1 Introduction

Materials whose properties rely on spin functionality are very important in the advancement of spintronics. Semiconductor spintronics is a field of dreams for the research community as it could pave the way for integrating spin-based mechanisms with current semiconductor technology. Lots of research is being carried out to induce ferromagnetism in nonmagnetic semiconductors, especially by doping 3d transition metals in semiconductors such as TiO2 [1,2], ZnO [3,4], CeO2 [5,6], SnO2 [7,8] and GaN [9,10]. It is well known that, when doped with transition metal elements, certain semiconductors exhibit ferromagnetism, and are called diluted magnetic semiconductors (DMS). Among all the semiconductors, ZnO is a promising candidate for integrating multiple functions in a single system because of its direct and wide bandgap [11], large free exciton binding energy [11] and good thermal and chemical stability [12]. A large share of research in the field of DMS had been based on the use of 3d transition metals [3,4] as dopants for a long time. However, the interest has currently shifted to rare-earth (RE) [13,14,15], non-transition metals [16], anions such as nitrogen and carbon as dopants [17,18] and even undoped ZnO [19]. In all these cases, ZnO system is inferred to be exhibiting room temperature ferromagnetism (RTFM), depending on growth conditions and methods [20]. This has puzzled the scientific community ever since.

According to studies, an intriguing observation is that doping percentage higher than the percolation threshold of ZnO (18%) is not a prerequisite for RTFM [21]. The conventional super-exchange mechanism cannot explain this fact. The ferromagnetic double-exchange mechanism requires mixed cation valence, which is not a common feature in DMS [21]. Hence, the DMS systems must be explained by some other mechanism. A large body of literature is based on the mechanism where ferromagnetism is mediated by bound magnetic polarons (BMPs), which are related to the lattice defects in the system. Oxygen vacancy (VO) based BMP model is widely discussed in the field of DMS [22,23,24,25,26,27]. There are some reports discussing zinc interstitial (Zni) and zinc vacancy (VZn) based BMP models as well. Recently, Ali et al [3] reported that VZn is responsible for RTFM in Cu-doped ZnO and Ag-doped ZnO [28]. Also, Wang et al [19] reported that RTFM in undoped ZnO is to be attributed to the presence of Zni.

The 3d transition metal-doped ZnO has already been investigated largely as DMS system over the last two decades. For the generalization of a model for the DMS system, it is better to avoid elements that are magnetic at room temperature, such as Fe, Co and Ni. RE transition metal-doped ZnO has also been studied as DMS system by many research groups. Gd-doped GaN exhibiting RTFM has been reported by Shvarkov et al [29]. RTFM in Gd-doped ZnO in various methods was reported [30,31,32,33]. Neither Gd nor its clusters with Zn are ferromagnetic at room temperature. Hence, ZnO with dilute Gd doping is considered as a suitable system for DMS.

In this article, pristine- and Gd-doped (0.05, 0.1 and 1 at%) ZnO films grown on Si(111) substrate by radio frequency magnetron sputtering under pure Ar atmosphere are discussed. Native defects (VO and Zni) are introduced in Gd-doped ZnO films to enhance ferromagnetism with the objective of investigating its effect on the magnetic properties of the films. We have proposed a mechanism that could be responsible for RTFM in Gd-doped ZnO thin film based on BMP model due to oxygen deficiency related defects manifested as VO and Zni [34].

2 Materials and methods

The sputtering targets of ZnO and Gd-doped ZnO (0.05, 0.1 and 1 at%) were prepared using ZnO and Gd2O3 powders (Alfa Aesar) with 99.99% purity by conventional solid-state reaction method. The powders were mixed in stoichiometric ratio and ball milled for 10 h followed by calcination for 30 min at 950°C. The ceramic targets prepared using hydraulic pelletizer were sintered for 6 h at 950°C. After attaining vacuum condition (10−6 mbar pressure) in the chamber, Gd-doped ZnO thin films were deposited on Si(111) substrate under Ar pressure of 0.02 mbar using the prepared ceramic targets as discussed above. The substrate temperature, RF power and deposition time were maintained as 450°C, 120 W and 30 min, respectively, for all films.

