Structural, Optical, Magnetic, and Dielectric Investigations of Pure and Co-Doped La_0.67Sr_0.33Mn_1-x-yZn_xCo_yO₃ Manganites with (0.00 < x + y < 0.20)

Abstract

Here, we report the structural, optical, magnetic, and dielectric properties of La_0.67Sr_0.33Mn_1-x-yZn_xCo_yO₃ manganite with various x and y values (0.025 < x + y < 0.20). The pure and co-doped samples are called S1, S2, S3, S4, and S5, with (x + y) = 0.00, 0.025, 0.05, 0.10, and 0.20, respectively. The XRD confirmed a monoclinic structure for all the samples, such that the unit cell volume and the size of the crystallite and grain were generally decreased by increasing the co-doping content (x + y). The opposite was true for the behaviors of the porosity, the Debye temperature, and the elastic modulus. The energy gap E_g was 3.85 eV for S1, but it decreased to 3.82, 3.75, and 3.65 eV for S2, S5, and S3. Meanwhile, it increased and went to its maximum value of 3.95 eV for S4. The values of the single and dispersion energies (E_o, E_d) were 9.55 and 41.88 eV for S1, but they were decreased by co-doping. The samples exhibited paramagnetic behaviors at 300 K, but they showed ferromagnetic behaviors at 10 K. For both temperatures, the saturated magnetizations (M_s) were increased by increasing the co-doping content and they reached their maximum values of 1.27 and 15.08 (emu/g) for S4. At 300 K, the co-doping changed the magnetic material from hard to soft, but it changed from soft to hard at 10 K. In field cooling (FC), the samples showed diamagnetic regime behavior (M < 0) below 80 K, but this behavior was completely absent for zero field cooling (ZFC). In parallel, co-doping of up to 0.10 (S4) decreased the dielectric constant, AC conductivity, and effective capacitance, whereas the electric modulus, impedance, and bulk resistance were increased. The analysis of the electric modulus showed the presence of relaxation peaks for all the samples. These outcomes show a good correlation between the different properties and indicate that co-doping of up to 0.10 of Zn and Co in place of Mn in La:113 compounds is beneficial for elastic deformation, optoelectronics, Li-batteries, and spintronic devices.

1. Introduction

LaMnO₃ perovskite (ABO₃) structures are more stable when the lattice distortion (LD) is 0.85 < LD < 0.90, and any deviation beyond that reduces the Mn–O–Mn bond angle by 180°. The substitution of Sr²⁺ for La³⁺ leads to a distortion in the local crystal lattice, shifting it away from its ideal cubic structure. The variation in ionic radii further contributes to this distortion, driving the structure toward different configurations, such as orthorhombic or monoclinic configurations [1,2,3]. When x = 0.33 (La_0.67Sr_0.33MnO₃), the Mn³⁺/Mn⁴⁺ ratio becomes 67/33, and then the Mn–O–Mn-bound angle, the lattice distortion, and the ionic size mismatch play a considerable role in the colossal magneto-resistance (CMR) behavior under smaller applied magnetic fields [4,5,6]. The partial replacement of 0.33 of La by Sr with an optimized stoichiometry produces some changes at the A site and generates a mixed M³⁺/M⁴⁺ valence that causes RT ferromagnetic ordering (RTFM) at the Curie temperature (T_C) [6,7]. In addition, it may also show an antiferromagnetic insulator (AFMI) with a Neel temperature (T_N) of 141 K [8]. Moreover, giant negative magneto-resistances close to RT have been obtained in these manganites, making them very attractive for a lot of potential applications, like spintronics, magnetic memory, disk-driven read heads, and magnetic sensors [9,10].

The Mn ion in LaMnO₃ perovskite is encircled by the oxygen octahedron MnO₆. However, the Jahn–Teller (JT) coupling of the e_g electron with the surrounding oxygen displacement also causes the deformation of the MnO₆. The partial splitting of the degeneracy into higher-energy e_g states and lower-energy t_2g states is associated with the 3D orbitals of the Mn atoms situated within the MnO₆ octahedra [11,12]. So, the Mn site exhibits an electronic configuration of t³_2ge¹_g with a spin of (S = 2) in Mn³⁺ [11,12]. The t_2g electrons, which exhibit less hybridization with O-2P states, remain localized when the hopping interaction is relatively weak, forming local spins (S = 3/2) even in metallic states, where the eg electrons act as charge carriers. This causes two-fold e_g electron localization states that strongly hybridize with the O-2P states, which eventually leads to the Mott insulating state. The hybridization between them usually depends on the local spin orientation and carrier density.

The presence of RTFM in the LaMnO₃ compound has been explained by the double exchange (DE) interactions resulting from the hopping of electrons (e_g) between the Mn³⁺(t²_2ge¹_g) and Mn⁴⁺(t²_2ge⁰_g) in the [Mn³⁺-O₂-Mn⁴⁺] network [13,14]. In addition, antiferromagnetic super-exchange and electron–phonon interactions have been taken into account to explain their advancement in high-temperature fields, such as the solid oxide fuel cell (SOFC) of cathode electrode devices and magnetic fluid hyperthermia [15,16,17].

