Optical characterization and defect-induced behavior in ZnAl_1.999Ho_0.001O₄ spinel: Unraveling novel insights into structure, morphology, and spectroscopic features

Abstract

The ZnAl_1.999Ho_0.001O₄ phosphor, prepared by the solid-state method, crystallizes in the cubic spinel structure. Morphology and chemical composition homogeneity were determined via Energy Dispersive X-ray and SEM analysis. The (E_g) optical band gap was evaluated from the UV/vis absorption spectrum, confirming direct transition behavior according to Tauc's law. The Urbach energy (Eu) in the ZnAl_1.999Ho_0.001O₄ spinel was higher than that in the ZnAl₂O₄ spinel, indicating increased disorder and a higher concentration of defects due to Ho³⁺ ions. The penetration depth (δ(λ)), optical extinction (k(λ)), and refractive index (n(λ)) were assessed across wavelengths (λ). The room temperature absorption spectrum revealed several peaks corresponding to the 4f-4f transitions of Ho³⁺ ions.

1. Introduction

Spinel is an important material family with remarkable physical properties [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]]. Its composition obeys a general formula given by AB₂X₄, A is a metal cation (Zn²⁺, Mg²⁺, ….) located at tetragonal site T_d, B is a cation (Al³⁺, Ga³⁺, …) occupying an octahedral site O_h and X = O, S, …, Optoelectronic devices like photovoltaic solar cells [12], light-emitting diodes [13], and others can benefit from the employment of these materials. Spinels are also thought to be extremely adaptable luminescent matrices with a B-site that can accept various luminescent centers, such as lanthanide (Ln) ions and/or transition metal (TM) ions, resulting in a variety of compounds with appealing luminescent properties [5,6,11]. Recently, using solid-state and sol-gel techniques, we synthesized a novel spinel persistent phosphor of ZnAl_0.095Cr_0.05O₄ [5,6,11]. Studies have been focused on its structural, electrical, vibrational, and optical characteristics [5,6,11]: the Raman and infrared spectra at ambient temperature have been analyzed; the gap E_g has been established from absorption UV/vis and reflectance Spectra, and Tauc's law has validated the direct transition. The Urbach energy E_u is found to be 0.63 eV for ZnAl_1.95Cr_0.05O₄ indicating a disorder condition in this spinel. In the O_h site symmetry, the crystal field study was used to identify the electronic structure of Cr³⁺ from the optical spectra [5,6,11]. The Ho³⁺ ion is part of the Lanthanide family with a 4f¹⁰ electronic configuration. When it is part of the spinel constitution, a potential up-conversion material emerges due to its large anti-Stokes shift, longer lifetime, high photostability, sharp tunable emissions and ladder-like 4f energy levels [14]. The incorporation of Holmium (Ho³⁺) into the spinel system was found to introduce defects that significantly influence its optical properties. This study explores the intricate relationship between the presence of Ho³⁺ ions and the induced defects, shedding light on their pivotal role in modulating the optical features of the material. From the comprehensive analysis, including absorption spectra and other optical measurements, we aim to elucidate the specific mechanisms by which the introduced defects impact the optical behavior of the spinel system [[15], [16], [17]]. The spinel ZnAl_1.999Ho_0.001O₄ is an important compound in advanced photonic applications due to the presence of the Ho³⁺ ion, which is an activate center that emits in the shortwave infrared region (λ∼1.20 μm). The main ⁵I₇ → ⁵I₈ emission band characterizes the PL spectra of Ho³⁺.

In this work, ZnAl_1.999Ho_0.001O₄ spinel were prepared by solid-state reaction and characterized by structural and optical techniques to take a decisive step in decoding the complexities inherent in oxide systems. Beyond its contribution to the fundamental understanding of these materials, our study has the potential to influence the development of advanced materials, presenting opportunities for tailoring properties that can be exploited in various applications. This study represents an important undertaking, laying the foundation for advances in the scientific understanding and practical use of oxide materials [[18], [19], [20]].

