Electronic Structures and Magnetic Properties of Co/Mn Co-Doped ZnO Nanowire: First-Principles LDA+U Studies

Abstract

The first-principle calculation method based on the density functional theory (DFT) in combination with the LDA+U algorithm is employed to study the electronic structure and magnetic properties of Co/Mn co-doped ZnO nanowires. Special attention is paid to the optimal geometric replacement position, the coupling mechanism, and the magnetic origin of Co/Mn atoms. According to the simulation data, Co/Mn co-doped ZnO nanowires of all configurations exhibit ferromagnetism, and substitution of Co/Mn atoms for Zn in the (0001) inner layer brings nanowires to the ground state. In the magnetic coupling state, the obvious spin splitting is detected near the Fermi level, and strong hybridization effects are observed between the Co/Mn 3d and O 2p states. Moreover, the ferromagnetic ordering forming Co²⁺-O²⁻-Mn²⁺ magnetic path is established. In addition, the calculation results suggest that the magnetic moment mainly takes its origin from the Co/Mn 3d orbital electrons, and the size of the magnetic moment is related to the electronic configurations of Co/Mn atoms. Therefore, a realistic description of the electronic structure of Co/Mn co-doped ZnO nanowires, obtained via LDA+U method, shows their potential for diluted magnetic semiconductor materials.

1. Introduction

Diluted magnetic semiconductors (DMSs) are a new type of semiconductor material, which exhibited ferromagnetism due to doping with transition metals (TMs). DMSs leverage the charge and spin characteristics of electrons to combine the properties of a semiconductor host with the magnetic characteristics of a dopant, which results in promising magneto-electric and magneto-optical effects. Among the potential applications of DMSs are high-density nonvolatile memory devices, magnetic sensors, spin field effect transistors, optical isolators, semiconductor lasers, and spintronics [1,2,3,4]. Particular attention from researchers is paid to oxide-diluted magnetic semiconductors (ODMSs) that are considered as the main material for fabricating microelectronic devices using electron spin degrees of freedom. At present, most of the ODMS materials are found to possess the ferromagnetic characteristics within or above the room temperature range. Meanwhile, the traditional III–V and II–VI diluted magnetic semiconductor materials are restricted by the antiferromagnetic exchange interaction of TM ions due to the magnetic exchange interaction. A lot of works have proved that the ferromagnetic exchange interaction is difficult to generate through n-type and p-type carrier injection. Thus, this type of diluted magnetic semiconductor materials shows ferromagnetism at low temperatures only, which has no practical significance [5]. Therefore, it is a challenge for modern spintronic device manufacturers to find semiconductor materials that may exhibit ferromagnetism at room temperature [6,7]. In turn, oxide-diluted magnetic semiconductors with a unique set of electrical, electronic, and magnetic properties seem to be promising candidates for the widespread use in spintronics, optoelectronics, microwave devices, magnetoelectronics, memory devices, and solar cells.

TMs-doped ZnO is a popular magnetic semiconductor material with a mature preparation process and broad application range. To further endow ZnO with attractive magnetic properties, TMs serve as dopants in a mainstream way, enhancing the magnetic characteristics at or above room temperature [8,9,10]. Different research groups reported the magnetic, electrical, and optical properties of TM ions in ZnO nanomaterials [11,12,13,14,15,16]. Meanwhile, despite a large amount of research, it remains a controversial issue to develop DMSs with promising magnetic properties. In view of the modulation position and occupancy of the Fermi level, the TM co-doping of ZnO has also proved to be a promising alternative technology for achieving stable optical and magnetic characteristics [10]. Therefore, various attempts were made to simultaneously embed two TM ions in ZnO, so as to establish their suitable combination to achieve room temperature ferromagnetism. Gao et al. [17] studied Mn/Ni co-doped ZnO nanorods, and their results showed that Ni atoms caused oxygen vacancies to amplify the room-temperature ferromagnetic properties of the doped system. Mustafa et al. [18] investigated the magneto-optical and magneto-electric properties of Co/Ni co-doped ZnO, concluding that the coexistence of semiconducting and magnetic phenomena significantly enhanced the room temperature ferromagnetism of the sample. Li et al. [19] successfully synthesized Co/Mn co-doped ZnO nanowires on silicon substrates via thermal evaporation in the presence of a gold catalyst, which enabled them to obtain the pronounced room temperature ferromagnetic characteristics and excellent conductivity. Gu et al. [20] prepared Co/Mn co-doped ZnO films using radio frequency magnetron sputtering (RFMS), and observed a coercive force of about 90 Oe and the enhancement in FM behavior at 300 K. However, there are some different studies over the results on co-doping of ZnO with two TM ions, such as Fe/Co [21,22,23], Ni/Mn [24], Mn/Co [25,26,27,28], and Cr/Ni [29] systems. Although the radii of TM ions are close to those of Zn ions, Mn and Co ions do not easily occupy the tetrahedron position in the ZnO lattice due to the non-magnetic main ion is difficult to be partially replaced by magnetic ion, which will result in no significant remarkable changes of the magnetic properties of co-doped ZnO DMSs. Therefore, it is of great application value to study the electrical and magnetic properties of one-dimensional Mn/Co co-doped ZnO nanomaterials. However, despite numerous experimental studies, there is still a lack of first-principle calculation works on Co/Mn co-doped ZnO nanomaterials. Specifically, the influence of replacement of Zn with Co and Mn magnetic elements and their effects on the lattice structure and magnetism need to be clarified. Therefore, a thorough analysis of the optical, electrical, and magnetic properties of Co/Mn co-doped ZnO nanomaterials would provide the important theoretical references.

