1 Introduction

Magnetism in semiconductors has brought about the search for the next-generation magnetic semiconductors. In these materials, rather than the electron charge, it is the electron spin that carries meaningful information [1]. These diluted magnetic semiconductors (DMSs) are formed when the cations in a non-magnetic semiconductor are partially replaced by magnetic transition metal ions [2,3,4,5]. They have garnered considerable interest as they possess the potential for interesting and practical applications in fields such as spintronics, spin-valve transistors, spin light-emitting diodes, and logic devices [6, 7]. One such DMS is the transition metal (TM)-doped ZnO, which has attracted a lot of attention. This is due to its superior potential for applications in the field of spintronic devices [1,2,3,4,5,6,7,8]. Wurtzite ZnO has a direct band gap (Eg) of about 3.4 eV and high exciton binding energy of 60 meV. It shows piezoelectricity, and high thermal and chemical stability with respect to the environment [9,10,11,12,13]. The electron Hall mobility (~ 200 cm2 Vs−1) and Curie temperature for doped ZnO are also quite high [10,11,12]. These qualities render ZnO a material of paramount significance for a variety of optoelectronic and electronic applications [14]. Depending on the growth conditions, TM doping in the identical host lattice of ZnO can yield both paramagnetism and ferromagnetism [15,16,17]. ZnO in nanoscale can be synthesized by several different methods including physical vapor deposition [18], metal organic chemical vapor deposition [19], and a low-temperature hydrothermal method [20]. The effect of doping on the structure, optical, electrical, and magnetic properties of ZnO has been studied by various groups [21,22,23,24,25,26,27,28,29,30].

The fundamental reason behind the origin of ferromagnetism in TM-doped ZnO is still not fully understood. Different models have been put forward to explain the mechanism for the ferromagnetism at room temperature in DMSs. Some of these suggested mechanisms on the nature of ferromagnetism are: (i) the interaction between bound magnetic polarons [31], (ii) a charge-transfer-based ferromagnetism model [32, 33], (iii) oxygen and zinc vacancies, VO and VZn, interstitials, and (iv) O and Zn, surfaces and grain boundaries [34,35,36,37,38,39,40]. The possibility of ferromagnetism in carbon-doped ZnO [41] or nitrogen [42] has paved the way for further research. However, this type of magnetism is known as d0 ferromagnetism [43] and experimentally observed in ZnO-based systems prepared by electron radiation [44] or ion implantation [45]. Zn interstitials or oxygen vacancies in C-doped ZnO (ZnO:C) has also shown to enhance ferromagnetism in pulsed laser-deposited films [46]. In general, the magnetic properties of TM-doped ZnO depend on the growth conditions. Particularly, these conditions form grain boundaries which resulted in ferromagnetic behavior. Importantly, the fundamental nature of the ferromagnetic behavior is debated and requires further studies.

In this work, a detailed study on the preparation of high-quality samples of Zn1-xRxO (R = Li, Mg, Cr, Mn, Fe and Cd) is reported, with constant weight percent of 3% from R ions versus ZnO. We found that the magnetic properties of ZnO strongly depended on type of R content in ZnO matrix. By controlling the R content, different and unprecedented magnetic properties are reported, along with structural, morphological, and optical properties. For the ab initio calculations, we considered direct replacement of the Zn atoms by the dopants and did not consider Zn or O vacancies. While the Li- and Cd-doped systems remained paramagnetic, the Mg-, Cr-, Mn-, and Fe-doped systems show ferromagnetism. In the Cr-, Mn-, and Fe-doped systems, the presence of d electrons can be held responsible for giving rise to magnetism, but a deeper explanation for the d0 ferromagnetism in the Mg-doped sample provides a route for future work. Importantly, these properties can be taken advantage of in spintronic applications.

2 Materials and methods

All the gradual steps leading to the preparation (weighing, mixing, grinding, and storage) were carried out in an Ar-filled glove box. Both O2 and H2O levels were kept at less than 0.1 ppm. The preparation of Zn1-xRxO (x = 0.03) in a nanoparticles (NPs) form has been achieved by using the co-precipitation method. Zinc sulfate (ZnSO4) and NaOH solutions were prepared separately and then eventually mixed together. This mixed solution was maintained at room temperature and stirred for 2 h. For drying purposes, the Zn(OH)2 was heated at 70 °C for 24 h. The dried ingots were heated at 400 °C for 4 h. Then, the powder was left to cool down slowly to room temperature to get pure zinc oxide (ZnO). In order to prepare mixed oxide DMSs, mixed solutions of ZnSO4 and the metal (R) sulfate were prepared. Finally, NaOH solution was added slowly to the mixed solution. This process was repeated to obtain Zn0.97 R0.03O nanoparticles for the different metals considered (R = Li, Mg, Cr, Mn, Fe and Cd).