The dielectric mechanism in solids can be characterized by complex dielectric parameters (ϵ^\ and ϵ^\\) over a wide range of frequencies (f) up to 10 GHz [18,19]. However, materials with a high ϵ^\ can be used in mobile phones and microwave-integrated circuits, whereas materials with a low ϵ^\ are convenient for devices with nonlinear optical and high-frequency antennas [20,21,22]. Koop’s theory indicates that solid materials consist of conducting grains that are dominant at high f values separated by boundaries of poor conductivity at low f values, such that the current is assumed to flow along parallel alignments of the grains [23,24]. In addition, the f-dependent AC conductivity follows Jonscher’s power law, indicating a hopping mechanism and the non-Debye relaxation process [21,25].

In this regard, studying Mn, including the remarkable coupling among the degrees of freedom, is of great significance. For example, mixed-valence manganites (La³⁺_1−xSr_x²⁺Mn³⁺_1−xMn_x⁴⁺O₃) can be harnessed by changing the bond angle, the Mn³⁺/Mn⁴⁺ ratio, the Mn-O bond length, and cation sizes A and B [26,27,28,29]. Changing the Mn⁺³/Mn⁺⁴ ratios is essentially achieved by doping in Mn sites for tuning its effective valence. This is caused by either aliovalent ions or a change in the overall oxygen content. Among them is the doping of 3D-transition metal (TMs) like Co, Ni, Fe, and Zn [30,31,32,33]. However, in most of them, T_C decreases as the TM content increases, and it usually disappears at higher doping contents above 0.20. In addition, some external factors, such as the synthesis method and the sintering temperature, can affect the grain boundaries necessary for the extrinsic CMR effect [34,35,36,37,38].

Even at RT, co-doping ions up to the concentration limit may reduce the RTFM magnetization, and it also shifts the T_c further than RT, which is not ideal for spintronic devices. Moreover, cooling to 10 K is necessary for investigating the magnetic behavior of the material in field cooling and zero field cooling (FC and ZFC). Likewise, tuning the material band gap (E_g) is necessary for most optoelectronic devices [39,40]. Lowering the E_g of semiconducting materials is required for light-emitting diodes (LED), solar cells, and optical filters. The opposite is true for higher E_g materials with uses in devices with higher breakdown fields, lower electronic noise, and high-power operation [40,41]. However, the energy gap (E_g) of such compounds is mainly influenced by the variations in the insulating states within the forbidden gap, carrier concentration, and oxygen incorporation during material synthesis, which collectively impact the charge transfer interactions between O²⁻ and Mn³⁺ [42,43].

With this purpose in mind, La_0.67Sr_0.33Mn_1-x-yZn_xCo_yO₃ manganites with equal amounts of x and y in the range (0.025 < x + y < 0.20) were synthesized by a conventional reaction method. The samples were characterized by XRD, SEM, and FTIR techniques. Additionally, the optical and magnetic measurements of the samples were performed. For simplicity, the samples are called S1, S2, S3, S4, and S5 for x + y = 0.00, 0.025, 0.05, 0.10, and 0.20, respectively. The co-doping by Zn and Co ions was utilized to adjust the carrier density through the different valences between these ions and Mn, especially as one is magnetic (Co) and the other is nonmagnetic (Zn). To the extent of our understanding, we could not find any reported data on Mn-site co-doping by Zn + Co in CMR materials and, therefore the current study will provide important insight into the properties of co-doped CMR materials.

2. Materials and Methods

La_0.67Sr_0.33Mn_1-x-yZn_xCo_yO₃ samples with (0.025 ≤ x + y ≤ 0.20) were synthesized by a solid-state reaction method. We weighted 4 g from La₂O₃, SrCo₃, Mn₂O₃, ZnO, and CoO powders with stoichiometric proportions according to the molecular weights ratio of each compound using a digital balance with up to 4 digits, as listed in

Table 1. Chemical formulas, molecular weights, and masses of the La_0.67Sr_0.33Mn_(1-x-y)Zn_xCo_yO₃ samples.

Compound	La0.67Sr0.33Mn(1-x-y)ZnxCoyO3		La2O3	SrCo3	Mn2O3	ZnO	CoO	Mw (g) (Total)	M (g) (Total)
Mw (g)			328.81	147.63	157.88	81.38	74.93
Sample	x	y	m (g)	m (g)	m (g)	m (g)	m (g)
S1	0.00	0.00	2.055	0.459	1.486	-------	--------	424.89	4
S2	0.0125	0.0125	2.066	0.461	1.457	0.044	0.009	422.59	4
S3	0.025	0.025	2.074	0.464	1.425	0.019	0.018	420.92	4
S4	0.05	0.05	2.095	0.467	1.363	0.039	0.036	416.92	4
S5	0.10	0.10	2.135	0.477	1.235	0.080	0.073	408.95	4

. After that, they were mixed, ground, and calcined for 24 h three successive times at 950 °C, 1000 °C, and 1050 °C, with an intermediate grinding between these calcination stages. After that, the powders were pressed into pellets and sintered in air at 1100 °C for 48 h. The samples were cooled to 600 °C and kept at this temperature for 24 h and then were left to cool slowly to RT. The synthesized samples were examined using X-ray diffraction (XRD) with Cu-Kα radiation (wavelength of 1.5418 Å), operating at 40 kV and 30 mA. The lattice parameters were determined, using Celref software, based on the XRD data and standard reference cards. The water displacement method was used for determining the experimental density, where a mass of 5 mL of water is m_w and the density of water is ρ_w = (m_w/5). The complementary mass and volume of water added to the 0.5 g of the sample m_w can be calculated as m_w = m_t − m_s, and its volume as V_w = (m_w/ρ_w). The volume of the sample then becomes V_s = (5 − V_w) and its density ρ_s = (m_s/V_s), where m_s is the mass of the sample (0.5 g).

