Synthesis, Structure, and Magnetic Properties of (Co/Eu) Co-Doped ZnO Nanoparticles

Abstract

Transition-metal and rare-earth element co-doped ZnO nanoparticles have attracted significant attention due to their potential applications in spintronics and optoelectronics. In this study, Zn_0.95Co_0.01EuxO (x = 0.01–0.05) nanoparticles were synthesized using the sol–gel technique. The estimated stress, strain, and crystallite sizes of the synthesized Co/Eu co-doped ZnO nanoparticles were calculated using the Williamson–Hall method, and their electron spin resonance (ESR) properties were investigated to examine the effect on their magnetic and structural properties. X-ray diffraction (XRD) analysis confirmed the presence of a single-phase structure. Surface morphology, elemental composition, crystal quality, defect types, density, and magnetic behavior were characterized using scanning electron microscope (SEM), electron-dispersive spectroscopy (EDS), and ESR techniques, respectively. The effect of Eu concentration on the linewidth (ΔBpp) and g-factor in the ESR spectra was studied. By correlating ESR results with the obtained structural properties, room-temperature ferromagnetic behavior was identified.

1. Introduction

In recent decades, the investigation of transition metal (TM)-doped ZnO systems—where TMs denote the d-block elements of the periodic table—has garnered significant attention due to their versatile optical and magnetic properties, offering potential applications in optoelectronic devices, spintronics, biomedical systems, sensors, and surface acoustic wave technologies [1,2,3,4,5,6,7,8].

The theoretical forecast of room-temperature ferromagnetism (RT-FM) in p-type Mn-doped GaN and ZnO by Dietl et al. [9] has since been experimentally supported, with similar phenomena observed in ZnO, GaN, and AlN doped with transition metals like Mn, Co, and Cu [10,11,12,13]. Notably, Cu-doped semiconductors are distinctive, as neither metallic Cu nor its secondary phases (except nanocrystalline CuO [14]) significantly contribute to ferromagnetism, effectively eliminating secondary phase contributions.

Electron paramagnetic resonance (EPR) is a powerful technique capable of precisely analyzing the structural and magnetic properties of magnetic nanoparticles. Parameters such as the g-factor, resonance field, and line width reveal information about the core structure and surface anisotropy [15]. It has proven to be an extremely effective method for investigating the magnetic properties of such doped systems and has been widely used in the study of TM-doped ZnO and AlN systems.

Despite ongoing research, the precise role of intrinsic defects—particularly oxygen vacancies (V₀)—in governing the magnetic behavior of ZnO remains incompletely understood. Increasing experimental evidence suggests that defect-induced ferromagnetism may arise even in the absence of magnetic dopants, underscoring the importance of defect engineering in non-magnetic oxide systems [15,16,17,18,19,20,21]. Controlled defect introduction through ion implantation offers a promising route to systematically modulate the magnetic properties of ZnO nanostructures.

In this study, the structural properties of Zn_0.95Co_0.01EuxO (x = 0.00–0.05) nanoparticles were analyzed using X-ray diffraction (XRD). ZnO was co-doped with the transition metal Co and the rare-earth element Eu to investigate its structural and magnetic behaviors. Structural parameters, including stress, strain (deformation), and crystallite size, were calculated using the Williamson–Hall method and compared with values obtained from the Debye–Scherrer equation. Morphological characteristics were examined by scanning electron microscopy (SEM). The g-factor values were determined from electron spin resonance (ESR) measurements, and the correlation between the structural parameters and magnetic properties was systematically evaluated.

2. Materials and Methods

Zn_0.95−xCo_0.05Eu_xO nanoparticles were synthesized through a sol–gel process by varying the Eu doping concentration within the range of x = 0.00 to 0.05. The precursor materials included zinc acetate dihydrate (Zn(CH₃CO₂)₂ 2H₂O, Sigma Aldrich, Saint Louis, MO, USA), cobalt(II) acetate tetrahydrate (Co(CH₃CO₂)₂·4H₂O, Alfa Aesar, Haverhill, MA, USA), and europium acetate tetrahydrate (Eu(CH₃COO)₂·4H₂O, Alfa Aesar). Methanol (CH₃OH) and acetylacetone (C₅H₈O₂) were used as solvents and chelating agents to achieve homogenous, transparent solutions. Following precise weighing, all reagents were combined and stirred at 300 rpm for a minimum of five hours at room temperature without the application of heat.

The solvents were then evaporated, and the resulting gels were preheated in air at temperatures ranging from 200 °C to 450 °C for 10 min to initiate phase formation, as reported in previous studies [3,4,8,22] (the optimum preheating condition was determined to be 400 °C for 10 min). Finally, each composition was annealed at 600 °C to obtain the desired crystalline phase and physical properties [23].