All the structures including the pristine and doped ones were relaxed within the framework of density functional theory (DFT) [47] by solving the Kohn–Sham equations [48]. Our total energy and electronic structure calculations were performed using the projector augmented wave (PAW) [49] formalism of density functional theory as implemented in the VASP package [50]. We used a well-converged energy cutoff of 550 eV, and the Brillouin zone was sampled employing a 2 × 2 × 3 Monkhorst–Pack k-point mesh [51]. The Zn, O, Li, Mg, Cr, Mn, Fe, and Cd potentials were employed with valence states of 3d104s2, 2s22p4, 2s1, 3s2, 3p63d54s1, 3d64s1, 3p63d54s1, and 4d105s2, utilizing the Perdew–Burke–Ernzerhof (PBE) exchange correlation functional [52]. All the structures were relaxed until the Hellmann–Feynman forces were less than 0.05 eV/Å. Typically, standard DFT calculations tend to grossly underestimate the electronic band gap of wide gap insulators or even semiconductors containing transition metals.

Therefore, a Hubbard parameter (U) is included to account for the d-d Coulomb interaction [53,54,55]. In order to add the on-site d-d Coulomb interaction, U, and the on-site exchange interaction, J, to the generalized gradient approximation (GGA) Hamiltonian for transition-metal elements, we use a typical value of U-J = 4.0 eV for our calculations that contain transition metals, i.e., Cr, Fe, and Mn. In order to mimic the experimental doping concentration, we constructed a periodic 5 × 5 × 2 supercell of ZnO containing 200 atoms (100 Zn and 100 O atoms). Since, in the experiments, the doping concentration was 3%, in our calculations we replaced 3 of the Zn atoms with the dopant atoms.

In our calculations, we explored two different atomic positions of the dopants and checked for the minimum energy configuration. In the first configuration, the dopant atoms are separated by one oxygen atom which we designate as ‘near’ (Fig. 1a). In the other configuration, the dopant atoms are separated by –O–Zn–O- and we call this one the ‘far’ configuration (Fig. 1b). We then calculated the minimum energy configuration and did further analyses with those structures.

Fig. 1
figure 1

Wurtzite supercell of ZnO doped with 3% dopant atoms. The grey, red and blue atoms represent Zn, O and the dopant atoms, respectively. Dopant atoms are separated by a an oxygen atom (near), and b –O–Zn–O– (far)

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3 Results and discussion

3.1 Structure and morphology studies

We first formed zinc oxide NPs. In order to check the morphology, the average size, and the shape of the prepared nanoparticles, we have done both high-resolution transmission electron microscopy (HR-TEM) (Fig. 2a) and scanning electron microscopy (SEM) (Fig. 2b). The synthesized NPs are generally isotropic in shape (Fig. 2a). Our ZnO NPs display the commonly observed wurtzite crystal structure (ICDD No. 36-1451, Fig. 2c) with a semi-spherical shape, and an average particle size is found to be about 14–16 nm, which is in good agreement with that obtained from TEM image and XRD analysis. It is well known that the crystallization of ZnO either presents a hexagonal wurtzite or cubic zincblende form. The latter is considered to be the most common. Our XRD confirms the synthesized ZnO NPs were free of impurities as it does not contain any characteristics XRD peaks other than zinc oxide peaks. On the other hand, the surface properties of the grown NPs are of great interested. This is due to the molecules are arranged on the surface of the NPs since the surface-to-volume ratio for the NPs is higher than their bulk counterparts [10]. To check the existence of the any vibrational modes of ZnO NPs and to reveal the composition of our samples, FTIR spectroscopy was measured in the range of 4000–400 cm−1 presented in Fig. 2d. The pronounced 450 cm−1 and 3398 cm−1 peaks are the well-known characteristic absorption of Zn–O bond and the characteristic absorption of hydroxy, respectively.

