubility of Mn. However, the initial charge doping in the II–VI-based DMSs, no matter whether n-type or p-type, was difficult, until the later progress in charge doping leads to the emergence of their ferromagnetism.^[19–22] Subsequently, the III–V-based DMSs were widely studied due to their compatibility with the present-day electronic materials. Among them, the (Ga, Mn)As has achieved a T_c around 200 K.^[13] Nevertheless, due to the hetero-valent (Mn²⁺, Ga³⁺) substitution, the equilibrium solubility of Mn in the III–V compounds is very small, such DMS samples are thus often prepared as films by a non-equilibrium epitaxial growth technique.^[22] Moreover, the hetero-valent (Mn²⁺, Ga³⁺) substitutions introduce spins and holes simultaneously, which makes the independent control of spin- and charge-dopings impossible.^[22] Recently, the I–II–V compound Li(Zn, Mn)As,^[23] the II–II–V compound (Ba, K)(Zn, Mn)₂As₂,^[24] and the III–VI–II–V compound (La, Ba)O(Zn, Mn)As,^[25] which are respectively isostructural to the well-known ‘111’, ‘122’, and ‘1111’ iron-based superconductors LiFeAs,^[26] BaFe₂As₂,^[27] and LaOFeAs,^[28] have been reported as new types of DMS materials. The T_c of (Ba_0.7K_0.3)(Zn_0.85Mn_0.15)₂As₂ even reaches ∼230 K,^[29] higher than the record value achieved in (Ga, Mn)As. More importantly, in this new ‘122’ type DMS material, the spin doping by isovalent (Mn²⁺, Zn²⁺) substitution and the charge doping by hetero-valent (Ba²⁺, K⁺) substitution decouple with each other, thus providing us with a unique opportunity to study the magnetic mechanism in DMS.

From the theoretical standpoint, previous works on the (Ba_1−xK_x)(Zn_1−yMn_y)₂As₂ compound^[30–33] propose the existence of both short-range antiferromagnetic (AFM) interactions via superexchange and long-range ferromagnetic (FM) interactions mediated by itinerant holes. Thus, the nearest-neighbour Mn atoms often take the AFM coupling, yielding a reduction of the mean magnetization of all Mn atoms compared with the local moment of Mn²⁺. Furthermore, the analysis based on density functional theory (DFT) calculations by Mazin et al. gave an excellent agreement of magnetization between their calculation results and experiment data, which demonstrates that the DFT can play an important role in understanding these recently discovered II–II–V type DMS materials.^[30]

As a counterpart of (Ba_1−xK_x)(Zn_1−yMn_y)₂As₂, (Ba_1−xK_x)(Zn_1−yMn_y)₂P₂ (with P atom substituting the same group As) is expected to be a similar DMS. More importantly, the substitution of As with P would introduce some changes in the magnetic properties of (Ba_1−xK_x)(Zn_1−yMn_y)₂P₂, the study on which may enable us a complete understanding on the exchange interactions in this prototypical DMS material and may provide guidance for searching more feasible DMS candidates. Here, we have carried out systematic investigations on the proposed (Ba_1−xK_x)(Zn_1−yMn_y)₂P₂ compound to explore the magnetic interactions in it.

First-principles electronic structure calculations were performed by using the projector augmented wave (PAW) method^[34,35] as implemented in the Vienna ab initio Simulation Package.^[36–38] The generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE) type was employed for the exchange–correlation functional.^[39] The kinetic energy cutoff of the plane-wave basis was set to be 400 eV. A fully variable-cell relaxation of BaZn₂P₂ unit cell with 10 atoms was first carried out to obtain the equilibrium lattice parameters under different pressures. The criteria for force convergence on all atoms was 0.01 eV/Å. Then the properties of the BaZn₂P₂ parent compound were studied. By tripling these relaxed unit cells along both a and b directions, we obtained the expanded supercells containing 90 atoms for later studies on the effects of spin- and charge-dopings.