Structural phase identification of the synthesized nanoparticles was carried out using a Rigaku X-ray diffractometer equipped with a Cu Kα radiation source. Surface morphology and microstructural features were characterized with a JEOL JSM-5910LV (JEOL Ltd., Tokyo, Japan) scanning electron microscope (SEM).

For magnetic property analysis, electron spin resonance (ESR) spectra were collected using a Jeol Mark-JES-FA300 (JEOL Ltd., Japan) Series X-band spectrometer operating at a frequency of 9.45 GHz, with a modulation amplitude of 0.5 mT and capable of generating DC magnetic fields up to 2 T. A TE₁₀₂ cavity was used for the measurements. The microwave power was set to 5 mW, the amplification (gain) level was adjusted to 50 arbitrary units, and the time constant was set to 0.03 s. During ESR measurements, the static magnetic field was swept from 0 to 1000 mT. To ensure measurement accuracy, background magnetic signals arising from the quartz sample tubes and the spectrometer cavity were eliminated from the data.

3. Results

3.1. Structural Characterization

The XRD patterns of Zn_0.95−xCo_0.05EuxO (x = 0.00–0.05) nanoparticles were recorded in the range of 20° ≤ 2θ ≤ 80° (Figure 1). The dominant diffraction peak corresponding to the (101) plane indicates a strong preferential crystallographic orientation along this direction, characteristic of the wurtzite ZnO structure. The absence of secondary phases in all samples confirms the high phase purity and crystallinity of the synthesized Co/Eu co-doped ZnO nanoparticles.

Structural parameters, including crystallite size (D), lattice constants (a, c), bond length (L), and unit cell volume (V), were calculated from the XRD data and are summarized in

Table 1. The average crystallite sizes, lattice parameters, atomic packing factor (c/a), and unit cell volume of Zn_0.95−xCo_0.05EuxO nanoparticles.

% Conc. (x)	D (nm)	a (Å)	c (Å)	c/a	Volume V (Å3)	SEM D (nm)
0	42.36	3.2388	5.1866	1.6014	47.117	42.91
1	37.44	3.2391	5.1892	1.6021	47.147	39.82
2	36.90	3.2351	5.1808	1.6014	46.957	39.45
3	37.02	3.2389	5.1866	1.6013	47.120	34.68
4	37.15	3.2351	5.1808	1.6014	46.957	36.49
5	37.15	3.2389	5.1864	1.6013	47.118	40.83

and

Table 2. Microstrain (ε), stress (σ), dislocation density (δ), atomic displacement (u), and bond length (L) in Zn_0.95−xCo_0.05EuxO nanoparticles.

% Conc. (x)	Ɛ	σ * 109 (N/m2)	δ (nm−2)	u	L (Å)
0	0.000818	−23.068	0.000557	0.37998	1.9708
1	0.000926	−23.056	0.000713	0.37987	1.9712
2	0.000939	−22.535	0.000734	0.37998	1.9686
3	0.000936	−23.049	0.000730	0.37999	1.9709
4	0.000933	−23.018	0.000724	0.37998	1.9686
5	0.000933	−23.030	0.000725	0.38000	1.9708

. The calculation procedures for dislocation density (δ), stress (σ), microstrain (ε), bond length (L), atomic displacement parameter (u), and crystallite size (D) were adopted from Guler et al. [17].

The Zn–O bond length was calculated as follows:

$$L=\sqrt{\left({\displaystyle \frac{a^2}{3}}\right)+{\left[0.5-u\right]}^2{c}^2}$$

(1)

where the internal parameter u for the wurtzite structure is as follows:

$$u=\left({\displaystyle \frac{a^2}{3c^2}}\right)+0.25$$

(2)

The lattice constants were determined from the following equation:

$${\displaystyle \frac{1}{{\mathrm{d}}_{\mathrm{h}\mathrm{k}\mathrm{l}}^2}}={\displaystyle \frac{4}{3}}\left({\displaystyle \frac{{\mathrm{h}}^2+\mathrm{h}\mathrm{k}+{\mathrm{k}}^2}{{\mathrm{a}}^2}}\right)+{\displaystyle \frac{{\mathrm{l}}^2}{{\mathrm{c}}^2}}$$

(3)

The crystallite size was calculated using the Debye–Scherrer equation as follows:

$$D={\displaystyle \frac{K \lambda }{{\beta }_{hkl}cos\left(\theta \right)}}$$

(4)

where βₕₖₗ is the integral breadth, K = 0.90, λ = 0.1540 nm (Cu Kα), and θ is the Bragg angle.