FEI Quanta 250 scanning electron microscope (SEM, Eindhoven, The Netherland) was utilized to acquire the structural morphology of the samples. Furthermore, the compositional weight percentage of the elements in the prepared samples was determined by an energy dispersive X-ray spectroscopy (EDS) attached to the SEM. An area scan was applied to determine the composition of the prepared samples. With a Spectrum 400-FT-IR/FT-NIR spectrometer (Perkin Elmer, Waltham, MA, USA), the FTIR absorption of the synthesized compositions was recorded. The optical measurements were carried out by a double-beam spectrophotometer (a Jasco V-570, Tokyo, Japan) in the range (200–900 nm). DC magnetization measurements were conducted as a function of the applied magnetic field, up to 20 kOe, using a Quantum Design MPMS SQUID magnetometer (Pfungstadt, Germany). Additionally, magnetization as a function of temperature was measured under both field-cooled (FC) and zero-field-cooled (ZFC) conditions, using a field of 100 Oe and a temperature range between 10 and 300 K. On the other hand, the samples were initially cooled to 10 K with no magnetic field applied ZFC), and data were recorded as the temperature rose (up to 300 K). The samples were then cooled once more, and the magnetization was measured under the influence of the magnetic field (FC). Dielectric properties were investigated using broadband dielectric spectroscopy (BDS) and a high-resolution Alpha analyzer equipped with an active sample head (Novo Control GmbH, Montabaur, Germany), operating over a frequency range of 0.10 to 20 MHz.

3. Results and Discussion

3.1. XRD and SEM Analysis

The XRD patterns shown in Figure 1 indicate that all samples (S1–S5) exhibit good crystallization and the presence of the main diffraction peaks of LSMO monoclinic structure with the space group P21/n, which is consistent with the monoclinic structure of a similar compound [30,40,44]. Additionally, a comparison with the reported orthorhombic structures with a Sr content above 0.30 or with changes in the oxygen content revealed that the obtained diffraction peaks are inconsistent with the orthorhombic structure [14]. Moreover, we could not find any noteworthy secondary lines that might indicate the presence of impurities in the samples S1, S2, and S3. However, a secondary line close to 2θ = 45° of a lower intensity can bee observed in the case of the samples S4 and S5, which implies the solubility limit of Zn and Co co-doping at Mn sites is reached in these samples. This behavior indicates that co-doping of Zn+Co up to 0.20 substitutes Mn sites well. The unusual change in structure is due to the deviation of β and γ angles from 120° to between (90.54–90.92°) and (90.43–90.62°), respectively, although the Mn³⁺–O–Mn⁴⁺ bonds are close to 180° for optimal double exchange [45].

The angles β and γ are slightly decreased as the co-doping content increases, but the structure remains monoclinic over the range of co-doping concentrations. It has been reported that the degree of long-range order in the perovskite lattice increases, as indicated by the lower peak intensity in the pure LSMO phase compared to the doped LSMO [46]. According to the data shown in

Table 2. Lattice parameters, unit cell volume, porosity, crystallite and grain sizes, and element weight percent of La_0.67Sr_0.33Mn_1-x-yZn_xCo_yO₃ samples.

S	a (Ẳ)	b (Ẳ)	c (Ẳ)	V (Ẳ)3	β (°)	γ (°)	PS	D (nm)
S1	5.480	7.773	5.493	238.98	90.92	90.62	0.117	23.50
S2	5.481	7.776	5.496	234.23	90.54	90.50	0.114	21.67
S3	5.469	7.774	5.501	233.89	90.68	90.43	0.138	20.97
S4	5.472	7.758	5.487	232.91	90.84	90.61	0.173	17.36
S5	5.468	7.776	5.494	233.61	90.71	90.53	0.159	20.19
S	DSEM (nm)	w% (La)	w% (Sr)	w% (Mn)	w% (O)	w% (Zn)	w% (Co)
S1	956	63.03	4.32	32.20	5.11	0.00	0.00
S2	788	57.91	1.76	27.54	5.21	0.90	2.01
S3	720	53.98	2.56	25.11	14.10	1.94	2.32
S4	841	59.50	1.90	22.85	9.40	2.49	4.05
S5	737	61.92	1.46	22.71	4.09	4.25	5.56

, it is observed that when co-doping is increased, the lattice parameters (a, b, and c) varied, which resulted in a slight rise in unit cell volume (V). This can be related to the differences in the ionic radii of the dopants compared to Mn (La³⁺ = 1.18 Å, Sr²⁺ = 1.32 Å, Mn³⁺ = 0.65 Å, Mn⁴⁺ = 0.54 Å, Zn²⁺ = 0.74 Å, and Co²⁺ = 0.71 Å). The values of ρ_th and ρ_exp were used to determine the porosity; PS = [1 − (ρ_exp/ρ_th)], as given in Table 2. The PS of co-doped samples is higher than that of S1 and reaches its maximum value for S4, indicating that the co-doping process helps generate larger pores and, as a result, higher adsorption of the dye molecules from waste water. The crystallite size D, as calculated by the Scherrer formula [47,48], is also decreased as co-doping increases, followed by an increase at a 0.20 co-doping concentration.