The supercell we used is schematically shown in Fig. 1(a). It contains two Zn layers stacked along the [001] direction. For the spin doping, we used two Mn atoms to substitute two Zn atoms respectively, which introduces a doping concentration of 5.6%. The two Mn atoms can locate either in the same Zn layer or in different Zn layers. In the same Zn layer, they can locate at sites 0, 1, 2, 3, 4, or 6 [Fig. 1(b)] to form Mn–Mn pairs denoted as 0–1, 0–2, 0–3, 0–4, and 0–6, corresponding to the first, second, third, fourth, and sixth neighbors, respectively. If the corresponding substitution sites of Mn in the other Zn layer are denoted by 0′, 1′, 2′, 3′, 4′, and 6′, the two Mn atoms can also form Mn–Mn pairs named 0–0′, 0–1′, 0–2′, 0–3′, 0–4′, and 0–6′ respectively. For all supercells of Ba(Zn_0.944Mn_0.056)₂P₂, we relaxed the internal atomic positions only. Regarding the charge doping, we employed the virtual crystal approximation (VCA), in which the Ba sites were composed of 75% Ba²⁺ and 25% K⁺. Both the concentrations of spin doping 5.6% and hole doping 25% are typical experimental values for the ‘122’ type DMSs.^[24] The electronic correlation effect among Mn 3d electrons was incorporated by the DFT + U formalism according to the method of Dudarev et al. (effective U).^[40] The value of effective U was set to 3.0 eV, which had been used and discussed carefully in the previous work for compounds Li(Zn, Mn)As^[41,42] and (Ba, K)(Zn, Mn)₂As₂.^[31]

Fig. 1.

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	Fig. 1. (color online) (a) The schematic diagram of the BaZn2P2 supercell. (b) The substitution sites of Mn atoms in the same Zn layer. Two Mn atoms are arranged as 0–1, 0–2, 0–3, 0–4, and 0–6 pairs, while the integers represent the sequences of Mn neighbors.

It is known that for the BaZn₂As₂, namely the counterpart of BaZn₂P₂, there are two crystalline phases: the low-temperature orthorhombic phase (α-BaZn₂As₂ with space group Pnma) and the high-temperature tetragonal phase (β-BaZn₂As₂ with space group I4/mmm).^[43] Experimentally, under low temperature, the stable β-BaZn₂As₂ at ambient condition can be obtained by the rapid quenching method.^[44] Moreover, 10% of K or Mn doping can stabilize the tetragonal β-BaZn₂As₂ down to 3.5 K.^[24] Here, we take the tetragonal β-BaZn₂P₂ to perform the calculations. At ambient pressure, the calculated equilibrium lattice constants of the BaZn₂P₂ (BaZn₂As₂) tetragonal unit cell are a = 4.039 Å (4.156 Å) and c = 13.280 Å (13.641 Å), which are in good accordance with the experimental values a = 4.019 Å (4.12 Å) and c = 13.228 Å (13.58 Å).^[24,43,45] Actually, according to our calculations, the energy of β-BaZn₂P₂ (β-BaZn₂As₂) is just 0.138 (0.148) eV per formula unit higher than that of α-BaZn₂P₂ (α-BaZn₂As₂).

We implement further first-principles calculations on the (Ba_0.75K_0.25)(Zn_0.944Mn_0.056)₂As₂ compound at the GGA level, in order to make a comparison with the (Ba_0.75K_0.25)(Zn_0.944Mn_0.056)₂P₂ compound. At ambient pressure, the calculated local moments on Mn atoms for all the defined Mn–Mn pairs [Fig. 1(b)] in (Ba_0.75K_0.25)(Zn_0.944Mn_0.056)₂P₂ range from 3.25 to 3.50μ_B, which are about 0.2μ_B smaller than those in (Ba_0.75K_0.25)(Zn_0.944Mn_0.056)₂As₂. This is a signal that the p–d hybridization is stronger in the former one. Furthermore, when two Mn atoms are located at different Zn layers in the supercell, the ferromagnetic couplings for all Mn–Mn pairs in (Ba_0.75K_0.25)(Zn_0.944Mn_0.056)₂P₂ are stronger than those in (Ba_0.75K_0.25)(Zn_0.944Mn_0.056)₂As₂ (Table 1). The stronger effective FM couplings between interlayer Mn–Mn pairs in (Ba_0.75K_0.25)(Zn_0.944Mn_0.056)₂P₂ may partially help the improvement of the T_c.