As shown in Figure 2, both the a and c lattice parameters exhibit a similar oscillating pattern as a function of Eu concentration, indicating no significant distortion in the crystal structure due to Eu incorporation.

Microstrain (ε) and stress (σ) values versus Eu concentration are plotted in Figure 3. Apart from 0% and 2% Eu doping levels, an inverse relationship between ε and σ is observed. Figure 4a illustrates the changes in lattice distortion factor (c/a) and Zn–O bond length (L) with Eu concentration. Figure 4b shows an inverse correlation between crystallite size (D) and microstrain (ε), implying that internal strain increases with decreasing crystallite size. The direct relationship between microstrain and dislocation density is consistent with the values reported in Table 2. Figure 4c demonstrates the correlation between crystallite size (D) and stress (σ), while Figure 5 presents the inverse trend between c/a ratio and unit cell volume as a function of Eu concentration.

A comprehensive analysis was further conducted using the Williamson–Hall (W–H) approach to quantify the lattice strain and stress contributions, as discussed in the following section.

3.2. Williamson-Hall (W-H) Analysis

The Debye–Scherrer equation provides a reasonable estimation of crystallite size (D); however, it does not account for the effect of internal strain within the crystal lattice. As originally demonstrated by Stokes and Wilson [24], peak broadening arises from both crystallite size (D) and microstrain (ε) contributions.

The microstrain (ε) can be calculated using the following relation:

$$\mathsf{\epsilon }={\displaystyle \frac{{\beta }_{hkl} }{4 tan\left(\theta \right)}}$$

(5)

Small crystallite sizes primarily contribute to the observed peak broadening and strain-induced line broadening. Equations (4) and (5) indicate that D and ε have different angular dependencies with respect to θ. Therefore, the Williamson-Hall (W-H) method offers a reliable means to decouple the size and strain effects on peak broadening.

Specifically, strain-induced broadening leads to a linear dependence of the integral breadth βₕₖₗ on tan θ, while size-induced broadening varies inversely with cos θ. In order to obtain more comprehensive information about the strain and stress characteristics, three different W-H methods were employed:

Uniform Deformation Model (UDM): Assumes homogeneous deformation across all crystallites. It provides estimates of ε (microstrain) and D (crystallite size) without considering stress or energy effects.

Uniform Stress Deformation Model (USDM): Takes the elastic modulus into account and enables the calculation of internal stress. In addition to crystallite size and microstrain, it allows the determination of internal stress.

Uniform Deformation Energy Density Model (UDEDM): Evaluates the energy density caused by lattice distortions and provides a more comprehensive analysis of structural deformation.

These complementary W-H models allowed for the simultaneous evaluation of crystallite size (D), microstrain (ε), internal stress (σ), and deformation energy density (u) in Co/Eu co-doped ZnO nanoparticles.

3.2.1. Uniform Deformation Model

Williamson and Hall presented a mathematical model that connected strain-induced broadening effects to crystallite diameters. Mote et al. [25] later refined this strategy and created the equation found in Equation (6):

$${\beta }_{hkl}\cos \left(\theta \right)={\displaystyle \frac{K\lambda }{D}}+4 ϵ sin(\theta )$$

(6)

With βcos(θ) on the vertical axis and 4εsin(θ) on the horizontal, Figure 6 depicts the Williamson–Hall analysis based on the Uniform Deformation Model (UDM). In this linear plot, the slope represents the strain (ε), and the equation $D={\displaystyle \frac{K\lambda }{y_{interception}}}$ is used to obtain the crystallite size (D) from the y_-intercept.

The crystallite sizes and lattice strain values for Co/Eu co-doped ZnO nanoparticles obtained using the UDM approach are shown in

Table 3. Structural parameters for Co/Eu co-doped ZnO NPs, obtained via three Williamson–Hall-based models: UDM, USDM, and UDEDM.

	UDM		USDM				UDEDM
%	D (nm)	ε (10−4)	D (nm)	σ (N/m2) (106)	εmax (10−4)	εavg (10−4)	D (nm)	u (103)	σmax (N/m2) (106)	σavg (N/m2) (106)	εmax (10−4)	εavg (10−4)
1	71.47	15.4	60.28	0.1843	14.48	13.26	67.31	0.1493	0.1569	0.1446	15.31	14.64
2	60.09	13.2	54.65	0.1503	11.81	10.82	60.09	0.1038	0.1308	0.1206	12.77	12.21
3	61.89	12.4	54.85	0.1484	11.66	10.68	59.35	0.0970	0.1265	0.1165	12.35	11.80
4	57.93	10.7	54.85	0.1484	11.66	11.37	57.24	0.0764	0.1122	0.1034	10.96	10.47
5	83.03	21.1	61.35	0.2448	19.23	17.61	72.59	0.2696	0.2108	0.1943	20.58	19.68

. In accordance with the information in Table 3, the crystallite size reaches its maximum value of 83.03 nm at 5% Eu doping and its minimum value of 57.93 nm at 4% Eu, as shown in Figure 6. In the Co/Eu co-doped ZnO structure, Eu doping up to 4% causes a general decreasing trend in crystallite size, which is then followed by a sudden increase. Similarly, when macrostrain is examined, the same behavior is observed, that is, the macrostrain decreases up to 4% Eu doping, and then a sudden increase occurs beyond this point.