No noticeable secondary phases or additional contaminants were detected at the grain boundaries in the SEM images presented in Figure 2, and the grains are well uniformly distributed over the matrix structure, but with a mixture of large and small sizes, such that smaller grains are connected with larger grains. Most of the formed grains have a spherical-like shape, and some of them are agglomerated, indicating a strong magnetic interaction moment of the perovskite. A higher concentration of co-doping (0.20) may create a few points of defects in the matrix structure via the oxidization of Mn³⁺/Mn⁴⁺, leading to a more conductive nature. The average grain size distribution (DSEM) shown in Table 2 was generally decreased by co-doping from 956 nm for S1 to its minimum value (788 nm) for S3. The biggest and smallest sizes formed for S1 and S3, respectively, indicate the great effect of adding co-doped ions to the crystal lattice of the host perovskite. According to the values of the ionic radii between the host and dopants, the co-doping could cause the shrinkage of the unit cell, in turn decreasing the size of the grains, which would be beneficial in many electronic storage devices. The EDS graphs shown in Figure 3 indicate that although the weight percentages of Zn, Co, and O are generally increased by co-doping, the Mn was decreased. Interestingly, the amount of oxygen is generally increased by the co-doping and reaches its maximum value for S3 and S4, but it decreases to its minimum for S5.

3.2. FTIR Analysis

The samples’ FTIR spectra are displayed in Figure 4. Although MnO₆ is known to have six vibrational modes and an octahedral symmetry, only two of these modes are visible in the infrared spectra [1]. Bending and stretching vibrations can result from changes in bond angles, internal motion, or alterations in the length of the Mn–O–Mn molecule. The absorption bands observed between 3416.96 and 3442.99 cm⁻¹ correspond to the stretching and bending modes of H-O-H in adsorbed water molecules [49]. The absorption peak at 2923.38 cm⁻¹ is present only in the pure sample and is attributed to the stretching vibrations of C–H groups. Meanwhile, the bands between 1633.29 and 1647.59 cm⁻¹ are associated with the C=C stretching and the carbonyl group (C=O) resulting from the bending vibrational modes of hydroxyl radical groups [2]. However, the bands near 3400 and 1600 cm⁻¹ are absent in sample S3. The bands between 1384.46 and 1426.72 cm⁻¹ are attributed to the bending vibrations of C–H groups [50]. The absorption bands ranging from 924.76 to 1084.92 cm⁻¹ are attributed to the symmetric and asymmetric stretching modes of oxygen, which are likely to influence the adsorption process. The broad peak at 605.28 cm⁻¹ indicates the presence of a metal–oxygen bond, which subsequently forms a MnO₆ octahedral structure [9,50]. These findings suggest that small amounts of water molecules and carbon dioxide may have been absorbed from the surrounding environment [51]. The bands in the range of 541.71 to 619.59 cm⁻¹ are associated with the stretching mode (ν_s) of the Mn-O or Mn–O–Mn bonds, while the bands between 406.09 and 497.83 cm⁻¹ correspond to the bending mode (ν_b) of the Mn–O–Mn bonds [52]. However, the variation in the wave number indicates a change in the energy needed to modify the Mn-O bond within the more distorted octahedron, where a geometric transition has taken place to alleviate or alter the induced strain.

The elastic properties can be related to the thermodynamic properties through the Debye temperature (θ_D), which is calculated using the following equation [44];

$${\theta }_D(K)={\displaystyle \frac{hc\overline{\Delta \nu }}{K_B}}=1.439\overline{\Delta \nu }$$

(1)

where $\overline{\Delta \nu }$ is the wave numbers against the absorption bands of the oxide structure. As shown in Figure 5a, the θ_D of S1 was decreased for S2, increased for S3 and S4, and then decreased for S5. In addition, the force constant K_t can be obtained using; K_t = 0.0076W$\overline{\Delta \nu }$² [53]. Also, the stiffness constants S₁₁ and S₁₂ are easily determined in terms of the c-parameter and Poisson’s ratio γ as S₁₁ = (K_t/c), S₁₂ = (S₁₁γ/1 − γ) and γ = 0.324 (1-1.043PS) [54].

Table 3. Debye temperature, Poisson’s ratio, elastic modulus, bond length, and effective mass of La_0.67Sr_0.33Mn_1-x-yZn_xCo_yO₃ samples.

S	θD (K)	γ	Y × 1012 (D/cm2)	β × 1012 (D/cm2)	G × 1011 (D/cm2)	L (M-O) nm	m* × 10−23 (g)
S1	720.54	0.285	5.27	4.07	2.05	0.549	5.07
S2	720.54	0.285	6.35	4.93	2.47	0.550	5.07
S3	747.60	0.277	6.96	5.21	2.72	0.550	5.07
S4	782.90	0.266	7.85	5.58	3.10	0.549	5.07
S5	665.49	0.270	5.61	4.07	2.21	0.549	5.07

shows that γ > 0.26, indicating a brittle nature for all samples [55]. The Young Y, bulk modulus β, and rigidity modulus G are determined by [56,57];

$$Y={\displaystyle \frac{(S_{11}-S_{22}(S_{11}+2S_{12})}{(S_{11}+S_{12})}};\beta ={\displaystyle \frac{S_{11}+2S_{12}}{3}};G={\displaystyle \frac{Y}{2(\gamma +1)}}$$

(2)