The structural properties of the fabricated films were studied using X-ray diffraction method (XRD) and Raman spectroscopy. XRD analysis was carried out with X-ray diffractometer (Rigaku/Smartlab XRD) using CuKα source (λ = 1.54 Å). Raman analysis was carried out with Horiba/Lab RAM HR (excitation wavelength = 532 nm). Atomic force microscopy (AFM, Bruker/Dimension Icon) images of the films were recorded for morphological analysis. Elemental analysis was done using X-ray photoelectron spectroscopy (XPS, Kratos/Axis Ultra DLD). Room temperature photoluminescence (PL, Perkin Elmer Ls55) was performed using Xe-lamp of wavelength 325 nm as an excitation source. The magnetic properties of the films were analysed using vibrating sample magnetometer (VSM-Lakeshore 7404) at room temperature. The thickness of the thin films was measured using the Filmetrics F20 system. The thickness of the 1 at% Gd-doped ZnO thin films grown at Ar:O2 = 100:0, 75:25 and 50:50 are 300, 260 and 227 nm, respectively. The thicknesses of 0, 0.05, 0.1 and 1 at% Gd-doped ZnO thin films deposited under pure Ar atmosphere are 280, 274, 267 and 300 nm, respectively.

It is important to mention that 1 at% Gd-doped ZnO thin film was deposited at three different Ar:O2 ratios (100:0,75:25 and 50:50), as preliminary study before growing different concentrations of Gd-doped ZnO films under pure Ar atmosphere. The film grown under pure Ar atmosphere showed RTFM, whereas the films deposited at other oxygen partial pressures exhibited a combination of diamagnetic and ferromagnetic properties. The discussion on the properties of these films is restricted to PL and VSM, as it is beyond the scope of this article.

3 Result and discussion

3.1 Structural analysis (XRD and Raman spectroscopy)

Crystal structure of the deposited films was studied using XRD patterns and the obtained XRD patterns are shown in figure 1. The observed peaks of pristine and Gd-doped ZnO films corresponding to the diffraction plane (002) show that all the films are grown with the c-axes perpendicular to the substrate surfaces. This confirms the wurtzite crystal structure of ZnO consistent with JCPDS card #36-1451. The XRD peak at an angle 34.51° for pure ZnO is found to have shifted to lower angles (34.37°, 34.41° and 34.42°) upon doping with Gd (0.05, 0.1 and 1 at%). This shows that the Gd3+ ions successfully occupied the lattice sites of Zn2+. Since the ionic radius of Gd3+ is 0.93 Å, which is larger than that of Zn2+(0.74 Å), strain was developed in the lattice, causing a shift of peak to a lower angle [30]. When the doping percentage was increased beyond 0.05 at%, the substitutional Gd3+ presumably formed complexes with defects. This might be the responsible factor behind the shifting of angle to higher values than that corresponding to 0.05 at% doping [35]. The crystallite size was calculated using Scherrer’s formula, as given below,

$$D=\frac{k\lambda }{\beta\,\mathrm{cos}\theta } ,$$
(1)

where D is the crystallite size, λ the wavelength of CuKα radiation (1.54 Å), β the full-width at half-maximum of 002 peak in XRD, θ the Bragg’s angle and k the shape factor. The lattice parameter ‘c’ was calculated using the following relation [14],

$$ c = \frac{\lambda }{\sin \theta }, $$
(2)

where \(\lambda \) is the wavelength of CuKα radiation (1.54 Å) and θ the Bragg’s angle.

Figure 1
figure 1

XRD pattern of ZnO with Gd doping percentage of (a) 0, (b) 0.05, (c) 0.1 and (d) 1 at%.

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The interplanar distance (d) of (002) planes was calculated using the following formula,

$$ \frac{1}{{d^{2} }} = \frac{{h^{2} + hk + k^{2} }}{{a^{2} }} + \frac{{l^{2} }}{{c^{2} }}, $$
(3)

where h, k and l are the miller indices of the corresponding peaks, a and c are the lattice parameters. The lattice constant a was calculated using the c/a ratio for wurtzite structure

$$\frac{c}{a}= \sqrt{\frac{8}{3}} ,$$
(4)

where a and c are lattice constants. The crystallite size, D, lattice parameters, a and c, and interplanar distance of (002) planes, d002, are shown in table 1. Crystallite size has been found to vary approximately between 10.9 and 9.7 nm. It is seen that the crystallite size of Gd-doped ZnO is less than that of pure ZnO. The lattice parameter a and c increased after doping with Gd in ZnO. The reduction in crystallite size after doping with Gd can be attributed to the distortion in ZnO structure [30].