3.2.2. Uniform Stress Deformation Model

In the Uniform Deformation Model (UDM), strain is assumed to be isotropically distributed across all crystallographic directions. However, due to the inherent anisotropy of nanoparticles, this assumption becomes inadequate for accurate modeling. The directional dependence of Young’s modulus within the crystal must be considered to provide a more realistic estimation of strain. To address this limitation, alternative models such as the Uniform Stress Deformation Model (USDM) and Uniform Deformation Energy Density Model (UDEDM) have been introduced [25].

In the modified formulation proposed by Mote et al. [25], the isotropic strain term εₕₖₗ is replaced by the ratio σ/Yₕₖₗ, where Yₕₖₗ represents Young’s modulus along specific crystallographic orientations. The W–H equation is thus rewritten as follows:

$${\beta }_{hkl}\cos \left({\theta }_{hkl}\right)={\displaystyle \frac{K\lambda }{D}}+4 \sigma /Y_{hkl} sin({\theta }_{hkl})$$

(7)

The directional Young’s modulus Yₕₖₗ for hexagonal structures is calculated as follows:

$$Y_{hkl}={\displaystyle \frac{{[h^2+\frac{{\left(h+2 k\right)}^2}{3}+(\frac{aı}{c})]}^2}{S_{11}{\left[h^2+\frac{{\left(h+2 k\right)}^2}{3}\right]}^2{+ S}_{33}{\left(\frac{al}{c}\right)}^4+\left(2 S_{13}+S_{44}\right){[h^2+\frac{{\left(h+2 k\right)}^2}{3}]\left(\frac{al}{c}\right)}^2}}$$

(8)

Here, S₁₁, S₁₃, S₃₃, and S₄₄ are the elastic compliance constants (in m²/N), which for hexagonal ZnO are given as follows: S₁₁ = 7.858 × 10⁻¹² m²/N, S₁₃ = −2.206 × 10⁻¹² m²/N, S₃₃ = 6.94 × 10⁻¹² m²/N, and S₄₄ = 23.57 × 10⁻¹² m²/N [4,26,27].

In the USDM approach, the uniform stress σ is assumed to be evenly distributed across all crystallographic orientations. The microstrain for each plane is computed as εₕₖₗ = σ/Yₕₖₗ. In practice, the plot of βcos θ versus $4sin\left(\theta \right)\left(1/Y_{hkl}\right)$ yields a straight line, where the slope corresponds to the uniform stress σ, and the y-intercept provides the crystallite size (D) through D = Kλ/y_intercept.

The USDM analysis results for the Co/Eu co-doped ZnO nanoparticles are presented in Figure 7, and the calculated values for stress, strain, and crystallite size are summarized in Table 3. Based on the slope analysis, the highest stress value of 0.2448 × 10⁶ N/m² was observed at 5% Eu doping, accompanied by the largest crystallite size of 61.35 nm. The results suggest that as nanoparticle size increases, the concentration of structural defects such as vacancies and dislocations decreases, leading to a more homogeneous crystal structure capable of sustaining higher internal stress.

3.2.3. Uniform Energy Density Deformation Model (UDEDM)

An alternative variant of the Williamson–Hall method, the Uniform Deformation Energy Density Model (UDEDM), was proposed by Mote et al. [25] to evaluate the elastic deformation energy density (u) in crystalline materials. This model assumes that the observed anisotropic strain arises from a uniform energy density distributed throughout the crystal structure.

The relation between energy density (u) and strain (ε) is given as follows:

$$u_{ed}={\displaystyle \frac{{\epsilon }^2{E}_{hkl}}{2}}$$

(9)

Substituting this expression into the modified Williamson–Hall equation results in the following equation:

$${\beta }_{hkl}\cos \left({\theta }_{hkl}\right)={\displaystyle \frac{K\lambda }{D}}+4 {\left(2 u_{ed}/Y_{hkl}\right)}^{{\displaystyle \frac{1}{2}}} sin({\theta }_{hkl})$$

(10)

Here, the slope of the linear fit provides information on the internal deformation energy density (u), while the intercept on the βcos(θ) axis yields the crystallite size (D).