The behaviors of the elastic modulus shown in Table 2 are typically similar to θ_D and D, which subsequently control the bond strength of the structure [58]. The increase in the elastic modulus values of S3 and S4 compared to S1 implies the hard strengthening of the different ions’ interatomic bond, and they demonstrate a strong tendency to revert to their equilibrium state, which is attributed to the higher stiffness or bond strength necessary for plastic deformation [59]. The effective mass (m*) and bond length (L) of the metal-oxide bond are given by [60,61]:

$$\left.\begin{array}{c}{m}^{\ast }\left(g\right)={\displaystyle \frac{m_1{m}_2}{m_1+m_2}}={\displaystyle \frac{K_t}{4\pi c^2{\left(\Delta \overline{\upsilon }\right)}^2}}=2.82\times {10}^{-23}{\displaystyle \frac{K_t}{{\left(\Delta \overline{\upsilon }\right)}^2}}\\ L\left(nm\right)=0.1\times {\left({\displaystyle \frac{17\times {10}^5}{K_t}}\right)}^{0.33}\end{array}\right\}$$

(3)

m₁ and m₂ represent the atomic masses of the bonded metal and oxygen atoms, respectively. However, the values of m* and L shown in Table 3 indicate that no change occurred in either of them. Additionally, a shift in λ_max towards lower values was obtained, indicating a blue shift as co-doping content increases [62].

3.3. Optical Behavior

Figure 5a illustrates the absorbance (A) as a function of the wavelength (λ), where A increases as λ decreases. All samples exhibited a distinct absorption edge in the UV range, which is attributed to the inorganic nature of the LSMO compound. Typically, direct transitions account for the weak absorption peaks observed around 260 nm [63]. A notable shift in this behavior is linked to the variation in the excitation energy necessary for electron transition. Below 250 nm, the absorbance (A) increases, suggesting a shift in carrier concentration states within the band structure. Compared to S1, the co-doped samples S2, S3, and S4 show higher absorbance values; however, for S5, the absorbance decreases at lower wavelengths, falling below the absorbance of S1. This behavior supports the notion that co-doped samples up to 0.10 are suitable for optoelectronic applications such as solar cells. The E_g can be determined using Tauc’s equation [64,65]:

$$\left(\alpha h\nu \right)=\beta {(h\nu -E_g)}^r$$

(4)

Here, α represents the absorption coefficient calculated using the formula α = 2.303 (A/d), where d = 0.85 cm, and r is equal to 1/2 for a direct allowed transition. The linear plots between (αhυ)² and hυ shown in Figure 5b give the values of E_g (see

Table 4. The energy gap, residual dielectric constant, carrier density, and single and dispersion oscillator energies of La_0.67Sr_0.33Mn_1-x-yZn_xCo_yO₃ samples.

S	Eg (eV)	ϵL	(N/m*) × 1046 (cm3·g)−1	Eo (eV)	Ed (eV)
S1	3.85	5.07	3.69	9.55	41.88
S2	3.82	6.87	6.77	6.98	8.79
S3	3.65	1.88	2.46	5.93	4.26
S4	3.95	1.99	2.46	6.28	5.19
S5	3.75	2.78	4.92	7.71	10.63

). The E_g was 3.85 eV for S1, but it decreased to 3.82, 3.75, and 3.65 eV for S2, S5, and S3. However, it increased and went reached maximum value of 3.95 eV for S4. Reducing E_g by co-doping up to 0.05 can be correlated with the decrease in the grain size, and it is usually due to a change in the number of polarons in the co-doped samples [66]. Increasing the E_g for S4 more than that of S1 can be explained by the hooping mechanism involved in the La113 system through a change in the Mn³⁺/Mn⁴⁺ ratio as a result of d-d transitions varying the composition stoichiometric ratio, which consequently affects the conductive nature [67]. However, these values of E_g close to 4 eV are comparable with those obtained for a similar compound [68,69,70]. The smaller band gap energy (Eg), which governs the materials’ sensitivity to light exposure, is a key characteristic for determining the potential applications of photocatalytic activity. [69]. Therefore, a higher E_g would not be suitable to enable electron hopping from the CB to the VB. For photocatalysis, the S3 of 3.65 eV can then be employed more effectively than the other samples. The empirical formula relating electron band width (W) with Mn–O–Mn bond length (L) and angle (Φ) is given by [71] as W α cos Φ/L^3.5, where Φ is ½ [π-(Mn–O–Mn)]. The band gap energy (E_g) is related to W by the equation E_g = Δ−W, where Δ represents the charge transfer energy. Additionally, the 3D conduction band edge (E_cb) of Mn⁴⁺ is positioned at (−5.83) eV, which is lower than that of Zn or Co. This leads to the introduction of holes into the d-band, thereby reducing the effective band gap between O_2p in the valence band (VB) and Mn^3d in the conduction band (CB). Consequently, the optical E_g decreases, as observed for samples S2, S3, and S5 [14].

The reflective index (n) is related to λ as [72,73]

$$(n^2-k^2)={\in }_L-\left({\displaystyle \frac{e^2}{4{\pi }^2{c}^2{\epsilon }_0}}\right)\left({\displaystyle \frac{N}{m^{\ast }}}\right){\lambda }^2$$