Table 1 Crystallite size D, lattice parameter c and interplanar distance d002 of (002) planes corresponding to different Gd doping percentages.
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Raman spectra of ZnO and Gd-doped ZnO films recorded between 50 and 900 cm−1 with an excitation wavelength of 532 nm are shown in figure 2. Wurtzite ZnO belongs to the space group C6V. The primitive cell of ZnO has 2 zinc atoms and 2 oxygen atoms. Hence, at the Γ point of the Brillouin zone, optical phonons have the symmetries, A1+2B1+E1+2E2 [36]. The 2B1 symmetry modes are not Raman active. Both polar A1 and E1 branches split into longitudinal optical (LO) and transverse optical (TO) modes. E2 modes are nonpolar and have two frequencies, E2 (low) and E2 (high). The E2 (low) mode predominantly involves vibrations of heavy Zn sublattice, while E2 (high) mode involves vibrations of lighter O sublattice. For the undoped and Gd-doped ZnO thin films grown on Si(111) substrate, Raman peaks were observed at 98.41, 437.31 and 579.80 cm−1, which correspond to E2 (low), E2 (high) and E1 (LO), respectively. The E1 (LO) peak at 579.80 cm−1 is associated with the defects in the ZnO films [37,38], which may be due to VO and Zni in the films. The intensity of E2 (high) and E2 (low) modes indicate the crystallization of ZnO crystal structure [38,39]. The intensity of E2 (high) and E2 (low) peaks are found to decrease with the increase in Gd concentration, which shows the restraint degree of crystallisation. Other peaks observed are due to the Si(111) substrate. Kumar et al [40] observed that, in Er-doped ZnO synthesized by solid-state reaction method, peaks attributed to Er2O3 appear, in addition to peaks corresponding to ZnO. However, in our results, the same peaks observed in pure and Gd-doped ZnO thin films confirm the absence of any secondary structures due to Gd doping.

Figure 2
figure 2

Raman spectra in the range 50–900 cm−1 of ZnO with Gd doping percentage of (a) 0, (b) 0.05, (c) 0.1 and (d) 1 at%.

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3.2 Morphological analysis (AFM)

The surface roughness of a thin film is an important parameter for better device fabrication. It influences the electrical conductivity, optical properties [8], structural integrity and mechanical reliability [41] of the film. For practical devices in spintronics applications, it is important to have low roughness value for thin films. The morphology and surface roughness of the films were studied by AFM analysis. The images were reconstructed on the 5 µm × 5 µm field scan area. It is observed from the AFM images shown in figure 3 that the grains are distributed throughout the surface of the substrate homogeneously and compactly. The root mean square roughness (Rq) values are displayed in table 2. It is seen that 1 at% Gd-doped ZnO thin film shows the lowest roughness value.

Figure 3
figure 3

2D AFM images of ZnO with Gd doping percentage of (a) 0, (b) 0.05, (c) 0.1 and (d) 1 at%.

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Table 2 Root mean square average of roughness (Rq) values corresponding to different Gd doping percentages.
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3.3 Elemental analysis (XPS)

X-ray photoelectron spectroscopy reveals the electronic states of elements present in the sample. Survey spectrum and high-resolution spectra corresponding to each element in the films were recorded. Calibration of the binding energy was done using the C 1s adventitious carbon layer on the surface of the sample. The binding energies corresponding to the peaks obtained in the spectra were compared with the existing literature database (NIST database). The wide scan spectrum of 1 at% Gd-doped ZnO film given in figure 4a shows the presence of zinc, oxygen and gadolinium in addition to adventitious carbon. The corresponding high-resolution spectra of Gd resolved into Gaussian components are shown in figure 4b. The spin-orbit split doublet is located at 1187.32 and 1221.06 eV for Gd 3d5/2 and Gd 3d3/2, respectively, which matches with that of Gd in Gd2O3. This shows that Gd exists in the sample in 3+ state. Two satellite peaks of Gd 3d3/2 are found at 1229.53 and 1238.66 eV, respectively [42]. The peak at 1194.94 eV corresponds to Zn 2s [43]. The O 1s high-resolution spectra of pure ZnO and 1 at% Gd-doped ZnO are shown in figure 4d. O 1s peak is deconvoluted into two Gaussian peaks at 529.5 and 531.2 eV. The first peak is attributed to the oxygen atoms associated with Zn atoms in the wurtzite structure [44]. The second peak is attributed to the O2− ions that are in the oxygen deficient region [44]. Relative ratios of peaks attributed to oxygen vacancy and the Zn-O bonding is increased in 1 at% Gd-doped ZnO thin film. This shows that the Gd doping introduced more oxygen vacancies in the film. In the high-resolution spectrum of Zn 2p in ZnO and 1 at% Gd-doped ZnO given in figure 4c, two peaks are found. The two peaks at 1020.6 and 1043.6 eV correspond to the binding energies of Zn 2p3/2 and Zn 2p1/2, respectively, which show 2+ electronic state of Zn.