2. Experimental details

The ZnAl_1.999Ho_0.001O₄ sample was synthesized via solid-state reaction using appropriate mixtures of ZnCO₃ (98%), Ho₂O₃(99%), and Al₂O₃ (99%). After annealing at 700 °C, the powders were crushed with an Agate Mortar and Pestle and gradually heated to the sintering temperature at 1200 °C, with a soaking time of 24h. Finally, the powders were compressed into pellets with an 8 mm diameter and annealed at 1200 °C for 24h.

The crystal structures were characterized using an X-ray Diffractometer (X-Ray Siemens D5000) equipped with a CuKα radiation source (λ = 1.5406 Å). Data collection was performed in the 2θ range of 20°–100° with a step size of 0.02°. A Horiba LabRam HR Evolution micro-Raman confocal system was used to obtain the Raman spectra within the 20-1000 cm⁻¹ range, with excitation at 532 nm. The acquisition parameters included an acquisition time of 10 s, 50 accumulations, and a laser power of approximately 17 mW at the sample. Wavenumber calibration was performed using the characteristic Si wafer band at 520.5 cm⁻¹. The morphology of the powder and chemical composition were examined using a TESCAN VEGA3 SBH scanning electron microscope (SEM) to assess compound homogeneity. Solid-state absorption spectra were acquired by measuring the reflectance using an AvaSpec-ULS-TEC Avantes Senseline Fiber Optic Spectrometer System coupled to a Mikropack DH-2000-BAL UV–Vis–NIR light source. A 45-degree angle probe tip fiber optic bundle (FCR-UV200/600-2-IND 1211040) was utilized for reflection measurements in powders and thick fluids. The 45-degree angle of the probe tip prevented direct back reflection from the window. Before determining the spectra of the solid samples, background correction was conducted by acquiring the baseline with 100% and 0% reflectance, using a Polytetrafluoroethylene (PTFE) reference sample and blocking the beam, respectively. A Thermo Scientific Nicolet 6700 device operating in the 400–4000 cm⁻¹ range was used to record the FTIR spectra. Room temperature EPR spectra of powder samples were obtained using a MiniScope MS 400 X-band EPR spectrometer (Magenttech Germany), equipped with a Suprasil Nitrogen Dewar (SP Wilmad-LabGlass, USA). The powder samples were placed in a 10 μL glass capillary (Duran Ringcaps, Hirschmann, Germany) for analysis. Structural Analysis (VESTA) software (Version 3 Copyright (C) 2006–2022, Koichi Momma and Fujio Izumi), Visualization Electronic and ImageJ software were employed for data analysis and visualization.

3. Results and discussion

3.1. X-ray diffraction study

The X-ray Diffraction patterns of the ZnAl_1.999Ho_0.001O₄ sample is shown in Fig. 1. Using the standard JCPDS data file [JCPDS. 82–1043], it is evident that the diffraction peaks are well indexed to (220); (311); (400); (331); (422); (333); (511); (440); (620) and (533) reticular crystal planes of cubic spinel structure phase Fd $\bar{3}$ m space group with lattice parameters a = b = c = 8.0884 Å. Using the Rietveld method, the X-ray diffractogram was refined and confirmed the presence of two phases for the spinel compound: a principal phase ZnAl_1.999Ho_0.001O₄ and an impurity phase with small amounts of ZnO as previously reported [5,21,22]. Table 1 illustrates the refined crystallographic parameters. The χ² refinement quality factors indicate the effective goodness of fit between the calculated and observed profiles. The structure of the ZnAl_1.999Ho_0.001O₄ compound is given in Fig. 2. As shown in this figure, the Zn cation resides in tetrahedral coordination (T_d sites), while the Al cation resides in octahedral coordination (O_h sites). The trivalent cation Ho³⁺, and generally the lanthanides Ln³⁺, substitute in the octahedral site of the Al³⁺ ions (Fig. 2) [23,24].

Fig. 1.

Rietveld refinement for the ZnAl_1.999Ho_0.001O₄spinel.

Table 1.

Results of Rietveld refinements.

Samples	ZnAl1.999Ho0.001O4
Space Group	Fd $\bar{3}$ m
a(Å)	8.0884
V(Å3)	529.1611
Rp	7.68
Rwp	8.75
χ2	3.04
Al–O (Å)	1.9191
Al–O–Al (°)	96.3309
ZnO (%)	4.84
ρth(g cm−3)	4.6086
ρexp(g cm−3)	2.3219
P(%)	49.6181
DW-H (nm)	67

Fig. 2.