(5)

where c, e, ε_o, m*, N, and ϵ_L denote light speed, electron charge, free space permittivity, effective mass of an electron, free carrier concentration, and lattice dielectric constant, respectively. The values of ϵ_L and (N/m*) were obtained from the linear fit of (n² − k²) against λ², as shown in Figure 6 and Table 4. The 0.025 of co-doping enhanced the (N/m*) from 3.69 × 10⁴⁶ to 6.77 × 10⁴⁶ (g·cm³)⁻¹, but it decreased with increasing co-doping content up to 2.46 × 10⁴⁶ (g·cm³)⁻¹ for S4, and then increased for S5 to 4.92 × 10⁴⁶ (g·cm³)⁻¹. So, the (N/m*) was increased for S2 and S5 to values more than that of S1. However, similar behavior was observed by co-doping, and it reached the highest value of 6.77 × 10⁴⁶ for S2. The Wemple-DiDomenico (WDD) single oscillator model, employed for obtaining the single and dispersion oscillator energies (E_o and E_d), is given by [74,75]

$${(n^2-1)}^{-1}=-{\displaystyle \frac{{(h\upsilon )}^2}{E_o{E}_d}}+{\displaystyle \frac{E_o}{E_d}}$$

(6)

The linear plots between (n² − 1)⁻¹ and (hυ)² shown in Figure 7 give the E_o and E_d values as summarized in Table 4. It is clear that the trends of the E_o and E_d values against co-dopant content are similar since they are both decreased by co-doping, and E_o is greater than E_d. The E_o values range from 5.93 to 9.55 eV, while the E_d values range from 4.26 to 41.88 eV, with S1 yielding the highest values among the prepared samples. The odd point of the S1 sample is the Ed reaching to 41.88 eV. Decreased particle diffusion leads to reduced scattering centers, which explains why co-doping depressed the E_o and E_d. The unusually higher value of E_d of 41.88 eV for S1 agrees with 33.72 and 51.93 eV for 10 kGy γ-irradiated In₂Se₃ films and Cr₂O₃-doped PVC reported in [76,77]. These studies attribute this behavior to some type of oxygen disorder. However, there is no previous data reported for the parameters (N/m*), ϵ_L, E_o, and E_d, and the present study may be considered the first to report them.

3.4. Magnetic Behaviors

The samples’ magnetic hysteresis loops at 300 and 10 K are displayed in Figure 8a,b, respectively. The samples S1–S5 show a mixture of paramagnetic and ferromagnetic behaviors at 300 K. The bulk of M-H curves’ domains are ferromagnetic despite their positive slopes and extremely small hysteresis area at low field. They exhibit a distinct blend of ferromagnetic and paramagnetic behavior when T decreases to 10 K. On the other hand, the M-H curve at 10 K exhibits the opposite behavior, suggesting that LSMO samples have several magnetic phases. Moreover, the bigger observed pinning centers generated at lower temperatures are the reason for the significantly greater magnetization values at 10 K compared to 300 K [78].

The total magnetization (M_t) values at 2000 Oe, as shown in Table 4, are increased by co-doping and reach their maximum values for S3 and S4, such that the Ms at 10 K is at least 10-times greater than that obtained at 300 K. But, M_t was decreased with the increase in co-doping concentration to 0.20 (S5), as a result of improving Jahn–Teller active Mn³⁺ for non-Jahn–Teller active Mn⁴⁺ [79]. For example, M_t was increased at 300 K from 0.70 (emu/g) for S1 to 1.27 (emu/g) for S3, which is consistent with the higher w% value of (O) for S3 (14.10), indicating a lower oxygen vacancy (Ov). Likewise, it increased at 10 K from 7.66 (emu/g) for S1 to 15.08 (emu/g) for S4, which indicates that M_t α w% (O) at 300 K. In contrast, the w% of O was increased by co-doping from 5.11 to 14.10, indicating a lower O_v, i.e., M_t α (1/O_v). Therefore, the observed increase in M originated from Zn and Co co-doping as a result of grain size and O_v variations.

This behavior suggests that while Co is a ferromagnetic ion (4.9 μB), it may also be viewed as a source of nonmagnetic Zn and paramagnetic domains at 300 K. Additionally, Zn can be regarded as a source of ferromagnetic domains. Thus, the paramagnetic behavior observed at 300 K can be attributed to the well-known ferromagnetic impurity phases or clusters of Co and Mn (3.6 μB). This serves as clear evidence of the lack of strong ferromagnetic domains at 300 K in the co-doped samples, likely due to the changes in D and O_v, which weaken ferromagnetic ordering and lead to super-exchange paramagnetic interactions instead [2,80].

For further clarification, the paramagnetic contributions were subtracted from the M-H curves to isolate the effective ferromagnetic parameters, as illustrated in Figure 9a,b. The behavior was characterized by parameters such as saturated magnetization (M_s), remnant magnetization (M_r), coercive field (H_c), anisotropy (γ = H_cM_s/0.98), squarness Sq = M_r/M_s, and magnetic moment (μ = WM_s/5585) [81,82,83], as shown in

Table 5. Total, saturated, and remnant magnetizations, coercive fields, anisotropy, squareness, and magnetic moment of La_0.67Sr_0.33Mn_1-x-yZn_xCo_yO₃ samples.