Figure 4
figure 4

(a) Wide spectra of 1 at% Gd-doped ZnO. (b) High-resolution spectra of Gd in 1 at% Gd-doped ZnO. (c) Zn 2p spectra of ZnO and 1 at% Gd-doped ZnO. (d) O 1s spectra of ZnO and 1 at% Gd-doped ZnO.

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3.4 Optical analysis (PL spectroscopy)

Photoluminescence spectra of the fabricated films were recorded to investigate the structural defects such as atomic and ionic vacancies, interstitials and substitutions. Figure 5 shows the PL spectra of 1 at% Gd-doped ZnO thin films grown at different oxygen partial pressures. The broad peak at around 2.7 eV in the PL spectra of 1 at% Gd-doped ZnO thin films is due to the presence of Zni and VO in the films. Peaks centred at around 3.2 eV in all the spectra corresponding to the near band edge (NBE) transition is attributed to electron–hole recombination between the conduction band and the valence band. It has been observed that the relative intensities of peaks corresponding to visible (blue and green) emissions and NBE transition (Ivis/INBE) are decreasing with the increase in oxygen partial pressure, which shows that the oxygen deficiency related defects are reduced as oxygen partial pressure is increased. In other words, the film grown under pure Ar atmosphere has more native defects.

Figure 5
figure 5

PL spectra in the energy range from 2.4 to 3.4 eV of 1 at% Gd-doped ZnO under Ar:O2 ratio of (a) 100:0, (b) 75:25 and (c) 50:50.

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PL spectra of 0, 0.05, 0.1 and 1 at% Gd-doped ZnO films are shown in figure 6. A broad peak was found at 2.0 eV, which corresponds to the transition of an electron from the conduction band to a deep level of doubly ionized oxygen vacancy. The red emission at 1.65 eV corresponds to the transition from zinc interstitial to doubly ionized oxygen vacancy [45]. The PL spectra in the range of 1.4 to 4 eV do not show any changes with varying concentrations. However, when the spectra are plotted between 2.4 and 3.4 eV, the difference is evident and is shown in figure 7. The PL spectra in the range 2.4 to 3.4 eV were deconvoluted into 4 peaks by Voigt function. The peak at 3.01 eV corresponds to weak violet emission due to the transition of an electron from zinc interstitial to valence band [45]. At 2.83 eV, all spectra show peaks that correspond to blue emission, which is a resultant of recombination between the electrons localized at the extended interstitial zinc and holes in the valence band [45]. The peak at 2.64 eV corresponds to blue-green emission due to electron transition from singly ionized oxygen vacancy to valence band [46]. Thus, the study confirms that pure Ar atmosphere growth condition results in more oxygen deficiency in films, which is manifested in the form of VO and Zni [34]. These two are the most stable defects found in ZnO [47]. A small increase in Iblue/INBE and Ired/INBE with the increase in Gd doping percentage was observed from the analysis of PL spectra, which shows that the Zni and VO defects are increased slightly by Gd doping. It might be due to structural disorders created by ionic size mismatched Gd atoms as opposed to Zn in the ZnO lattice [45].

Figure 6
figure 6

PL spectra ZnO films in the range of 1.4 to 4 eV for Gd doping percentage of (a) 0, (b) 0.05, (c) 0.1 and (d) 1 at%.

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Figure 7
figure 7

Deconvoluted PL spectra of ZnO films in the range of 2.4 to 3.4 eV for Gd doping percentage of (a) 0, (b) 0.05, (c) 0.1 and (d) 1 at%.