Structural Figure with Vesta software of ZnAl_1.999Ho_0.001O₄ spinel [25].

The calculated density was determined by the formula [26]:

$${\rho }_{\text{th}}=\frac{\mathit{Z}\mathit{M}}{\mathit{V}{\mathit{N}}_{\mathit{A}}}$$ (1)

where N_A = 6.02 × 10²³ mol^-1 stands for the Avogadro number, Z = 8 represents the number of the unit cells for a cubic structure and M is the molar mass of the compound.

While the experimental density was calculated using the following formula [27]:

$${\rho }_{\exp }=\frac{\mathit{m}}{\mathit{\pi }\mathit{h}{\mathit{r}}^{\mathbf{2}}}$$ (2)

The radius, thickness, and mass of the pellet are represented by r, h, and m, respectively.

The difference between the theoretical and experimental density was evaluated by the following equation to assign the idea of porosity [28]:

$$\mathbf{P}(\%)=\frac{{\mathit{\rho }}_{\mathit{t}\mathit{h}}-{\mathit{\rho }}_{\mathit{exp}}}{{\mathit{\rho }}_{\mathit{t}\mathit{h}}}\mathbf{x}\mathbf{100}$$ (3)

The X-ray density ρ_th and the porosity P (%) are shown in Table 1.

It was found that the density value of ZnAl_1.999Ho_0.001O₄ is equal to 2.321₉ g cm⁻³. When comparing densities, the experimental density is lower than the theoretical density. Indeed, the sample prepared in practice has internal pores. Additionally, adding a small amount of Holmium has virtually no effect.

To calculate the average crystallite size we used the Williamson–Hall relation D_W-H [29,30]:

$$\mathrm{\beta }\cos \left(\mathrm{\theta }\right)=\frac{\mathit{K}\mathit{\lambda }}{{\mathit{D}}_{\mathit{W}-\mathit{H}}}+4\mathrm{\epsilon }\sin \left(\mathrm{\theta }\right)$$ (4)

where λ (1.5406 Å) is the wavelength, ԑ is the effective strain, β is the full-width at half maximum (FWHM), θ is the Bragg angle and K is the shape factor.

The value of the crystallite size was determined by the intercept of the linear fit of βcos(θ) as a function of 4sin(θ) (Fig. 3). Accordingly, the D_W-H values of this compound is illustrated in Table 1.

Fig. 3.

The Williamson-Hall plot of ZnAl_1.999Ho_0.001O₄ spinel.

3.2. SEM and EDX study

By the use of Scanning electron microscopy (SEM), we estimate the microstructure and morphology of ZnAl_1.999Ho_0.001O₄ spinel. As shown in Fig. 4, the grains are agglomerated with irregular shapes. In fact, the large surface area of the particles and their interaction with the weak van der Waals force are the causes of these agglomerations. Using ImageJ software, the average particle size distribution was found centered at 331 nm by the Lorentz fit, as shown in Fig. 4. Additionally, we displayed the energy dispersion spectrum (EDS) of ZnAl_1.999Ho_0.001O₄ in Fig. 5 to confirm their chemical composition. The spectrum affirms the presence of all the constituent chemical elements of Ho³⁺ substituted ZnAl₂O₄, such as Zn, Al, Ho and O, which demonstrates the purity of our sample. However, the map images presented in Fig. 5 reveal a homogeneous and uniform distribution of the constituent chemical elements of this material. The quantitative analysis of elements presented in the spinel ZnAl_1.999Ho_0.001O₄ is shown in Table 2.

Fig. 4.

SEM image and the average particle size histograms of ZnAl_1.999Ho_0.001O₄ spinel.

Fig. 5.

EDS spectrum of ZnAl_1.999Ho_0.001O₄ spinel.

Table 2.

EDX data of ZnAl_1.999Ho_0.001O₄ spinel.