Table 1.

Table 1.

Table 1. Energy differences per Mn (Emag = ΔE/2 = (EFM − EAFM)/2, in unit of meV) between the FM and AFM states of Mn–Mn configurations 0–1, 0–2, 0–3, 0–4, 0–6, 0–0′, 0–0′, 0–0′, 0–0′, 0–0′, and 0–0′ at 0 GPa for the (Ba0.75K0.25) (Zn0.944Mn0.056)2P2 (BaZn2P2-based) and (Ba0.75K0.25) (Zn0.944Mn0.056)2As2 (BaZn2As2-based) compounds, respectively. . 0–1 0–2 0–3 0–4 0–6 0–0′ 0–0′ 0–0′ 0–0′ 0–0′ 0–0′ BaZn2P2-based 153.2 –6.3 –24.6 –45.2 –11.5 –44.4 –48.2 –33.9 –25.0 –26.8 –25.6 BaZn2As2-based 100.8 –17.5 –29.7 –43.8 –21.5 –36.8 –40.1 –29.0 –23.3 –23.3 –21.0

Table 1. Energy differences per Mn (Emag = ΔE/2 = (EFM − EAFM)/2, in unit of meV) between the FM and AFM states of Mn–Mn configurations 0–1, 0–2, 0–3, 0–4, 0–6, 0–0′, 0–0′, 0–0′, 0–0′, 0–0′, and 0–0′ at 0 GPa for the (Ba0.75K0.25) (Zn0.944Mn0.056)2P2 (BaZn2P2-based) and (Ba0.75K0.25) (Zn0.944Mn0.056)2As2 (BaZn2As2-based) compounds, respectively. .

Nevertheless, in both compounds, the 0–1 Mn–Mn pair takes robust AFM coupling, which reduces the concentration of the effective FM coupled Mn²⁺ ions and leads to the reduction of net magnetization.^[24,30] Moreover, among all configurations for (Ba_0.75K_0.25)(Zn_0.944Mn_0.056)₂P₂, the AFM coupled 0–1 one has the lowest energy, indicating that the Mn atoms would like to form clusters under an equilibrium growth condition. This goes against the improvement of the sample quality and the T_c.

Based on above analyses, the substitution of P for As can modulate the magnetic coupling effectively, especially the strength of effective FM coupling between the interlayer Mn–Mn pairs. However, the robust AFM superexchange always induces the AFM coupling for the nearest-neighboring Mn–Mn pairs in both compounds, and may hinder the improvement of sample quality and T_c for these II–II–V type DMS materials. Therefore, searching for a material with intrinsic p–d hybridization and transition metal ions far apart without direct bridging anions may serve as a new clue to exploring more feasible DMS materials.

We have systematically studied the magnetic interactions in the proposed BaZn₂P₂-based diluted magnetic semiconductors by using first-principles electronic structure calculations. For the compound with only spin doping, the antiferromagnetic coupling by the short-range AFM superexchange dominates, while the distant Mn–Mn pairs do not show apparently favored magnetic coupling due to the weak interactions. For the compound with both spin and hole dopings, except for several very near Mn–Mn pairs, the ferromagnetic coupling prevails. This originates from the combined effects of the p–d exchange between the Mn d orbitals and the neighboring P p orbitals as well as the long-distance interactions transmitted by spin-polarized itinerant hole carriers, while the latter is indeed a critical factor for the rising of ferromagnetism. Furthermore, with applied pressure, the ferromagnetism in (Ba_0.75K_0.25)(Zn_0.944Mn_0.056)₂P₂ is first strengthened and then weakened due to the competition among the pressure-induced changes in the p–d hybridization, the band broadening, and the spin polarization of itinerant carriers. The robust AFM coupling of the short-range Mn–Mn pairs bridged by anions hinders the improvement of the sample quality and the T_c for these II–II–V type DMSs. We propose that the combination of intrinsic p–d hybridization and far apart magnetic ions may be a new clue to searching for more feasible DMS materials.