The results obtained from the UDEDM model for the Co/Eu co-doped ZnO nanoparticles are presented in Figure 8. The corresponding values of crystallite size, energy density, stress, and microstrain derived from the UDEDM analysis are listed in Table 3.

As observed in Table 3, all structural parameters (D, u, σ, and ε) display a decreasing trend up to 4% Eu concentration, followed by a sharp increase at 5% Eu doping. The highest values recorded for 5% Eu doping were D = 72.59 nm, u = 0.2696 × 10³ J/m³, σ = 0.2108 × 10⁶ N/m², and ε = 20.58 × 10⁻⁴.

The experimental X-ray diffraction data were validated against the JCPDS reference file (Card No. 36-1451) for wurtzite ZnO, confirming the presence of diffraction peaks corresponding to the (100), (002), (101), (102), (110), (103), (200), (112), and (201) crystallographic planes. The calculated stress and strain values for each crystallographic plane are provided in

Table 4. Microstrain (ε) and stress (σ) values for Co/Eu co-doped ZnO nanoparticles, evaluated using three Williamson–Hall-based models—UDM, USDM, and UDEDM—across the (100), (002), (101), (102), (110), (103), (200), (112), and (201) crystallographic planes.

Zn0.94Co0.05Eu0.01O	Williamson-Hall Method			Zn0.93Co0.05Eu0.02O	Williamson-Hall Method			Zn0.92Co0.05Eu0.03O	Williamson-Hall Method
	USDM	UDEMD			USDM	UDEMD			USDM	UDEMD
h k l	ε (10−4)	σ (N/m2) (106)	ε (10−4)	h k l	ε (10−4)	σ (N/m2) (106)	ε (10−4)	h k l	ε (10−4)	σ (N/m2) (106)	ε (10−4)
1 0 0	14.48	0.138	15.32	1 0 0	14.48	0.138	15.32	1 0 0	11.81	0.115	12.77
0 0 2	12.79	0.147	14.40	0 0 2	12.79	0.147	14.4	0 0 2	10.43	0.122	12.01
1 0 1	12.42	0.149	14.18	1 0 1	12.42	0.149	14.18	1 0 1	10.13	0.124	11.83
1 0 2	11.18	0.157	13.46	1 0 2	11.18	0.157	13.46	1 0 2	9.12	0.131	11.22
1 1 0	14.48	0.138	15.32	1 1 0	14.48	0.138	15.32	1 1 0	11.81	0.115	12.77
1 0 3	11.34	0.156	13.55	1 0 3	11.34	0.156	13.55	1 0 3	9.25	0.130	11.30
2 0 0	14.48	0.148	15.32	2 0 0	14.48	0.138	15.32	2 0 0	11.81	0.115	12.77
1 1 2	14.44	0.138	15.30	1 1 2	14.44	0.138	15.3	1 1 2	11.78	0.115	12.76
2 0 1	13.76	0.141	14.93	2 0 1	13.76	0.141	14.93	2 0 1	11.22	0.118	12.45
Zn0.91Co0.05Eu0.04O	Williamson-Hall Method			Zn0.90Co0.05Eu0.05O	Williamson-Hall Method
	USDM	UDEMD			USDM	UDEMD
h k l	ε (10−4)	σ (N/m2) (106)	ε (10−4)	h k l	ε (10−4)	σ (N/m2) (106)	ε (10−4)
1 0 0	11.66	0.099	10.96	1 0 0	19.23	0.185	20.58
0 0 2	10.30	0.105	10.30	0 0 2	16.99	0.197	19.34
1 0 1	9.99	0.106	10.15	1 0 1	16.49	0.2	19.06
1 0 2	9.00	0.112	9.63	1 0 2	14.85	0.211	18.09
1 1 0	11.66	0.099	10.96	1 1 0	19.23	0.185	20.58
1 0 3	9.13	0.111	9.69	1 0 3	15.06	0.209	18.21
2 0 0	11.66	0.099	10.96	2 0 0	19.23	0.185	20.58
1 1 2	11.62	0.099	10.94	1 1 2	19.18	0.185	20.56
2 0 1	11.07	0.101	10.68	2 0 1	18.27	0.19	20.06

.

Table 1 summarizes the crystallite sizes obtained via the Debye–Scherrer method, while Table 3 presents the structural parameters calculated using the UDM, USDM, and UDEDM approaches. A strong agreement is observed among the average strain values obtained from all models, while stress and energy density show a clear correlation with the average strain values.