Element/Symbol	Series	Atomic (%)	Error (%)
Aluminum/Al	K-series	61.83	6.31
Holmium/Ho	K-series	1.23	0.26
Zinc/Zn	K-series	36.94	1.09

3.3. Raman and FTIR study

Raman spectroscopy is recognized as a crucial analytical tool for phase structure studies, offering greater sensitivity compared to XRD. This heightened sensitivity stems from the fact that Raman energy is less penetrating than X-ray excitation energy [31]. The spinel unit cell contains 56 atoms, but the simplest primitive cell can be made with just 14 atoms. According to group theory, which is presented first by White and DeAngelis [32], spinels possess 42 normal modes divided into 39 optical and 3 acoustic modes at the Brillouin zone center. These modes can be shown in terms of symmetry species given by Equation (5):

Γ(k = 0) = A_1g(R)⊕E_g(R)⊕ 3T_2g(R) ⊕ 5T_1u(IR)⊕ T_1g⊕ 2A_2u⊕ 2E_u ⊕ 2T_2u (5)

where R and IR correspond to Raman and infrared-active, respectively. Five modes are Raman active (A_1g + E_g + 3T_2g) and one mode is Infrared active T_1u (IR) [33,34]. The A_1g, E_g and 3T_2g modes are, respectively, one, doubly and triply degenerate. These five modes are observed in the case of spinel structures. The Raman spectra of the cubic direct spinel structure of ZnAl_1.999Ho_0.001O₄, belonging to the Fd $\bar{3}$ m space group, agree well with the literature [32,34] and have been shown in Fig. 6. Table 3 illustrate the observed frequencies of these phonons.

Fig. 6.

Raman spectrum of the ZnAl_1.999Ho_0.001O₄ sample collected using a green laser line at 532 nm.

Table 3.

Observed IR and Raman bands (in cm⁻¹) for ZnAl_1.999Ho_0.001O₄ spinel.

	Raman modes	Infrared modes
T1u	–	663
T2g	658	–
T1u	–	556
T2g	517	–
T1u	–	478
Eg	416	–
T2g	195	–

High-intensity prominent peaks at 658 cm⁻¹ and 416 cm⁻¹ correspond to T_2g mode (movement of oxygen atoms within AlO₆ octahedra) and E_g (asymmetric bending movement of oxygen atoms in ZnO₄ tetrahedra), respectively. Other modes are observed with relatively low intensities bands at 517 cm⁻¹ and 195 cm⁻¹are assigned to T_2g mode. However, as the cationic species change, the peak positions and intensities change [22]. The highest frequency movements (>250 cm⁻¹) are mainly due to O and Al ions and the lower ones are due to Zn, with a dominant contribution of O [35]. It is evident from Fig. 6 that the peaks assigned to T_2g mode were asymmetric, indicating the presence of a disorder in spinel.

The FTIR spectra for the spinel in the 400–4000 cm⁻¹ spectral range are seen in Fig. 7. The sample has extreme bands peaking at 663, 556 and 478 cm⁻¹ which are assigned to Al–O/Ho–O and Zn–O stretching vibrations modes of T_1u mode symmetry.

Fig. 7.

FTIR spectrum of ZnAl_1.999Ho_0.001O₄ spinel.

3.4. Determination of the band-gap energy

Fig. 8 portrays the UV–Visible absorption coefficient α(λ) of the ZnAl_1.999Ho_0.001O₄ spinel, recorded at ambient temperature in the range 300–800 nm. The absorption peaks in the mid-infrared region 400–800 nm may be associated with crystal field transitions of Holmium. Understanding the optical absorption behavior of holmium in this range is relevant for applications in areas such as solid-state physics, materials science, and potentially in the development of optical devices. Fig. 8 presents the absorbance spectrum (in arbitrary units) as a function of wavelength. The Beer-Lambert Law is expressed as [36]:

$$\mathit{A}=\mathit{log}\left(\frac{\mathit{I}}{{\mathit{I}}_{\mathbf{0}}}\right)=\mathbf{0.4343}\mathit{\alpha }\mathit{d}$$ (6)

Where A is the absorbance, $I_0$ is the intensity of the incident light, I is the intensity of the transmitted light, $\alpha$ is the absorption coefficient and d is the sample thickness. To obtain the band gap energy of the ZnAl_1.999Ho_0.001O₄ spinel, first the absorption coefficient (α) was estimated according to the formula:

$$\mathit{\alpha }\left(\mathit{h}\mathit{\nu }\right)=\frac{\mathbf{2.303}\mathit{A}}{\mathit{d}}$$ (7)

where h is the Planck constant and ν is the photon's frequency.