In this study, the electronic structure and magnetic properties of Mn/Co co-doped ZnO nanowires are systematically studied, and the magnetic source with magnetic coupling mechanisms are analyzed using the first-principle calculation method within the framework of density functional theory in combination with the LDA+U algorithm. The influence of doping on magnetic and electrical properties was discussed, and the mechanism of spin carrier injection was revealed, so as to effectively control the spin state of charge carriers. The results of the research provide a theoretical basis for the experimental preparation of ZnO magnetic nanomaterials with high quality and high Curie temperature.

2. Theoretical Model and Calculation Method

The theoretical model of Mn/Co co-doped ZnO nanowires was obtained by cutting off all the atoms outside the red line on the basis of the supercell model of wurtzite ZnO 7 × 7 × 2 (as shown in Figure 1a), whose structure is similar to the ZnO nanowire supercell structure, as shown in Figure 1b. The ZnO nanowire supercell contained 48 Zn and 48 O atoms. In order to avoid the influence of the interactions between nanowires on the results, the thickness of the vacuum layer of the model was set to 15 Å along the $\left[01\overline{1}0\right]$ and $\left[10\overline{1}0\right]$ directions, respectively, and the ZnO nanowires along the [0001] direction were assumed to have periodic structures. To describe the magnetic coupling mechanism in Mn/Co co-doped ZnO nanowires, two Zn atoms were replaced with Mn and Co atoms. Six possible magnetic coupling models were established, as shown in Figure 2. Among them, the configuration VI is a case of indirect magnetic coupling that Mn and Co atoms achieve through the oxygen atoms in the middle layer, while the other models are examples of direct coupling between O atoms and TMs. The doping concentration is 4.2% for all six models.

In this work, the calculations were carried out using the DS-PAW software package [30] integrated in Device Studio program [31], in which model building and partial simulations, including geometry structure simulation, are performed based on the Perdew–Burke–Ernzerhof (PBE) exchange-correlation function. All pseudo-potentials were calculated via projector augmented-wave (PAW) method using the local density approximation (LDA). The energy cutoff of the plane wave was set to 400 eV, The convergence in energy and force on each atom were set to 2.0 × 10⁻⁵ eV/Å and 0.001 eV/Å, respectively, and the integral of Brillouin zone is summed up for the full Brillouin zone with the 1 × 1 × 16 Monkhorst-Pack special K-point, the fast Fourier transform (FFT) mesh was 144 × 144 × 75, and the smearing was set to 0.05. To account for a strong electron correlation effect caused by TM’s 3d orbital electrons on the electronic structure and magnetism, the LDA+U approach proposed by Dudarev et al. [32] was applied to deal with the Coulomb repulsions between the local 3d electrons. The LDA+U method is considered an effective and reliable tool in calculating the electronic structure of the electron localization system caused by the Coulomb interactions. Here, after several tests, when U_d−Zn and U_p−O were set to 10.0 eV and 7.0 eV, respectively [33,34,35], the calculated band gap for pure ZnO was 3.35 eV, which are in good agreement with the experimental values [36]. The following values of U_d−Co and U_d−Mn were reported earlier as 3.0 eV and 5.0 eV, respectively [37,38]. So the Coulomb potential of U_d−Zn, U_p−O, U_d−Co and U_d-Mn were set as 10.0 eV, 7.5 eV, 3.0 eV, and 5.0 eV, respectively, and the outer valence electron configurations were Zn−3d¹⁰4s², O−2s²p⁴, Co−4s²3d⁷, and Mn−4s²3d⁵, respectively. In addition, during the geometry optimization, we fixed the lattice parameters of a and b, and the structural optimization was carried out only along the [0001] direction.