Linear plots of βcos(θ) versus 4sin(θ) for the UDM model are shown in Figure 6. Similar linear trends are observed for βcos(θ) versus 4sin(θ)(1/Yₕₖₗ) in Figure 7 (USDM) and for βcos(θ) versus $4sin\left(\theta \right)\sqrt{(2⁄E_{hkl}) }$ in Figure 8 (UDEDM). The consistent positive slopes in all models indicate the presence of tensile uniform stress throughout the Co/Eu co-doped ZnO samples.

Figure 9 displays the crystallite size variations calculated by the Debye–Scherrer, UDM, USDM, and UDEDM methods as a function of Eu concentration. The crystallite size decreased up to 4% Eu doping and showed a sharp increase at 5% Eu concentration, with the maximum size observed under UDM conditions (83.03 nm).

As shown in Figure 10a, both microstrain and stress values decrease steadily up to 4% Eu doping, followed by a significant increase at 5% Eu. The highest stress value was recorded using the USDM model (0.2448 × 10⁶ N/m²), while the highest microstrain was observed in the UDM model (21.1 × 10⁻⁴).

The structural properties of Co/Eu co-doped ZnO nanoparticles were analyzed using three different Williamson–Hall models: the Uniform Deformation Model (UDM), the Uniform Stress Deformation Model (USDM), and the Uniform Deformation Energy Density Model (UDEDM). Among these, the UDEDM was identified as the most reliable and comprehensive approach. Unlike UDM and USDM, which focus primarily on crystallite size, microstrain, and internal stress, the UDEDM also accounts for the elastic deformation energy density, providing a more holistic understanding of the lattice distortions caused by Eu incorporation. At 5% Eu concentration, the UDEDM yielded the highest deformation energy density (0.2696 × 10³ J/m³), reflecting significant structural modifications. Moreover, the values obtained using UDEDM demonstrated a more consistent and physically meaningful trend compared to the other models. Therefore, UDEDM was concluded to be the most accurate and reliable model for assessing the structural behavior of Co/Eu co-doped ZnO nanoparticles.

3.3. The Morphology Characteristics of Zn_0.95−xCo_0.05Eu_xO Structures

The surface morphology and elemental composition of the synthesized Zn_0.95−xCo_0.05EuxO nanoparticles were analyzed using Scanning Electron Microscopy (SEM (JOEL Ltd., Japan)) and Energy-Dispersive X-ray Spectroscopy (EDS (JOEL Ltd., Japan)), respectively. The SEM micrographs and corresponding EDS spectra for all samples are presented in Figure 11a, Figure 12a, Figure 13a, Figure 14a, Figure 15a, Figure 16a and Figure 11b, Figure 12b, Figure 13b, Figure 14b, Figure 15b, Figure 16b. The EDS spectra reveal the presence of Zn, Co, Eu, and O elements only, confirming the successful incorporation of Co and Eu into the ZnO lattice without any impurity phases or additional elemental contamination.

The SEM images, captured at a magnification of 1 µm, demonstrate that the nanoparticles exhibit predominantly spherical morphology with varying degrees of agglomeration. The particles appear to be partially fused and form dense, sponge-like clusters as the Eu concentration increases. In Figure 11c, Figure 12c, Figure 13c, Figure 14c, Figure 15c, Figure 16c, the Gaussian distribution curves of particle sizes obtained using ImageJ software (Imaje J bundled bit Java 8) are presented. It is clearly observed that most of the particle sizes are in the range of 34.68 nm to 42.91 nm. The trend observed in the SEM micrographs is consistent with the crystallite size data previously calculated via XRD (Table 1). Specifically, higher Eu doping levels promote increased agglomeration and densification of the nanoparticle clusters. Changes in surface energy and increased grain development brought on by the addition of Eu are responsible for this morphological transformation. However, because it decreases surface area and ruins uniformity, this kind of aggregation is typically undesirable for nanoscale applications.

3.4. ESR Studies

Electron spin resonance (ESR) spectroscopy is an effective technique to investigate magnetic centers in nanomaterials. It is especially useful for identifying the locations of magnetic ions or vacancies within the lattice structure. The spin Hamiltonian that describes the magnetic centers is expressed as follows:

H = μ_BSg_eH + H_cf + SDS + SAI + μ_NIg_nH + SJS + JS₁S₂

(11)

In this equation, μ_B represents the Bohr magneton, S is the electron spin operator, g_e denotes the electron g-factor tensor, and H is the external magnetic field. H_cf stands for the crystal field Hamiltonian, D is the zero-field splitting tensor, and A represents the hyperfine interaction tensor. I denotes the nuclear spin operator, μ_N is the nuclear magneton, g_n is the nuclear g-factor, and J corresponds to the exchange interaction constant between spins.