Fig. 8.

Absorbance spectrum at room temperature. Intra-4f absorption pics from the ⁵I₈ ground state to the excited states of Ho³⁺ are showed.

In general, the well-known quadratic equation [37] named as Tauc law relates the absorption coefficient (α) to photon energy (hν) by the following formula:

$$\mathit{\alpha }=\frac{\mathit{A}}{\mathit{h}\mathit{\upsilon }}{\left(\mathit{h}\mathit{\nu }-{\mathit{E}}_{\mathit{g}}\right)}^{\mathit{m}}$$ (8)

$${\left(\mathit{\alpha }\mathit{h}\mathit{\upsilon }\right)}^{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathit{m}$}\right.}=\mathit{A}\left(\mathit{h}\mathit{\nu }-{\mathit{E}}_{\mathit{g}}\right)$$ (9)

where A is a constant named the band tailing parameter, E_g is the band gap and m is the power factor described the transition mode, it varies depending on whether the material is amorphous or crystalline. For crystalline compounds, direct transitions can be confirmed by the Tauc's relation [37,38]. For the ZnAl_1.999Ho_0.001O₄ spinel, put m = ½, hence:

$${\left(\mathit{\alpha }\mathit{h}\mathit{\upsilon }\right)}^{\mathbf{2}}=\mathit{A}\left(\mathit{h}\mathit{\nu }-{\mathit{E}}_{\mathit{g}}\right)$$ (10)

Hence, plotting (αhυ)² against the photon energy (hν) yields a straight line within a specific range. Extrapolating this line to intercept the (hν)-axis provides the value of the direct optical energy gap, Eg Ref. [39]. Fig. 9 illustrates the behavior of the direct optical energy gap, Eg, for our material. The optical band gap is estimated to be 3.44 eV.

Fig. 9.

Evolution of (αhν)² with the energy hν relative to ZnAl_1.999Ho_0.001O₄ spinel.

For confirming the nature of the optical band transition, we have reorganized equation (9) as following:

$$\mathit{Ln}\left(\mathit{\alpha }\mathit{h}\mathit{\nu }\right)=\mathit{L}\mathit{n}\mathit{A}+\mathit{m}\mathit{Ln}\left(\mathit{h}\mathit{\nu }-{\mathit{E}}_{\mathit{g}}\right)$$ (11)

Fig. 10 represents the evolution of Ln(αhν) against Ln(hν- 3.44). A straight line is obtained whose slope gives the factor (m). For E_g = 3.44 eV, m is close to 1/2 assuring the direct transitions behavior of the studied sample is illustrated in Fig. 10. The wide band gap of this spinel is an improve of the semiconductor character and its application in optoelectronic devices [40]. As reported in the article by I. Elhamdi et al. [5], we observed an increase in the gap energy when estimating it for Ho-substituted spinel. This variation implies that the gap energy decreases as particle size increases.

Fig. 10.

Evolution of Ln(αhν) against Ln(hν - 3.44) for ZnAl_1.999Ho_0.001O₄ spinel.

3.5. Determination of Urbach energy E_u

The Urbach energy E_u, which rises from phonon dynamics and statistical structural disordering, is an important parameter that characterizes disordered and amorphous materials. This parameter is determined from the Urbach model [41] and is assigned to the width of the tail describing the localized states between conduction and valence bands. A high Urbach energy value indicates significant disorder, often resulting from the introduction of a large concentration of foreign atoms into the structure. This typically leads to a reduction in the effective optical gap. The Urbach energy (Eu) value can be calculated using the following relations, where B is a constant:

$$\mathit{\alpha }\left(\mathit{h}\mathit{\nu }\right)=\mathit{B}\mathit{e}\mathit{x}\mathit{p}\left(\frac{\mathit{h}\mathit{\nu }-\mathit{E}\mathit{g}}{{\mathit{E}}_{\mathit{u}}}\right)$$ (12)

$$\mathit{Ln}\left(\mathit{\alpha }\right)=\mathit{Ln}\left(\mathit{B}\right)+\frac{\mathbf{h}\mathrm{\nu }-\mathbf{Eg}}{\text{Eu}}$$ (13)

In Fig. 11, the slope of the curve Ln(α) versus energy hν yields a value of Eu = 660 meV, representing 19.18% of the energy band-gap. This indicates significant disorder in the ZnAl_1.999Ho_0.001O₄ spinel.