S	Mt (300 K) (emu/g)	Mt (10 K) (emu/g)	Ms (300 K) (emu/g)	Ms (10 K) (emu/g)	Hc (300 K) (Oe)	Hc (10 K) (Oe)	Mr (300 K) (emu/g)	Mr (10 K) (emu/g)
S1	0.70	7.66	0.053	4.30	103	870	0.0045	1.23
S2	0.83	8.64	0.098	5.19	54	1170	0.0036	1.60
S3	1.27	13.78	0.191	7.76	12	1055	0.0072	2.45
S4	1.21	15.08	0.060	8.44	44	2216	0.0028	3.22
S5	0.93	10.11	0.128	5.18	60	2095	0.0059	2.08
S	γ (300 K) (emu·Oe/g)	γ (10 K) (emu·Oe/g)	Sq (300 K)	Sq (10 K)	μ (300 K) (μB)	μ (10 K) (μB)
S1	5.570	3817.35	0.085	0.286	0.002	0.182
S2	5.400	6196.22	0.037	0.308	0.004	0.220
S3	2.339	8353.88	0.038	0.316	0.008	0.329
S4	2.694	19084.74	0.047	0.382	0.003	0.358
S5	7.837	11073.57	0.046	0.402	0.005	0.219

. It is seen that M_s, and M_r have similar behaviors at both temperatures (300 and 10 K). In contrast, at 300 K, the co-doping shifts the S1 from a hard to a soft magnetic material, since the coercive field decreases from 103 Oe for S1 to 54, 12, 44, and 60 Oe for S2, S3, S4, and S5, respectively [84]. In contrast, H_c increased at 10 K from 870 Oe to 1170, 1055, 2216, and 2095 Oe, indicating a hard magnetic-type material [85]. However, Hc increases with decreasing DSEM, as estimated using H_c = H_c,o + (KM/DSEM), where H_c,o reflects the H_c due other effects, such as internal stresses and impurities, and KM is a constant. Therefore, the difference between H_c at 300 and 10 K can also be attributed to H_c,o, indicating that some of the grains of co-doping domains remain blocked at 300 K. Likewise, the behaviors of γ and μ are typically similar to those obtained for Ms. Sq is found to be less than 0.50, and has a similar trend in H_c, indicating strong magneto-static interactions (see Table 4) [86,87]. However, the large Sq value obtained by co-doping at 10 K indicates the homogeneity of the grains and confirms the presence of ferromagnetic domains [88].

The magnetization as a function of temperature for S3 measured in the field-cooled (FC) and zero-field-cooled (ZFC) configurations at an applied magnetic field of 100 Oe is shown in Figure 10. The FC and ZFC curves for S3 show an obvious bifurcation, which indicates the existence of magnetic nanoparticles with a blocking temperature of T_b = 60 K, smaller than that of S1 where the magnetic nanoparticles blocking temperature of T_b = 80 K. The FC and ZFC in the whole temperature range of 10–300 K suggest that there is no existence of an order–disorder phase transition, which reveals that the Curie temperature (T_C) is higher than 300 K. However, the ZFC curve shows the phenomenon of a negative magnetization (or magnetization sign reversal) at low temperature due to the dominance of diamagnetic contribution at low temperature. Such behavior has been reported elsewhere [3,89,90,91,92,93], and it is mainly explained by the coexistence in LSMO of ferromagnetic order and magnetically inhomogeneous regions made up of spin clusters with a lower oxidation state. Similar behavior was observed in the other samples as well.

3.5. Dielectric Analysis

The real part of the dielectric constant (ε′), the loss factor (tan δ), and the quality factor (q-factor) are expressed as follows [94,95]:

$${\epsilon }^{\backslash }={\displaystyle \frac{Cd}{{\epsilon }_{\circ }A}};\tan \partial ={\displaystyle \frac{{\epsilon }^{\backslash \backslash }}{{\epsilon }^{\backslash }}}$$

(7)

where C and C₀ are the capacitances of the sample and the empty cell (C₀ = ε₀A/d), respectively. ε’’ is the imaginary part of ε. Figure 11a plots the relationship between ε′ and frequency (f) and shows that ε^\ steadily declined as f is decreased up to 1 MHz, the point at which ε^\ saturated. The higher values of ε^\ at lower f clearly indicate the presence of interfacial polarization caused by the polarization of the space charge. Elevating f beyond 1 MHz may result in a dipolar polarization, where the carriers are unable to track the field reversal [96]. However, the addition of co-doping helps to decrease the ε^\ of the samples S1 to S4, followed by a slight increase in the case of S5 to be higher than those of S4, inconsistent with the space charge polarization explanation provided by Maxwell–Wagner [97]. However, the co-doped samples can be used in the devices of nonlinear optics and high-frequency antennas [98,99].

The total electrical conductivity (σt) is determined by following equation [100]:

$${\sigma }_t(\omega )={\sigma }_{dc}+{\sigma }_{ac}={\sigma }_{dc}+B{\omega }^s$$

(8)

where s represents the frequency exponent, ac denotes the ac conductivity, B is constant, and dc denotes the dc conductivity. The plot of σ_ac against f in Figure 11b illustrates how σ_ac increases progressively as f increases up to 20 MHz. Furthermore, σ_ac behavior against co-doping is comparable to that of ε^\. The decrease in both ε^\ and σ_ac by the co-doping might be because of the rapid movement of charge carriers from the grains, which accumulate at the grain boundaries and impede the tunneling of these carriers, leading to a reduction in polarization, as previously reported [101,102,103].

The real and imaginary components of the electric modulus (M^\, M^\\) for the samples are plotted against f in Figure 12a,b. It is seen that M^\ increased with increasing f for all samples and then saturated above 10 kHz. As compared to S1, M^\ was decreased for S2 and S3, followed by a significant increase for S4, and then decreased to be lower than that of S4. The same behavior is observed for the curves of M^\\, but with different relaxation peaks (RPs). For example, M^\\ shows RP at 353 Hz for S1, but is shifted to a low f of 168, 199, and 65.2 Hz for S2, S3, and S4, followed by a shift to 137 Hz for S5. However, the RP values of the samples indicate a non-Debye relaxation type and have substantially shorter spin-relaxation periods than expected between 100 and 150 ns, which is highly advantageous for spintronic devices [69].