Fig. 2
figure 2

Characterization of typical ZnO nanoparticles synthesized with the co-precipitation method. a TEM image (the scale bar is 100 nm). b SEM image. c XRD pattern (the ZnO wurtzite reference ICDD no. 36–1451 is highlighted). d Fourier transform Infrared (FTIR) spectroscopy for ZnO nanoparticles

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Under ambient conditions, ZnO has a hexagonal wurtzite structure with lattice parameters a = 3.25 Å and c = 5.20 Å [56]. In this work, we have, further, substituted 3% of the Zn atoms with Li, Mg, Cr, Fe, Mn and Cd. The crystal structures of the doped systems have been studied using X-ray diffraction (XRD) in order to find any deviation from that of pure ZnO. The XRD patterns of all the systems (pristine and doped) are shown in Fig. 3.

Fig. 3
figure 3

XRD patterns of Zn1−xRxO (R = Li, Mg, Cr, Mn, Fe and Cd)

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One can see that the X-ray diffraction patterns of the Zn0.97R0.03O NPs compared to the pure ZnO nanostructure, where (R = Li, Mg, Cr, Mn, Fe and Cd). Pure ZnO has a hexagonal wurtzite structure with diffraction peaks (100), (002) (101), (102), (110), (103) and (112), consistent with standard XRD data [see JCPDS 36-1451]. Only the characteristic peaks of ZnO were observed, which confirms that all synthesized samples are crystalline and are free of significant amounts of impurities. On other hand, the peaks slightly shifting with doping should be due to the different ionic radii of the dopant ions as follows: the peaks are shifted to higher angle for Fe (r = 0.77 Å), Mn (r = 0.80 Å) and Cd (r = 0.9 Å) doped ZnO, while for Cr (0.62 Å), Li (0.73 Å), and Mg (0.71 Å) slightly shifted to lower angle doped ZnO; this shifted may be due to the different ionic radii of the dopant ions with the ionic radius of Zn (0.74 Å). Furthermore, with the addition of R ions into ZnO, the intensity of diffraction peaks slightly increased, whereas after insertion of Cr ions into ZnO matrix, the diffraction peaks for Zn0.97Cr0.03O become more intense. This may be due to the improvement in the crystallinity of the formed composite. The lattice parameters a and c are determined from the following relation:

$$\frac{1}{{d_{{\left( {hkl} \right)}}^{2} }} = \frac{4}{3}\left[ {\frac{{h^{2} + hk + k^{2} }}{{a^{2} }}} \right] + \frac{{l^{2} }}{{c^{2} }}$$
(1)

where h, k and l are the Miller indices, d is the interplanar distance, and ‘a’ and ‘c’ are the lattice parameters and listed in Table 1. Average crystallite sizes (D) were calculated by using the Debye–Scherrer’s equation (\(D = k\lambda /\beta \cos \theta\)) and are also listed in Table 1, where k = 0.94 (a constant), λ is the wavelength of the X-rays, β is the full width at half maximum (FWHM), and θ is the diffraction angle.

Table 1 Crystallite size, lattice strain, lattice parameters and the unit cell volume (v) of pure ZnO and Zn0.97R0.03O nanoparticles
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One can see that the Li- and Mg-doped samples have smaller average crystallite sizes, compared to the undoped ZnO. The ionic radius of Zn2+ is 0.74 Å, while that of Li2+ and Mg2+ is 0.73 Å and 0.71 Å, respectively, for fourfold coordination. Zn in ZnO is tetrahedrally coordinated with oxygen. Therefore, the decrement in the crystal size for the Li- and Mg-substituted ZnO in place of Zn is expected. Chromium in the four-fold coordination can have valencies 4+ , 5+ and 6+, and their ionic radii are 25.6 34.5 and 45.9% smaller than that of Zn2+. Therefore, the smaller crystal size of Zn0.97Cr0.03O compared to pure ZnO is also justified. In order to maintain charge neutrality, Fe and Mn should have valency of 2+.  But the ionic radii of Fe2+, Cd2+ and Mn2+ are 0.77, 0.90 and 0.80 Å, respectively. Therefore, on substituting Zn2+ with these ions, the crystallite size is found to be increased which may be due to an increase in nucleation rates of ZnO nanoparticles. Also, the slight variation in lattice parameter likely results from the substitution of different ionic radii doped ions with Zn. Furthermore, it is noted that there is an increase in its lattice strain (ε = βhklcosθ/4) due to R-doping inside the ZnO matrix (Table 1), which causes the local distortion of the crystal structure. This is expected and has been found in previous studies [57].