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3.5 Magnetic analysis (VSM)

The magnetization measurement has been carried out for Si(111) substrate alone at room temperature using vibrating sample magnetometer, and then, performed for Gd-doped ZnO films on Si(111) substrate. The magnetization data of thin films were corrected by subtracting the diamagnetic response of Si(111) substrate. M–H loop of 1 at% Gd-doped ZnO thin films deposited at different oxygen partial pressures are shown in figure 8. It is worthy to note that film deposited at Ar:O2 = 100:0 condition exhibited RTFM, and at other oxygen partial pressures, films exhibited a mix of diamagnetic and ferromagnetic nature. This preliminary study is the driving force to investigate the effect of Gd-doped ZnO films in pure Ar atmosphere as mentioned earlier.

Figure 8
figure 8

M–H loop of 1 at% Gd-doped ZnO grown under Ar:O2 ratio of (a) 100:0, (b) 75:25 and (c) 50:50.

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M–H loop of deposited ZnO thin films doped with different concentrations of Gd in Ar atmosphere is given in figure 9. ZnO films with 0.1 and 1 at% percentage Gd shows ferromagnetic nature with saturation magnetization (Ms) values of 3.29 and 4.83 emu cm−3, respectively. The total magnetic moment per Gd is estimated to be 2.71 and 0.4 µB per Gd, respectively, for 0.1 and 1 at% Gd-doped ZnO (summarized in table 3). Hence, Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange interaction cannot explain the mechanism for magnetism here, as RKKY interaction will result in a large value of magnetic moment per Gd [48]. The doping percentages chosen here are far less than the percolation threshold of ZnO. Since the distance between Gd3+ ions is higher than the lattice constant of ZnO, the mechanism related to super-exchange is not applicable here. Moreover, Gd is in its only oxidation state 3+ as evident from XPS studies. Hence, the double-exchange mechanism also could not explain the magnetic properties observed [21]. By analysing the PL and magnetic studies of 1 at% Gd-doped ZnO thin films at different oxygen partial pressures, it becomes clear that the oxygen deficient condition that caused the formation of a critical amount of VO or Zni defect is responsible for RTFM. The magnetic study reveals that the pure ZnO film exhibits diamagnetic nature. This demonstrates that the lattice defect is not the only reason for RTFM in Gd-doped ZnO system. It also points out that the ferromagnetism induced in other films is not due to the presence of any magnetic impurities. The 0.05 at% Gd-doped ZnO film shows a mixture of diamagnetic and ferromagnetic nature. With further increase in Gd doping concentration, the ferromagnetic property was realized. Hence, it can be inferred that the Gd doping has certainly induced RTFM when the oxygen deficiency related defects are in sufficient numbers. Roqan et al [47] and Venkatesh et al [33] suggested that defects related to oxygen deficiency–Gd complex mediate ferromagnetism in Gd-doped ZnO systems. Aravindh et al [49] used density functional theory to show that Gd-doped ZnO nanowire exhibits RTFM due to s-f coupling when oxygen vacancy is present in it. Vijayaprasath et al [50] observed that RE transition metal-doped ZnO shows ferromagnetism due to s-f coupling between RE ions and ZnO host states in the presence of oxygen vacancy and zinc interstitials. In the case of Gd-doped ZnO thin films, Roqan et al [51] have proven by DFT calculation that ferromagnetism through s-f or s-d coupling is not possible because the f state is far from the conduction band minimum and does not overlap with the Fermi level. Hence, the possibility of RTFM due to s-f coupling is ruled out in our samples. There is a lot of literature suggesting that VO and Zni together contribute to RTFM in ZnO [52,53,54]. Although some of the literature points out which of the above defects is dominating in each case, the exact contribution of each defect to the magnetic properties goes unmentioned. Oxygen vacancies in the state of VO++ carry no trapped electron and hence VO++ could not be responsible for ferromagnetism in Gd-doped ZnO films [16]. Now, we are left with Zni+ and VO+. Either of the two or both together play a role in ferromagnetism mechanism along with the Gd3+ ions. From the PL analysis, Zni+ appears to be the dominant defect, which is a shallow donor defect formed by the Frenkel reaction [55],

Figure 9
figure 9

VSM of ZnO with Gd doping percentage of (a) 0, (b) 0.05, (c) 0.1 and (d) 1 at%.