Figure 13a,b presents the Cole–Cole (Nyquist) plots of Z^\\ as a function of Z^\ for all samples. The plots are single semicircles followed by straight lines or arcs of positive or negative slopes at the tail of the curve for S1, S3, S4, and S5. In this case, the frequency (f) is unable to distinguish the impedance of the grains from their boundaries. Therefore, it can be modeled using a parallel combination of a resistor (R) and a capacitor (C), as shown in Figure 14. In contrast, for sample S2, two successive semicircles spanning the frequency range are observed, indicating that the applied frequency range is sufficient to separate the conductivity of the grains from that of their boundaries. This behavior can be further represented by a series combination of two parallel RC circuits, as depicted in Figure 14. The radius/diameter of each plot is employed to obtain the impedances of grains and their boundaries as Z^\(g), Z^\(gb), as summarized in

Table 6. Frequency exponent, binding energy, impedance of gains and their boundaries, bulk resistance, and effective capacitance of La_0.67Sr_0.33Mn_1-x-yZn_xCo_yO₃ samples.

S	f (M\\) (Hz)	Z\(g) (MΩ)	Z\(gb) (MΩ)	RB (MΩ)	Ceff (nF)
S1	353	80.30	57.40	333	0.424
S2	168	211	638	952	0.145
S3	199	254	173	1000	0.134
S4	65	1050	657	5000	0.045
S5	137	411	192	909	0.105

. It was found that the values of Z for S1 gradually increased until they reached their maximum values for S4, and then decreased for S5, which is in direct correlation with those obtained for Ms. However, the opposite is true for the example. The parallel combination’s series resistance (RB) and effective capacitance (Ceff) are given by [104,105];

$$Z^{\backslash }(\omega )={\displaystyle \frac{R_B}{1+{(\omega C_{eff}{R}_B)}^2}}\to {\displaystyle \frac{1}{Z^{\backslash }}}={\displaystyle \frac{1}{R_B}}+{\omega }^2{C}_{eff}^2{R}_B$$

(9)

The slope and intercepts of the linear plot between [1/Z^\(ω)] and (ω²) were used to determine the values of RB and Ceff (see Table 6). The behavior of RB is comparable to that of Z^\ of grains and grain borders; however, Ceff exhibits the opposite behavior, meaning that [(Z^\ or RB α (1/C_eff)] [106]. It is interesting to note that lower RB and C_eff values are indicative of good Li-ion batteries for oxidation and reduction reactions [107]. On the other hand, to restrict the amount of energy lost in the RB, a supercapacitor ought to have a smaller RB and a greater C_eff [108]. These results strongly suggest the use of S1 as a supercapacitor, whereas S4 can be used in Li-ion batteries.

It can be concluded that an increase in oxygen deficiency led to a reduction in the relative concentration of Mn⁴⁺/Mn³⁺, which weakened the ferromagnetic interaction and resulted in a decreased magnetization. However, the data reported for individual doping of transition metals (TMs) such as Co, Ni, Fe, and Zn in place of Mn in the La:113 system showed a monotonically decreasing trend as magnetization increased to approximately 0.20. This behavior may be attributed to the antiferromagnetic alignments induced by the dopants in the sample. Therefore, co-doping with two different ions—one magnetic and the other nonmagnetic—can be recommended to diminish the antiferromagnetic domains while maintaining the ferromagnetic characteristics of the sample, albeit with slightly reduced magnetization. Based on the above, it is found that co-doping up to 0.10 (S4) generally decreased V, D, D_SEM, E_g, E_o, E_d, ε^\, σ_ac, and C_eff, whereas the opposite is true for the behaviors of PS, ϴ_D, Y, M_s, W_m, M, Z, and RB. In addition, it changed the magnetic material from hard to soft at 300 K and from soft to hard at 10 K. These results show a universal relationship between the internal structural and optical parameters and those obtained from the other current measurements. In addition, they indicate that co-doping up to 0.10 by two different ions (Zn and Co) in place of Mn in the La:113 compounds is beneficial for elastic deformation, optoelectronics, Li-batteries, and spintronic devices.

4. Conclusions

The structural, optical, and magnetic properties of La_0.67Sr_0.33Mn_1-x-yZn_xCo_yO₃ manganite with various x and y were investigated. We show evidence for MnO₆ octahedral and electronic conduction in all samples. The co-doping up to 0.10 (S4) generally decreased V, D, DSEM, E_g, E_o, E_d, ε^\, σ_ac, and C_eff, whereas the opposite is true for the behaviors of PS, ϴ_D, Y, M_s, M, Z, and RB. At 300 K, the samples (S1–S5) exhibited paramagnetic behaviors as observed at a high magnetic field range, but they showed ferromagnetic behavior at low temperature, such that M_s values at 10 K were 10-times greater than those at 300 K. However, the magnetization sign reversal (negative magnetization) phenomena was observed in the samples due to the dominance of the diamagnetic contribution at the low-temperature region. Additionally, most of the dielectric parameters were investigated, and it was found that the dielectric constant and ac conductivity were reduced with the increasing concentration of the co-dopants in the samples. These outcomes indicate that the co-doping up to 0.10 by two different ions (Zn and Co) in place of Mn in the La:113 compounds is beneficial for elastic deformation, optoelectronics, Li-batteries, and spintronic devices.