In order to further check both the average size and shape of our grown samples, we have done SEM for all grown NPs (Fig. 4). The morphology of Zn0.97R0.03O nanoparticles was also studied using SEM imaging (Fig. 4a–f). The SEM image represents the agglomeration of particles and also shows a narrow particle size distribution.

Fig. 4
figure 4

a–f SEM images for Zn1−xRxO samples, for 3% R concentrations. a Mn, b Cr, c Cd, d Li, e Mg, and f Fe, respectively

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We have, further, performed Fourier transform infrared (FTIR) spectroscopy for all investigated samples to determine the vibrational modes present. Figure 5 shows the FTIR spectrum of the Zn0.97R0.03O nanoparticles compared to the pure ZnO, where (R = Li, Mg, Cr, Mn, Fe and Cd) synthesized from zinc sulfate acquired in the range of 400–4000 cm−1 are observed at different regions of FTIR spectrum. The observed spectra exhibited well-defined absorption peaks in the range of 550 cm−1 which is a manifestation of the stretching vibrational mode of ZnO. These data are similar to the results observed previously [58].

Fig. 5
figure 5

FTIR spectra of pure ZnO and Zn0.97R0.03O samples

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The absorption peaks in the range of 460–550 cm−1 can be attributed to the stretching vibrational mode of ZnO [58]. In addition, the observed strong band at 459 cm−1 indicates the existence of pure ZnO which shifted to 463 cm−1 as a result of metal dopant ions. Shoulder peaks are seen to exist around the bands at around 1420 cm−1. The peak around 1636 cm−1 is due to the H–O–H bending vibration. The absorption peak that appears at 3420 cm-1 is due to the O–H stretching vibrations of H2O, which is present in trace amounts of the nanomaterial [59]. Due to the replacement of R for Zn, the Zn0.97R0.03O bands display a small difference in peak position compared to the pure ZnO sample. The same results were reported for Ni- and Mn-doped ZnO NPs [60, 61].

3.2 DFT calculations

The energy difference of the two configurations is shown in Fig. 6, left panel. It is clear that for Li, Mg, and Cd, the far configuration is energetically more favorable. Although, for Mg and Cd, the energy differences between the near and far configurations are very small compared to that of Li, we still proceeded with the far configuration for our calculations. For the transition metals, Cr and Fe, the near configuration turns out to be the lower energy structure, while it is opposite for Mn. This trend for Cr, Mn and Fe is in excellent agreement with that obtained by Gopal et al. [62].

Fig. 6
figure 6

Left panel: Enear–Efar for substitutional dopant ions. A negative energy difference indicates that the TM ions prefer to be in a near spatial configuration. Right panel: magnetic moment per dopant atom

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The magnitudes here are different from those shown in Ref. [62]. This is due to the difference in the dopant concentration and the different pseudopotentials used in our calculations. The doped structures were allowed to relax with respect to all the degrees of freedom and eventually, with the end results showing agreement with the experimental findings. For all the doped cases, the wurtzite morphology of ZnO is maintained and no structural phase transition is observed, as seen in our XRD measurements. The structural parameter of all the doped systems is presented in Table 2. The lattice parameters do not show significant differences for the different dopant cases in comparison with the pristine wurtzite ZnO structure. The maximum deviation is seen for Cd, which can be attributed to the larger ionic radii. The almost constant c/a value confirms the consistency of the wurtzite structure. As can be seen, the experimental (Table 1) and calculated (Table 2) data are in very close agreement.

Table 2 Lattice constants and the dopant-oxygen bond length obtained from calculations
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With respect to chemical bonding, ZnO is a tricky material as it shows a mixture of both ionic and covalent bonding. The electron transfer from Zn to O is 1.15, which is not strong enough for ionic bonding or not enough for covalent bonding. We calculated the Bader charge transfer (Table 3) using the atoms in molecules theory [63]. Among all the doped systems studied in this work, the Zn–O bonds still remain partially covalent and partially ionic. However, for Li, Mg, Cr, Mn and Fe, the dopant and oxygen bonding tend more toward being ionic. Given that Zn and Cd belong to the same group elements (d10), the electron transfer from them to oxygen is almost the same, and therefore, the Cd-doped system retains both the ionic and covalent traits.