3. Results and Discussion

3.1. Geometric Structure and Stability Analysis

First, the geometry and electronic structure of pure Zn₄₈O₄₈ nanowire supercells were analyzed. The total energy of the optimized Zn₄₈O₄₈ nanowires is 2.34 eV lower than that of the non-optimized supercells, indicating that the optimized model is more stable. The Zn–O bond lengths of the outer layer of the nanowire after relaxation along the z axle and vertical z axle are 1.888 Å and 1.897 Å, respectively, being 6.87% (1.992 Å) and 3.85% (1.973 Å), respectively, shorter than those of the non-optimized nanowire. In turn, the Zn–O bond lengths of the inner layer of the nanowire after relaxation along the z axle and vertical z axle are 2.015 Å and 2.003 Å, respectively, exceeding those of the non-optimized nanowire by 1.15% (1.992 Å) and 1.52% (1.973 Å), respectively. The optimization data show that the relaxation of the atoms in the inner layer of the nanowire is less pronounced than that in the outer layer. This is consistent with the results on ZnO surface study in Ref. [39]. Figure 3a displays the total density of states (DOS) of the pure ZnO nanowires under the condition of spin polarization. It can be seen from the DOS diagram that there is no spin-spin splitting in the spin-up and spin-down states, indicating that the undoped ZnO nanowires are not magnetic.

Table 1. Energies, bond lengths, magnetic moments, and magnetic coupling states of Co/Mn co-doped ZnO nanowires.

	ΔE(eV)	Δε(eV)	Coupling	dCo−O (Å)	dMn−O (Å)	dCo−Mn (Å)	μCo (μB)	μMn (μB)	μO (μB)
I	0.542	0.000	FM	1.815	1.863	2.407	2.94	5.08	−0.346
II	0.236	0.118	FM	1.917	1.786	2.193	2.83	4.98	−0.014
III	0.162	0.362	FM	1.778	1.731	2.669	2.80	4.96	0.033
IV	0.391	0.133	FM	1.763	1.680	3.211	2.86	5.01	−0.136
V	0.145	0.397	FM	1.743	1.692	3.045	2.78	4.92	0.028
VI	0.107	0.417	FM	1.858	1.802	5.361	2.74	4.86	0.064

depicts the geometric parameters, energy change, bond length, and magnetic distance of six types of Co/Mn co-doped ZnO nanowires. The energy difference between the anti-ferromagnetic (AFM) and ferromagnetic (FM) coupling (ΔE = E_AFM − E_FM) reflects the relaxation configuration of the nanowires: when ΔE is smaller than zero, it indicates that the AFM state of the system is more stable than the FM state, and vice versa. In order to compare the magnetic coupling effects of the Co/Mn co-doped system, there is also the energy difference Δε between the six types of doped systems and the ground state (configuration I). It can be seen from the data in Table 1 that FM is formed under different coupling states of the Co/Mn co-doped system, and the best stability is achieved for configurations I and II. It can be seen from the energy change of Δε that configuration Ⅰ has the minimum energy under the ground state. The energy of the FM state is 542 meV lower than that of the AFM state, while being far greater than the thermal energy k_BT (30 meV). Therefore, the room-temperature FM coupling is more likely to appear in the Co/Mn co-doped system. This configuration corresponds to a serrated structure (with the Co–O–Mn bond angle of 81.73°) formed by replacing two Zn atoms in the inner layer of the nanowire with Co and Mn atoms along the [0001] direction. The length of the Co–Mn bond along the [0001] direction is 2.407 Å, and those of the Co–O and Mn–O bonds are 1.815 Å and 1.863 Å, respectively. In addition, it can also be seen from the value of Δε that there is no great difference between the energies of six types of coupling structures, indicating that stable FM coupling can be present in Co–Mn Co–doped ZnO nanowires, which is consistent with the magnetic coupling state of Co–Mn co-doped ZnO nano materials prepared in previous experiments [19,27,28]. Moreover, the magnetic moments of Co and Mn atoms in Co–Mn co-doped ZnO nanowires are relatively large, being 2.74–2.94 μ_B and 4.86–5.96 μ_B, respectively, which suggests that Co and Mn atoms are more likely to be ferromagnetic coupled. Whereas the magnetic moments of adjacent O atoms is −0.346 μ_B—0.064 μ_B, thus, the magnetic coupling state formed by the adjacent O atoms includes both FM and AFM, and the O atoms corresponding to the ground state ferromagnetic coupling of configuration I have the magnetic moment of −0.346 μ_B, which is of great significance to the formation of FM coupling.