Fig. 11.

Variation of Ln(α) with Photon Energy (hν) for Determination of Urbach Energy (Eu) in ZnAl_1.999Ho_0.001O₄ spinel.

Comparing the Urbach energy of ZnAl₂O₄ at 48 meV, as reported in the article by I. Elhamdi et al. [5], we observe a rise in the Urbach energy when estimating it for ZnAl_1.999Ho_0.001O₄ spinel. This observation implies that there has been an augmentation in disorder and defects concentration within the Holmium-substituted material. It also signifies a higher density of localized states in this material, as indicated in Ref. [5].

3.6. Penetration depth and optical extinction

It is widely acknowledged that when light traverses a sample, some of the incident photon flux is attenuated as certain radiation is absorbed by the material. Therefore, we employed the concept of penetration depth (or skin depth, δ) to illustrate how deep light or incident radiation can penetrate our investigated compound.

We calculated the penetration depth (δ) based on the absorption data using the following equation:

$$\mathrm{\delta }\left(\mathrm{\lambda }\right)=\frac{\mathbf{1}}{\mathit{\alpha }\left(\mathit{\lambda }\right)}$$ (14)

Fig. 12 presents the relationship between incident wavelength and penetration depth for the ZnAl_1.999Ho_0.001O₄ spinel. As illustrated, there is a significant reduction in penetration depth as photon energy increases. This phenomenon could be explained by the decrease in incident photon energy near the material's surface, potentially influencing neighboring Ho³⁺ ions.

Fig. 12.

Variation of δ versus energy for the ZnAl_1.999Ho_0.001O₄ spinel.

In summary, the reduction in penetration depth with increasing photon energy observed in Fig. 12 for the ZnAl_1.999Ho_0.001O₄ spinel is likely due to the material's absorption and optical properties, dependent on its electronic structure. This phenomenon is crucial for understanding how different wavelengths of light interact with the material and can have implications for various applications, such as optical devices and sensors.

The extinction coefficient (k) quantifies the absorption and scattering of light within a medium per unit distance. We determined the extinction coefficient using the following formula:

$$\mathit{k}=\frac{\mathit{\alpha }\mathit{\lambda }}{\mathbf{4}\mathit{\pi }}$$ (15)

where α is the absorption coefficient.

The spectral distribution of the extinction coefficient is shown in Fig. 13. The extinction coefficient has been found to decrease as wavelength increase. Our findings closely align with those reported by Marquez et al. [42], exhibiting a similar trend to the results presented by El-Sayed and Amin [43].

Fig. 13.

Evolution of k versus wavelength for the ZnAl_1.999Ho_0.001O₄ spinel.

3.7. Refractive index

Measuring the refractive index (n) is essential when designing components for optical devices [[44], [45], [46]]. The coefficient k, which relates to reflectance and extinction, can be expressed in the following manner:

$$\mathit{n}=\frac{\mathbf{1}+\mathit{R}}{\mathbf{1}-\mathit{R}}+\sqrt{\frac{\mathbf{4}\mathit{R}}{{\left(\mathbf{1}-\mathit{R}\right)}^{\mathbf{2}}}-{\mathit{k}}^{\mathbf{2}}}$$ (16)

Fig. 14 depicts the variation of n versus wavelength for the ZnAl_1.999Ho_0.001O₄ sample. As observed, the refractive behavior of our compound exhibits high sensitivity to changes in wavelength. Upon comparison with ZnAl₂O₄ [5], a reduction in the refractive index is seen in the doped spinel. This phenomenon may be qualified to the presence of Ho³⁺ ions in the substituted material, which modifies the density of localized states. This information is important in understanding the impact of doping on the electronic behavior of materials and is valuable in various applications such as semiconductor, optoelectronics devices and energy storage.

Fig. 14.

Evolution of n as a function of the incident photon wavelength λ for the ZnAl_1.999Ho_0.001O₄ spinel.