Table 3 Bader charge transfer from Zn and dopant atoms to O
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Experimentally (vide infra), we observed that by introducing Cr, Mn, and Fe to the ZnO, clear hysteresis loops can be observed and the existence of ferromagnetism in these materials has been verified. From our calculations, the magnetic moments that were obtained are 3.67, 5.0, and 4.33 μB per dopant atom for Cr, Mn, and Fe respectively (Fig. 6, right panel) [64, 65]. While Cr and Fe tend to form clusters, Mn has more propensity to remain evenly distributed within the system, avoiding cluster-derived magnetism. As reported by Xing et al., the occurrence of ferromagnetism in transition metal-doped ZnO could possibly be due to the increase in the number of defects and oxygen vacancies [66]. Another opinion, according Chu et al., is that the exchange interaction between transition metal ions and O ion spin moments can lead to ferromagnetism [67].

3.3 Magnetic Properties

Understanding the fundamental properties in DMS materials and the development of methods to characterize and control their collective behavior is a topical area that attracts enormous interest. DMS offers a plethora of functional properties that are not only of fundamental interest, but are essential for the development of new technological applications. To gain a better understanding of the magnetic behavior of these doped ZnO nanoparticles, we have studied the temperature and field dependences of the magnetic properties of the doped DMS. The temperature dependencies of the magnetization upon zero-field cooling (ZFC) and field cooling (FC) are shown in Fig. 7 for the doped ZnO nanoparticles. At room temperature, Fig. 8b–d illustrates the isothermal magnetization M vs. H, while Fig. 8a–d shows the isothermal magnetization M versus H loops of Zn0.97R0.03O [R = Fe (a), Mn(b), Mg(c), Cr(d)] measured at different temperatures in Fig. 8a ranging from 1.8 to 300 K up to 7 T. being collected at 300 K.

Fig. 7
figure 7

The temperature dependence of the magnetization (M) in an external field of 0.01 T. M has been deduced from the dc magnetization measured by following ZFC and FC protocols

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Fig. 8
figure 8

a–d show the isothermal magnetization M vs. H loops of Zn0.97R0.03O [R = Fe (a), Mn(b), Mg(c), Cr(d)] measured at different temperatures in (a) ranging from 1.8 to 300 K up to 7 T. From (b–d) the isothermal magnetization M versus H being collected at 300 K

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A distinct ferromagnetic transition is seen for the Fe/Mn/Mg-doped samples. The ferromagnetic transition temperature (Tc) is estimated from the derivative of the magnetization data in Fig. 7. Iron doping enhances the ferromagnetism of Zn1−xFexO with the Tc increasing from 39 K for 2% doping to 44 K for 8% doped samples [64]. As shown in [64], the decrement vanishes upon applying high magnetic fields and the ZFC curve overlaps with the FC curve. This downturn is similar to that seen in Ref. [43] and can be attributed to the antiphase ferromagnetic domains.

One can noticed that the doped samples exhibit a clear magnetic hysteresis loop (Fig. 8) for the Mg, Mn, and Fe cases. Substituting Mg, Mn, and Cr ions into ZnO induced weak ferromagnetism and illustrates a magnetic moment without any distortion in the geometrical symmetry. It is important to note that the reduced moment values might occur due to large numbers of disordered spins on the surface. It could also be due to grain boundaries that constitute a considerable fraction of volume of the nano-sample. Vacancies will be ordered along the unique axis of magnetization (c-axis) in our case, as the samples exhibit hexagonal symmetry. Therefore, ferromagnetism in our investigated samples could be arising from spin–orbit interaction, through s-d orbitals coupling [68], or interaction between bound magnetic polarons. In the latter case, the fluctuations of magnetization have an important role in binding and may cause non-trivial thermal behavior [69]. Thus, the formation of charge carrier quantum states exists on the doped ZnO. However, the interaction between bound magnetic polarons is still not well understood when considering its role in ferromagnetism.