3.2. Magnetic Properties

In order to establish the magnetic origin and magnetic coupling mechanism of Co/Mn co-doped ZnO nanowires, the DOS and PDOS plots of Zn₄₆CoMnO₄₈ were further obtained (Figure 4). For Zn₄₆CoMnO₄₈ nanowires, the Co and Mn atoms are found in the crystalline field (T_d) of the tetrahedron, corresponding to a coupling structure shown in Figure 5. The energy level of each TM atom in the tetrahedron will be split into a three-fold degeneracy t_2g state (d_xy, d_yz, d_xz), and a two-fold degeneracy e_g state (${\mathrm{d}}_{z^2-r^2}$, ${\mathrm{d}}_{x^2-y^2}$). The non-localized wave function of the ${\mathrm{t}}_{2\mathrm{g}}$ state will hybridize and couple with the O 2p state wave function to form a valence band (VB). At this time, the bonding state appears in the valence band, while there is the anti-bonding state near the bottom of the conduction band (CB). In addition, the localized wave function of the e_g state emerges near the Fermi level, and the coupling between the expanded wave function and the valence band becomes weak, thus forming a bond-free state. Thus, the magnetic coupling depends not only on the relative distance between Mn–Co, but also on the difference in orientation and position, which is the unique manifestation of nanowires, we also found that the coupling strength gets reduced with increased Co–Mn bond length. The findings indicate that coupling is mediated by O 2p orbital, and, therefore, the observed FM can described by double exchange mechanism. These coupling characteristics can be observed from the Mn 3d and Co 3d states in Figure 5c,d. It can be seen from Figure 3b that the whole DOS diagram of Co/Mn co-doped ZnO nanowires is asymmetric at the top of the valence band and at the bottom of the conduction band. Spin electrons are redistributed, resulting in obvious spin-spin splitting at the top of the valence band and at the bottom of the conduction band. In turn, the whole DOS diagram of Co/Mn co-doped ZnO nanowires shifts toward the lower energy range accordingly. It can be seen from the PDOS plot in that the upper valence band (from −6.2 eV to −1.5 eV) of Co/Mn co-doped ZnO nanowires is mainly influenced by Zn 3d orbital electrons. Therefore, the ${\mathrm{t}}_{2\mathrm{g}}$ state wave function of the Co/Mn 3d orbital in this band and the corresponding O 2p state wave function are strongly overlapped and coupled to form the upper valence band, i.e., the bonding state of the doping system appears in the valence band, while the anti-bonding state appears in the top of the valence band and the conduction band. A non-bonding state is formed in the band gap as the result of minimum overlap of the wave functions from the top of the valence band and the bottom of the conduction band with their coupling at the localized e_g state near the Fermi level. In addition, according to Figure 3 and Figure 4, the impurity energy levels of all calculated Co/Mn co-doped nanowires are relatively diffuse, and the spin-up energy levels are mainly distributed in the upper valence band, and the energy levels are relatively diffuse. Meanwhile, the spin-down energy level is distributed in the conduction band and has the non-localized characteristics. The above circumstances are conducive to accurate modulation of magnetic coupling between magnetic atoms. The e_g states appearing in the band gap and the conduction band have a sharp DOS peak, indicating their localized characteristics. In particular, the introduction of the U parameter induces the emergence of separate occupied states near the Fermi level. In the Zn₄₆CoMnO₄₈ nanowires, the DOS diagrams of O 2p and Co 3d/Mn 3d states showed an obvious orbital hybridization effect on the upper valence band, meaning that the coupling was mediated by O 2p orbitals. Therefore, the observed FM can be explained by the dual exchange system. According to the Hund’s rule and the dual exchange mechanism, Zn²⁺ ions replaced by Co²⁺ and Mn²⁺ ions have 3d⁷ and 3d⁵ electronic configurations, respectively, so that Co²⁺ ions ensure the high spin ground state with various levels serially