To characterize the n index of our sample, we employ the Cauchy dispersion relationship, which is expressed as follows [47,48]:

$$\mathit{n}\left(\mathit{\lambda }\right)={\mathit{n}}_{\mathbf{0}}+\frac{\mathit{A}}{{\mathit{\lambda }}^{\mathbf{2}}}+\frac{\mathit{B}}{{\mathit{\lambda }}^{\mathbf{4}}}$$ (17)

where (n₀, A, B) correspond to the Cauchy's constants and λ is the wavelength of the incident photons. The obtained values for n₀, A and B are respectively 2.39, 0.339 (μm)² and 0.035 (μm)⁴ (Fig. 15). The obtained results closely align with those reported in the literature with TPA-CoBr₄ [49] and DMA-CoCl₄ [50].

Fig. 15.

Plot of the refractive index versus 1/λ² for ZnAl_1.999Ho_0.001O₄ spinel.

3.8. The 4f-4f transition of Ho³⁺ ions in ZnAl_1.999Ho_0.001O₄ spinel

The spectrum of Fig. 8 shows several absorption peaks at 417, 451, 475, 494, 532, 659 and 762 nm. these peaks are attributed to the 4f-4f transitions of holmium with 4f¹⁰ electronic configuration [51]. The 3d-3d transitions of the metal ions are highly responsive to variations in the local environment, often resulting in broad absorption and emission bands [[52], [53], [54], [55], [56], [57]]. On the contrary to metal transition ions, the 4f electrons optically active for the lanthanides are screened by the 4s²4p⁶ layers. Then these electrons weakly feel the effects of the outside and it is a weak crystal field. The rare earth ions optical spectra are characterized by narrow 4f-4f transitions. Furthermore, the positions of these transitions are almost identical to those of the free ion and don't depend on the host matrix in which they are incorporated. For this reason, the assignment of the 4f-4f transitions of Ho³⁺ is based on the comparison with energy level scheme of Ho³⁺ in HoCrO₃ perovskite compound [51]. Also, the weak crystal field effect allows for consistency in the energy transitions, resulting in similar absorption and emission spectra for rare earth elements across various environments. This feature makes rare earth elements valuable for applications in optics, as their predictable and consistent spectroscopic behavior facilitates the design and engineering of materials for specific applications, such as lasers, phosphors, and other optoelectronic devices. Table 4 presents the Ho³⁺ transitions from the ground state ⁵I₈ (Ho³⁺) to different excited states. The presence of these transitions indicates that the incorporation of Ho³⁺ ions into the normal spinel ZnAl_1.999Ho_0.001O₄ has been successful. From Fig. 8, we remark that the absorption bands ⁵I₈(Ho³⁺) → ⁵G₅(Ho³⁺) (417 nm), ⁵I₈(Ho³⁺) → ⁵G₆(Ho³⁺) ⁵F₁(Ho³⁺) (451 nm), ⁵I₈(Ho³⁺) → ⁵F₂(Ho³⁺) (475 nm), ⁵I₈(Ho³⁺) → ⁵F₃(Ho³⁺) (494 nm), ⁵I₈(Ho³⁺) → ⁵F₄(Ho³⁺)+⁵S₂(Ho³⁺) (532 nm), ⁵I₈(Ho³⁺) → ⁵F₅(Ho³⁺) (659 nm) and ⁵I₈(Ho³⁺) →⁵I₄(Ho³⁺) (762 nm) are relatively intense and sharp.

Table 4.

4f-4f (Ho³⁺) absorption energy (in nm) for ZnAl_1.999Ho_0.001O₄ spinel.

Peaks	Transitions
417	5I8(Ho3+) → 5G5(Ho3+)
451	5I8(Ho3+) → 5F1,5G6(Ho3+)
475	5I8(Ho3+) → 5F2(Ho3+)
494	5I8(Ho3+) → 5F3(Ho3+)
532	5I8(Ho3+) → 5F4(Ho3+) + 5S2(Ho3+)
659	5I8(Ho3+) → 5F5(Ho3+)
762	5I8(Ho3+) → 5I4(Ho3+)