In this expression, the first term corresponds to the static Zeeman effect, which determines the main resonance field position and linewidth, while the last term describes dipolar and exchange interactions between spins located at different sites. Other terms account for crystal field energy, zero-field splitting, hyperfine interactions between electron and nuclear spins, spin-orbit coupling, and nuclear Zeeman interactions [4,18,28].

The ESR spectra of Co/Eu co-doped ZnO nanoparticles were recorded at room temperature using the first derivative of the absorption signal. The samples were aligned such that the sample tubes were parallel to the microwave magnetic field and perpendicular to the DC magnetic field. The spectrometer was operated with a field modulation frequency of 100 kHz and microwave power of 5 mW [29,30]. After subtracting background signals originating from the spectrometer cavity and empty sample tubes, the ESR signals were recorded in the field range of 200–400 mT. The resulting spectra are presented in Figure 17 [31,32].

Figure 17 shows the ESR spectra of Zn_0.95Co_0.05O and Zn_0.90Co_0.05Eu₀.₀₅O nanoparticles recorded in the magnetic field range of 200–400 mT. Prior to analysis, background signals arising from the microwave cavity and empty sample tubes were subtracted to isolate the intrinsic resonance signals. The spin Hamiltonian introduced in Equation (11) provides a framework for interpreting the observed spectral features.

The Zeeman interaction (Sg_eH) plays a central role in defining the resonance peak position and line broadening. This interaction primarily governs the main resonance field. In Zn_0.95Co_0.05O nanoparticles, the resonance peak appears with a g-factor of approximately 2.20, which is characteristic of Co²⁺ ions under tetrahedral coordination. Upon doping with Eu³⁺, as in Zn_0.90Co_0.05Eu₀.₀₅O nanoparticles, the g-factor shifts to approximately 2.05, reflecting changes in the local crystal field environment induced by Eu incorporation.

The zero-field splitting term (SDS) becomes significant for Co²⁺ ions (3d⁷, S = 3/2). In Zn_0.95Co_0.05O, this splitting remains relatively moderate, but in Zn_0.90Co_0.05Eu₀.₀₅O, lattice distortion caused by Eu³⁺ doping leads to enhanced zero-field splitting, resulting in broader line shapes and resonance shifts toward higher fields.

Dipolar and exchange interactions (SJS, JS₁S₂) are also observed. In Zn_0.95Co_0.05O, weak dipolar coupling exists between neighboring Co²⁺ ions through Co–O–Co pathways. Eu³⁺ substitution modifies the spatial arrangement of Co²⁺ ions, enhancing Co–O–Eu–O–Co dipolar interactions. This leads to a noticeable increase in the peak-to-peak linewidth (ΔB_pp) in the Eu-doped sample. The consistent observation of g > 2 in all ESR spectra is indicative of ferromagnetic behavior in Co/Eu co-doped ZnO nanoparticles. Such high g-values typically reflect localized magnetic moments and strong spin-orbit coupling effects within tetrahedrally coordinated Co²⁺ sites.

Hyperfine interactions (SAIs) are theoretically present; however, no resolved hyperfine structure is observed in either sample due to dominant spin relaxation and strong dipolar broadening effects.

Crystal field distortions (H_cf) are negligible in Zn_0.95Co_0.05O but become significant in Zn_0.90Co_0.05Eu₀.₀₅O. The incorporation of Eu³⁺ alters the local electric field distributions, which directly influence the Zeeman interaction and contribute to the observed spectral shifts and broadening.

In conclusion, the dominant resonance peak observed within 200–400 mT primarily originates from the Zeeman effect. The introduction of Eu³⁺ significantly modifies the magnetic resonance behavior by enhancing dipolar interactions, increasing crystal field distortions, and intensifying zero-field splitting effects.

3.5. Magnetic Analysis

ESR measurements were conducted at room temperature to investigate the magnetic properties of the samples. The spectra exhibited a broad single resonance peak, which is indicative of ferromagnetic behavior, as shown in Figure 17. From these ESR spectra, both the g-factor and the peak-to-peak linewidth (ΔB_pp) were determined. The recorded spectra for Zn_0.95Co_0.05O and Zn_0.90Co_0.05Eu₀.₀₅O nanoparticles were scaled and analyzed using X-band ESR spectroscopy. For Zn_0.90Co_0.05Eu₀.₀₅O nanoparticles, a stronger and broader resonance signal was observed near 335 mT, indicating significant magnetic interaction influenced by Eu doping. The trend in g-factor values, as illustrated in Figure 18, confirms the influence of Eu doping on spin–orbit coupling and magnetic field response of the system.