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Table 3 Magnetic saturation value of ZnO for different Gd doping percentages.
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$${\mathrm{Zn}}_{\mathrm{Zn}}\iff {{\mathrm{Zn}}_{\mathrm{i}}}^{*}+{\mathrm{V}}_{\mathrm{Zn}}$$
(5)

Further, electron transition occurs from Zni to conduction band and Zni+ is generated.

$${{\mathrm{Zn}}_{\mathrm{i}}}^{*}\iff {{\mathrm{Zn}}_{\mathrm{i}}}^{+}+{\mathrm{e}}^{-}$$
(6)

This donor electron remains weakly bound to the defect state Zni+ and thus is confined to a hydrogenic orbital with large Bohr radius [56]. When the donor concentration reaches the critical value, these hydrogenic orbitals form an impurity band [21]. These donor electrons interact with Gd3+ to form BMPs. When the number of BMPs is above the BMP percolation threshold of ZnO, they overlap with one another and the spins of Gd3+ get into parallel alignment.

Also, VO+ is formed by Schottky reaction in the ZnO lattice [57],

$$0 \iff {{\mathrm{V}}_{\mathrm{Zn}}}^{*}+{{\mathrm{V}}_{\mathrm{O}}}^{*}$$
(7)
$${{\mathrm{V}}_{\mathrm{O}}}^{*}\iff {{\mathrm{V}}_{\mathrm{O}}}^{+}+{\mathrm{e}}^{-}$$
(8)

The donor electron associated with VO+ is locally trapped in the hydrogenic orbital formed by VO+. The donor electron forms an impurity band when it reaches the critical value. These hydrogenic electrons also interact with Gd3+ ions to contribute to the formation of BMP. Thus, ferromagnetism is set by magnetic coupling between inter Gd3+ ions mediated by oxygen deficiency related defects (Zni+ and VO+).

It is observed that even when Zni+ and VO+ are present, pure ZnO thin film grown does not exhibit RTFM. Gd is in +3 state, and its electronic configuration is [Xe] 4f7. Hence, the effective coupling between two Gd3+ ions in the same donor orbital is ferromagnetic [21]. When the atomic percentage of Gd is 0.05, although ferromagnetism appears, the diamagnetic contribution from ZnO dominates as the number of Gd3+ is too low to establish long-range RTFM. This results in a system with a mixture of diamagnetic and ferromagnetic nature. When the doping percentage is increased, more Gd3+ ions are accommodated inside the hydrogenic orbital associated with the defect, which gives rise to long-range ferromagnetic order in 0.1 and 1 at% Gd-doped ZnO.

The effective magnetic moment per Gd is more for 0.1 at% Gd-doped ZnO compared to 1 at% Gd-doped ZnO. The effective magnetic moment of one Gd3+ ion in the sample is 7.9 µB calculated from the following equation [58],

$${\mu }_{\mathrm{eff}}=g{\mu }_{\mathrm{B}}[{J(J+1)]}^\frac{1}{2},$$
(9)

where g is Landé g factor, \({\upmu }_{\mathrm{B}}\) is Bohr magneton value and J the total angular momentum quantum number. For lower doping percentages of Gd, the effective magnetic moment per Gd should approach this value. The number µB/Gd3+ in the prepared samples was calculated using the following relation [59],

$${n}_{\mathrm{eff}}=\frac{\mathrm{Saturation\; magnetization}}{(\mathrm{Bohr\; magneton})*(\mathrm{number\; of\; magnetic\; atoms\; per \;unit\; volume})}$$
(10)

Due to large ionic radii of Gd3+ ion (0.93 Å) compared to that of Zn2+ ion (0.74 Å), only a lesser number of Gd3+ ions presumably occupied the Zn2+ sites. Another assumption taken was that all of the Gd3+ ions occupied at Zn2+ sites contribute to ferromagnetism, which may not be true in the actual case. There could be uncoupled Gd ions. Hence, the calculated Ms value for 0.1 at% Gd-doped ZnO is 2.71 µB per Gd [60,61]. When the doping percentage of Gd in ZnO is increased to 1 at%, the magnetic moment per Gd3+ decreases to 0.40 µB per Gd. Number of magnetic atoms per unit volume in 1 at% Gd-doped ZnO is expected to be 10 times higher than that in 0.1 at% Gd-doped ZnO. However, the Ms values in units of emu cm–3 did not increase proportionally corresponding to the doping concentration, because (i) some Gd3+ ions would have moved to interstitial positions, and (ii) all Gd3+ ions at Zn2+ sites are not coupled ferromagnetically. Thus, interstitial Gd3+ ions, presence of uncoupled Gd3+ ions at Zn2+ sites and large ionic radius all together cause the large deviation from the expected effective magnetic moment per Gd3+.