3.9. Electronic paramagnetic resonance (EPR)

Electronic paramagnetic resonance (EPR) or electron spin resonance (ESR) spectroscopy is a magnetic resonance technique for detecting the resonance transitions between energy states of unpaired electrons in an applied magnetic field. This technique is particularly useful for studying paramagnetic species and their electronic structure. Fig. 16 shows the EPR spectrum of ZnAl_1.999Ho_0.001O₄ spinel recorded at room temperature. The rare earth ion Ho³⁺, with electronic configuration 4f¹⁰, is a non-Kramer's ion. This ion is EPR silent in theory. The g-factor is a dimensionless quantity that characterizes the splitting of energy levels in magnetic systems. The g-factor is defined as the ratio of the magnetic moment to the angular momentum of a particle. For electrons, the g-factor is approximately 2.0023, but it can be influenced by the local environment and the nature of the magnetic interaction. Fig. 17 displays several resonance signals with effective g values measured at g = 4.5, 3.87, and 2.0. Three values are also observed in the EPR spectra of Cr³⁺-doped Zn₂SnO₄ phosphors (g = 1.99, 3.93 and 4.40) and are assigned to three different traps [58]. These traps are integral to the persistent phosphorescent behavior of Cr³⁺-doped Zn₂SnO₄ phosphors [56,59]. The V⁻ centers (a hole trapped at a cation vacancy) and F⁺ centers (an electron trapped at an anion vacancy) are the primary centers observed in ZnAl₂O₄, identifiable by the resonance peak at g = 2.0 [60]. The EPR spectrum of ZnAl₂O₄: Cr³⁺ has been also studied and shows signals at g = 1.960, 2.003 and 2.010 [61]. These signals are assigned to simple ionized oxygen vacancies (g = 1.960), and to superoxide anions (O²⁻) (g = 2.003 and 2.010). The growing signal strength at about g = 3.84 indicates that there are more emission centers in spinel lattices [62]. The EPR signals observed on Fig. 17 indicates the presence of three type of traps which are instrumental in driving the persistent phosphorescence of ZnAl_1.999Ho_0.001O₄ spinel. As expected, there was no resonance signal at room temperature corresponding to Ho³⁺ ions [63]. The nature of the traps in ZnAl_1.999Ho_0.001O₄ spinel is contingent upon the role played by the holmium ions in the material. If Ho³⁺ acts as a donor, contributing additional electrons to the lattice, it creates donor-type traps. These traps involve specific energy levels within the band gap where electrons become localized. On the other hand, if Ho³⁺ acts as an acceptor, capturing electrons from the lattice, it establishes acceptor-type traps. These traps entail localized states within the band gap, affecting the electronic and optical properties of the materiel.

Fig. 16.

EPR spectrum of ZnAl_1.999Ho_0.001O₄ spinel at room temperature.

Fig. 17.

The g-factor of ZnAl_1.999Ho_0.001O₄ spinel.

4. Conclusion

The study of ZnAl_1.999Ho_0.001O₄ significantly contributes to the comprehension of its structural and optical properties. The structural and morphological study establishes a fundamental basis for the crystallographic arrangement and provides insight into the microstructure and uniformity of the synthesized material. Spectroscopic analyses, including room temperature Raman and infrared spectra, provided a comprehensive examination of vibrational modes and structural characteristics. The determination of the band gap (E_g) from the UV/vis absorption spectrum, in accordance with Tauc's law, enhances our understanding of the electronic transitions within the material. The observed higher Urbach energy (Eu) in the ZnAl_1.999Ho_0.001O₄ spinel compared to ZnAl₂O₄ signifies increased disorder and a higher concentration of defects, attributed to the presence of Ho³⁺ ions. Additionally, the wavelength-dependent assessment of optical properties and the identification of 4f-4f transitions in the ambient temperature absorption spectrum further contribute to the comprehensive characterization of ZnAl_1.999Ho_0.001O₄. These findings collectively advance our knowledge of the material's behavior, paving the way for potential applications in diverse fields such as optoelectronics and luminescent devices.

Data availability

No data were used for the research described in this article.

CRediT authorship contribution statement

I. Elhamdi: Methodology. H. Souissi: Visualization. O. Taktak: Writing – original draft. S. Kammoun: Supervision. E. Dhahri: Supervision. J. Pina: Visualization. B.F.O. Costa: Visualization, Validation. E. López-Lago: Supervision.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.