filled up as e_g (2↑) and ${\mathrm{t}}_{2\mathrm{g}}$(3↑) (the arrow represents the spin direction, and the number represents the number of electrons). In turn, Mn²⁺ favors the high spin ground state with serially filled up levels e_g (2↑), e_g (0↓), ${\mathrm{t}}_{2\mathrm{g}}$ (3↑) and ${\mathrm{t}}_{2\mathrm{g}}$ (0↓), all of which have partially occupied ${\mathrm{t}}_{2\mathrm{g}}$ orbital electron layouts. Under the condition of Coulomb interactions, a few spin orbitals in the semi-filled energy bands of Co 3d and Mn 3d orbitals undergo spin-spin splitting with some occupied orbitals being pushed to the VB, and others tending to the CB. In the unoccupied and occupied Co 3d states (spin-down state) of the Co d orbital, the e_g (2↓) and the ${\mathrm{t}}_{2\mathrm{g}}$ (0↓) state spins are split by 2.3 eV, while in the unoccupied and occupied Mn 3d state of the Mn d orbital, the e_g (2↑) and the ${\mathrm{t}}_{2\mathrm{g}}$ (0↓) state spins are split by 4.8 eV. At this time, the electrons on the e_g and ${\mathrm{t}}_{2\mathrm{g}}$ orbitals of Co²⁺/Mn²⁺ doped nanowires undergo dual exchange through the Co²⁺-O²⁻-Mn²⁺ coupling. In addition, the experiments [19] also showed that Co/Mn was an unlikely source of FM, their results of XRD and TEM clearly showed no Co/Mn clusters in the ZnO nanowires, and the origin of the ferromagnetic behavior observed in Co/Mn co-doped ZnO NWs is due to the doping of Co²⁺ and Mn²⁺ cations into ZnONWs. The orientation of these electrons in the energy level is arranged according to the principle of minimum energy, resulting in a stable FM of Zn₄₆CoMnO₄₈ nanowires. It can be seen from Figure 4b–d that the impurity energy level is broadened after co-doping with Co/Mn, which results in a decrease in the energy of the e_g state of Co/Mn 3d orbital, while increasing the energy of the ${\mathrm{t}}_{2\mathrm{g}}$ state of Mn 3d orbital. The FM ordering is stabilized by the wide impurity bands [40,41,42,43], especially in the spin orbital near the Fermi level, where obvious orbital hybridization effects occur between the Co/Mn 3d states themselves, and between the Co/Mn 3d and O 2p states. Therefore, the electron exchange in the Co/Mn 3d orbital is through the Co²⁺-O²⁻-Mn²⁺ atomic chains, which significantly reduces the kinetic energy of Zn₄₆CoMnO₄₈. The above results agree with the dual exchange mechanism proposed by Sato [43] for interpreting FM coupling. Therefore, the above theoretical discussion indicates that Mn/Co co-doped ZnO nanowire tend to stabilize in ferromagnetic ground state. Thus, the Co/Mn co-doped ZnO nanowires have great potential for realizing room-temperature ferromagnetism.

4. Conclusions

The geometric structure, electronic structure, and magnetic properties of Co/Mn co-doped ZnO nanowires were systematically studied using density functional theory in combination with LDA+U algorithm. The ferromagnetic coupling characteristics were observed when Co/Mn co-doping was used to replace Zn atoms at different positions, The computed formation can show that configuration I is the ground state, and it is easier to form a stable FM coupling order. The strong p-d hybridization effect between unpaired electrons of Co/Mn 3d orbitals and O 2p orbital electrons near E_F, a diffuse bonding state emerged in the upper valence band, and a localized non-bonding state occurred near the Fermi level. A relatively localized anti-bonding state formed in the conduction band. The findings indicate that the FM coupling is mediated by O 2p orbital, and theoretical calculations further revealed the dominance of ferromagnetic double exchange interactions. The magnetic moment was mainly influenced by Co/Mn 3d orbital electrons, and the nearest Co-Mn electron pair was shown to be conducive to the ferromagnetic interactions. Therefore, the practice of controlling the flexibility of ferromagnetic coupling and magnetic moment by selecting the appropriate size and dimension of co-doped nanowires may be very promising in applications. Our present results are conductive to design room temperature ZnO based dilute magnetic semiconductors.