The asymmetry factor (P_asy) was calculated using the relation:

$$P_{asy}=1-{\displaystyle \frac{h_u}{h_L}}$$

(12)

where h_L and h_U represent the peak heights below and above the baseline of the ESR absorption spectrum, respectively [17]. The number of spins (Ns) was estimated using:

$$N_s=0.285\times I_{pp}\times {\left({∆B}_{pp}\right)}^2$$

(13)

where $I_{pp}$ is the peak-to-peak intensity and ${∆B}_{pp}$ is the line width. The calculated parameters are listed in

Table 5. ESR parameters for Zn_0.95−xCo_0.05O and Zn_0.95−xCo_0.05Eu₀.₀₅O nanoparticles.

Sample	hL	hU	Pasy	Ns	Ipp	line-Widths (ΔBpp mT)	g-Values
Zn0.95Co0.05O	95.25	114.23	−0.19	352.23	209.48	34.81	2.11
Zn0.90Co0.05Eu0.05O	−330.16	427.99	2.29	148.80	97.82	28.49	2.05

.

At 0% Eu concentration, lower $P_{asy}$ and higher $N_s$ values were observed, whereas at 5% Eu concentration, the asymmetry factor increased and the spin population decreased. These changes reflect the influence of Eu doping on the relaxation and distribution of spins within the crystal lattice. To further explore the spin relaxation mechanisms, the g-factor and ${∆B}_{pp}$ values were analyzed. As indicated in Table 5, ${∆B}_{pp}$ decreased from 34.81 mT to 28.49 mT upon Eu doping.

At 0% Eu concentration, lower $P_{asy}$ and higher $N_s$ values were found compared to 5% concentration. To understand the relaxation mechanism of the spins in the ESR spectrum, the g-factor and ${∆B}_{pp}$ were analyzed. As shown in Table 5, the ${∆B}_{pp}$_p values of the ESR signals were found to be in the range of 34.81 to 28.49 mT.

The g-factor values were calculated using the fundamental ESR resonance condition:

$$h\nu =g{\mu }_{\beta }H$$

(14)

where h is Planck’s constant, ν\nuν is the operating frequency (9.45 GHz for X-band ESR), μ_B is the Bohr magneton, and H is the applied magnetic field. Rearranging the equation yields:

g = 71.4477 ν/H

(15)

Using this expression, the g-factor values were determined and plotted in Figure 18. A g-factor greater than 2 indicates ferromagnetic characteristics of the ZnCoEuO nanoparticles, as supported by the data in Table 5. This ferromagnetic behavior can be attributed to microstrain and internal stress within the samples. With increasing Eu content, an initial decrease in crystallite size and microstrain was observed; however, at 5% Eu doping, a significant increase in crystallite size (UDM: 83.03 nm) was accompanied by notable increases in microstrain (UDM: ε = 21.1 × 10⁻⁴), internal stress (USDM: σ = 0.2448 × 10⁶ N/m²), and deformation energy density (UDEDM: u = 0.2696 × 10³ J/m³). In ESR analysis, the g-factor decreased from 2.11 to 2.05, while the linewidth narrowed with increasing Eu content. These findings suggest that Eu doping alters crystal symmetry, enhances dipolar interactions, and increases zero-field splitting, leading to significant modifications in both structural and magnetic properties.

4. Conclusions

Zn_0.95−xCo_0.05Eu_xO (x = 0.01–0.05, with increments of 0.01) nanoparticles were successfully synthesized using the sol–gel technique. The crystallite sizes and macrostrain values of Co/Eu co-doped ZnO nanoparticles were determined using four distinct methods: Debye–Scherrer, Uniform Deformation Model (UDM), Uniform Stress Deformation Model (USDM), and Uniform Deformation Energy Density Model (UDEDM). The results indicated that both crystallite size and macrostrain decreased with increasing Eu concentration up to 4%, followed by a sharp increase at 5% Eu content. The maximum crystallite size of 83.03 nm was observed in the UDM model, while the highest internal stress of 0.2448 × 10⁶ N/m² and the maximum microstrain of 21.1 × 10⁻⁴ were obtained from the USDM and UDM models, respectively.

The ESR analyses were conducted for 0% and 5% Eu-doped samples, correlating the observed magnetic behavior with the structural data obtained from the different models. The g-factor decreased from 2.11 at 0% Eu to 2.05 at 5% Eu, accompanied by a narrowing of the resonance linewidth. These changes indicate that Eu incorporation induces lattice distortion, enhances dipolar interactions, and intensifies zero-field splitting, collectively altering both the structural and magnetic characteristics of the nanoparticles. The ESR data revealed ferromagnetic characteristics at room temperature, with Eu doping enhancing magnetic coupling between Co²⁺ ions via Co-O-Eu-O-Co linkages.