Structural, morphological, magnetic and electrical properties of La_0.8Na_0.2−x□_xMnO₃ (0.00 ≤ x ≤ 0.15) manganites

Abstract

La_0.8Na_0.2−x□_xMnO₃ (0.00 ≤ x ≤ 0.15) manganites were successfully synthesized using the solid-state route. X-ray diffraction was performed to check the samples' purity and phase structure. Scanning electron microscopy analysis reveals a decrease in the average grain size with an increase in the deficiency amount. Analysis of the temperature dependence of magnetization proved the presence of ferromagnetic–paramagnetic transition in all the studied samples. The magnetization derivative (d²M/dT²) curves demonstrated a decrease in the transition temperature with an increase in the deficiency amount. Such experimental observations can be correlated with bandwidth evolution, which affected double-exchange interactions. It can be equally accounted for by the average grain size decrease. In this regard, the experimental measurements of effective paramagnetic moments revealed the existence of ferromagnetic correlations within the paramagnetic phase. Notably, different electrical findings were addressed. Indeed, the frequency dependence of electrical conductivity displayed the coexistence of two frequency slopes reflecting the presence of Jonscher's double power law for all the studied samples. A significant decrease in conductivity values was observed when the deficiency amount increased. This experimental observation could be assigned to the decrease in the grain size (conductor region). Such assumption was confirmed by the evolution of the grain boundary resistance with deficiency level. Indeed, a significant mounting in the grain boundary resistance values was obtained presenting the increase of the resistive region for x = 0.15. It is worth noting that the Curie temperature for the x = 0.10 sample was found to be close to room temperature (T_C = 297 K). These findings make the La_0.8Na_0.1□_0.1MnO₃ compound a powerful candidate for many technological applications.

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1. Introduction

The discovery of the colossal magnetoresistance phenomenon^1–3 and magnetocaloric effect^4–6 has fueled much research on the outstanding physical properties of manganite compounds. Owing to such physical properties, manganites can be used for numerous applications, including magnetic refrigerants, magnetic sensors, magneto-resistive transducers, computer memory systems, spintronic devices, catalysts, and infrared detectors.^7–11 Different interesting behaviors such as charge-ordering (CO),¹² metamagnetic transition,¹³ colossal magnetoresistance^14,15 and large magnetocaloric effects^6,16 have been observed. In fact, several studies have widely reported many investigations on the structural, morphological, optical, magnetic, electronic and electrical properties of manganites.^17–32 The parent compound (LaMnO₃) of lanthanum manganite (La_1−xA_xMnO₃) systems is an anti-ferromagnetic material.³³ Substitution by a monovalent (Na⁺, Ag⁺, K⁺…) or divalent ion (Ca²⁺, Sr²⁺, Ba²⁺…) generates mixed-valence properties. Indeed, the partial substitution of La element by Na element provokes the hopping of an e_g electron from the Mn³⁺ cation to the adjacent Mn⁴⁺ cation by the intermediary oxygen anion O²⁻. Such hops manifest into double-exchange (DE) interactions between these manganese cations.³⁴ Accordingly, the Mn³⁺/Mn⁴⁺ ratio can be controlled by doping (site of doping, doping element, doping amount), leading to an improvement in physical properties. In this context, the effect of sodium doping on lanthanum manganite systems has been frequently studied.^35–41 Arunachalam et al.³⁶ reported that the particle size decreases with increasing sodium concentration. Such structural change has an effect on the electrical and magnetic properties. In addition, the ferromagnetic–paramagnetic phase transition temperature is increased with the increasing Na concentration.⁴⁰ Furthermore, it was observed that the system resistivity values showed a significant decrease with the increase in the Na amount.⁴⁰ Besides, the literature^42–49 has presented that the creation of deficiencies can affect the physical properties of these kinds of systems. Indeed, A-site deficiency can modify the Mn³⁺/Mn⁴⁺ amount, which in turn can alter their magnetic and electrical properties. A magnetocaloric effect (MCE) was also reported in several deficient manganites. Indeed, Smari et al.⁵⁰ argued that the La_0.5Ca_0.5−xAg_xMnO₃ deficient manganite had a large ΔS^max_M of 2.9 J K⁻¹ kg⁻¹ under a magnetic field of 0.9 T with a T_C of 272 K. This indicates that La_0.5Ca_0.5−xAg_xMnO₃ could be used as an active magnetic refrigerant within the sub-room-temperature range. In addition, M'nassri et al.⁵¹ examined the effect of barium-deficiency on the structural, magnetic, and magnetocaloric properties of La_0.6Sr_0.2Ba_0.2−x□_xMnO₃, where ΔS^max_M did not exceed 4 J K⁻¹ kg⁻¹ under a magnetic field of 4.5 T for all the studied samples.