As inferred by Karmakar et al. [70], native defects in the ZnO host can give rise to ferromagnetism in the TM-doped ZnO system. According to Jin et al. [71], the bound magnetic polaron (BMP) model can be applied to explain room-temperature ferromagnetism. The BMP model puts forward the idea that the long-range ordering is either due to the direct overlaps between BMPs or indirect interactions between the BMPs and magnetic impurities. Thus, doping with Cr increases the density of magnetic impurities, facilitating the ferromagnetic alignment of BMPs. It has also been proposed in the literature [72] that the spin-polarized carriers and the hybridization between the O-p and TM-d orbitals may be responsible for the ferromagnetism in Cr-doped ZnO. From our calculations the average magnetic moment of each Cr atom is found to be about 3.65 μB/Cr. This value is much larger than our experimental data. The reason behind this discrepancy can be explained as follows. The processes of preparing a film is often a non-equilibrium process. During the process, Cr atoms may get embedded in the antiferromagnetic far state which does not contribute to the ferromagnetism. It is widely proposed that defects, Zn or O vacancies, along with the presence of magnetic dopants, also play a crucial role in the enhancement or suppression of ferromagnetism [73,74,75,76,77,78,79,80]. However, in our calculations, the simplest cases have been treated with only replacement of Zn atoms by the dopants.

It is well known that the undoped ZnO is diamagnetic in nature. Thus, the ferromagnetism observed in our investigated samples is intrinsic and cannot be attributed to any kind of defect [81]. Furthermore, from our XRD, FTIR and SEM studies, there is no evidence for the formation of a secondary phase or clusters upon introducing dopant to ZnO. These illustrations show that magnetization is not due to a secondary phase or clusters. Based on the above findings, we can summarize that the magnetization of the dopant ions is associated mainly with an increase in defects. On the other hand, iron-doped ZnO nanoparticles show high saturation magnetization as compared to Cr, and Mn along with Mg into ZnO. Ruderman–Kittel–Kasuya–Yosida interactions (RKKY) show that in case of doped diluted magnetic semiconductors, exchange interaction takes place between conduction electrons and impurity spin. RKKY interactions also illustrated that upon introducing Fe into the diluted magnetic semiconductors increased the saturation magnetization. Therefore, our observation on the ferromagnetism in this system is due to the joint effects of intrinsic exchange interactions and bound magnetic polarons. In the absence of magnetic impurities, exchange interactions between localized electron spin moments resulting from oxygen vacancies at the surfaces of nanoparticles can be the cause of ferromagnetism. A common consensus with regard to the ferromagnetic property in transition-metal-doped ZnO is that defects such as oxygen or zinc vacancies might be responsible [82,83,84]. It has already been shown that oxygen vacancy is crucial for Mn-doped In2O3 [85]. Although the reason behind the intrinsic ferromagnetism in Mn-doped oxides is still not completely understood, it is believed that defects do play a role in the origin of the ferromagnetism in the Mn-doped ZnO system. Finally, the diamagnetic dilution in the hexagonal diamagnetic lattice films of wurtzite structure resulted in improved values of the magnetic moment and ferromagnetic character which need further investigation. We believe that for the case of Mg in our work, it is defects such as Zn and O vacancies which give rise to the d0 ferromagnetism. From our theoretical calculations, we did not consider any defects (VZn or OZn) in the lattice and also did not find any ferromagnetic moment for the Mg-doped case. In general, the occurrence and improvement in the ferromagnetic behavior are also dependent on the synthesis route.

4 Conclusions

In summary, pure and metal (Li, Mg, Cr, Mn, Fe and Cd)-doped ZnO nanoparticles were successfully synthesized. The original hexagonal wurtzite structure (P63mc) was retained for all samples. Pure ZnO exhibits paramagnetic behavior, as expected, but the Fe, Mn, Mg, and Cr doping induced ferromagnetism at different levels. The spatial configuration of the dopant atoms is determined theoretically, giving a better understanding of the dopant atom orientation responsible for magnetism. The Fe and Cr atoms tend to form clusters giving rise to ferromagnetism, while the Mn atoms remain more spread out. Several reasons behind the observed ferromagnetism have been discussed. Specifically, the role of defects has been emphasized when explaining the observed ferromagnetism. This is further strengthened by the case of the Mg (non-magnetic)-doped case, where the formation of defects in the system can give the best justification for the occurrence of ferromagnetism.