The measured magnetization of 1 at% Gd-doped ZnO and 0.1 at% Gd-doped ZnO are fitted to the relation given below to find out the number of BMPs [62],

$$ M = M_{0} L\left( x \right) + \chi_{{{\text{m}} }} H, $$
(11)

Here, M0 = Nms, where N is the number of BMPs in the sample and ms the magnitude of the aligned spontaneous magnetic moment of single BMP. L(x) is the Langevin function with \(x=\frac{{m}_{\mathrm{eff}}H }{{k}_{\mathrm{B}}T}\), where kB is the Boltzmann constant and meff the effective spontaneous magnetic moment per BMP. \({\chi }_{\mathrm{m}}\) is the susceptibility of the matrix. So, the first term in the equation represents BMP contribution and the second term, the matrix contribution. On fitting with the above equation, the number of BMPs in 1 and 0.1 at% Gd-doped ZnO thin films are estimated to be 5.233 × 1017 and 1.5485 × 1017 cm−3, respectively, which is higher than the BMP percolation threshold for ZnO (1.5 × 10−3 cm−3) [21]. The BMP fit has been given in figure 10.

Figure 10
figure 10

Fit of the M–H curve with BMP model for 0.1 and 1 at% Gd-doped ZnO.

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There must be a critical number of carriers that would have caused the overlapping of 1s orbitals of electron associated with the oxygen deficiency related defects, which further leads to the formation of BMP. According to BMP model, this critical number of carriers should be in the order of 1019 cm−3 for ZnO [21,63]. The presence of Zni and VO clearly shows that all the samples prepared are n type. According to BMP model, it is expected that the donor electron concentration must be in the range of 1019 cm−3 or above for 0.1 and 1 at% Gd-doped ZnO thin films grown at oxygen deficient conditions.

From our analysis, it is evident that the oxygen deficient condition favours ferromagnetism. There are two prerequisite conditions for the film to exhibit RTFM, namely, (1) oxygen deficiency related defects in +1 oxidation state in sufficient number so that the BMPs percolate, and (2) an appropriate amount of Gd doping for the film. Under these conditions, the Ms value will vary with Gd concentration.

4 Conclusion

In this article, the effect of Gd on ZnO thin films in pure Ar ambience was investigated to realize ferromagnetism. As part of the investigation, 1 at% Gd-doped ZnO thin film was deposited at different Ar:O2 ratios (100:0, 75:25 and 50:50) on Si(111) substrate. The film deposited under oxygen deficient condition (pure Ar) exhibited RTFM, whereas the films deposited at other oxygen partial pressures exhibited a mixture of diamagnetism and ferromagnetism.

Based on this preliminary investigation, different concentrations (0, 0.05, 0.1 and 1 at%) of Gd-doped ZnO films were grown under pure Ar atmosphere to introduce more native defects (VO, Zni). The structural, morphological, elemental, optical and magnetic properties were analysed. It has been found that for 0.1 and 1 at% Gd-doped ZnO films exhibit long-range RTFM as the critical amount of Zni+ and VO+, and the appropriate amount of Gd3+ ions exist for these films. These conditions have been investigated and discussed in detail. Pure ZnO has been observed to exhibit diamagnetism. The 0.05 at% Gd-doped ZnO film showed a vortex state, as one of these prerequisite conditions, the appropriate amount of Gd3+ ions, had not been satisfied. The values of saturation magnetization for 0.1 and 1 at% Gd-doped ZnO film have been found to be 2.71 and 0.40 µB per Gd, respectively. The number of BMPs formed in 0.1 and 1 at% Gd-doped ZnO samples are obtained by BMP fit as 1.5485 × 1017 and 5.233 × 1017 cm−3, respectively, which are well above the BMP percolation threshold of ZnO. It is proved that the appropriate Gd doping along with a sufficient number of oxygen deficiency related defects are required for the system to be ferromagnetic. The magnetic properties of Gd-doped ZnO DMS system are well explained with BMP model based on oxygen deficiency related defects.