In the present investigation, interesting properties of La_0.8Na_0.2−x□_xMnO₃ (0.00 ≤ x ≤ 0.15) manganites were observed and discussed. The deficiency effect was obviously manifested in the structural, morphological, magnetic, and electrical properties. For instance, a decrease in the grain size was observed in the SEM study. The increasing deficiency level also provoked a decrease in the Curie temperature T_C. The experimental measurements of the effective paramagnetic moments exceeded the corresponding theoretical values. Such a result proved the existence of ferromagnetic correlations within the paramagnetic phase. On the electrical side, the presence of double slopes in the dispersive region of the conductivity spectra was revealed for all the studied samples, which equally displayed a significant decrease in the conductivity values when the deficiency amount rose. For x = 0.10, the Curie temperature was found to be close to room temperature (T_C = 297 K). Such an experimental observation makes the 10% deficiency sample a promising candidate for several technological applications.

2. Experimental details

The La_0.8Na_0.2−x□_xMnO₃ (0.00 ≤ x ≤ 0.15) materials were synthesized via the solid-state ceramic technique. The used precursors were lanthanum La₂O₃ and manganese MnO₂ oxides as well as sodium carbonate Na₂CO₃ with purities greater than 99.9%. Lanthanum oxide and sodium carbonate were dehydrated at 400 °C for 1 h so as not to distort the weighing. The first synthesis step consisted of weighing the precursors in the desired stoichiometric proportions. These precursors were then finitely ground for 20 min to obtain a homogeneous mixture. The obtained powders were subsequently placed in alumina nacelles and brought to increasingly high temperatures, going from 700 °C to 1100 °C at an increase of 100 °C per day, interspersed with grinding. This step, called calcination, allowed, on the one hand the decomposition and release of gases (O₂ and CO₂) and, on the other hand, the partial formation of the intended phase in line with the following reaction:

The obtained powders were ground again for 30 min in a dry environment. This grinding reduced the grain size, homogenized the product, and minimized the intergranular porosity. The next step consisted of pelletizing the samples to promote diffusion and vaporization–condensation mechanisms during the solid-state reaction. During this phase, the powders were molded into pellets under an axial pressure of 4 tons per cm². The final step was sintering, which consisted of placing the pellets, in alumina or platinum crucibles to guarantee that a foreign phase was not formed by interaction with the crucible, in an oven under air at 1200 °C for an annealing time sufficient for the formation and growth of and grains. Rapid quenching in air was necessary to help maintain the structure at ambient temperature in equilibrium with the annealing temperature. These reactions are slow and result in a long-distance diffusion of the different ions. These methods have the advantage of being very easy to implement; however, they require several grinding and annealing cycles at high temperatures.

Alternatively, the samples underwent X-ray diffraction analysis using a Bruker D8 diffractometer, which featured a copper anticathode (λ_Cuα1 = 1.5406 Å) and a rear graphite monochromator. The recording of the X-ray powder patterns was carried out at room temperature in an angular range varying from 10° to 100° in the 2θ mode at steps of 0.02° and an acquisition time of 1 s for each step.

The microstructure was examined by scanning electron microscopy (SEM). A vibrating sample magnetometry (VSM) instrument by Quantum Design was employed for the measurements of the magnetic fields. The magnetization versus magnetic field curves were recorded by varying the magnetic field between 0 and 5 T at temperatures both below and above the Curie temperature.

Electrical measurements were performed using an Agilent 4294A impedance analyzer for each prepared sample over a wide frequency range (40 Hz to 1 MHz) at room temperature.

3. Results and discussion

3.1. Scanning electron microscopy

The secondary electron SEM images for La_0.8Na_0.2−x□_xMnO₃ (0.00 ≤ x ≤ 0.15) are shown in Fig. 1(a)–(d). The micrographs obtained showed grains with various polygonal shapes with a non-uniform distribution. We could also observe in these images some black contrast voids associated with the porosity of the samples. The particle-size distribution was analyzed statistically using ImageJ software. Fig. 2(a)–(d) depicts histograms illustrating the grain sizes of the samples under investigation. As observed, the histograms were well modeled by the Lorentzian function. The average grain size was affected by the sodium vacancy rate, resulting in different values for the four samples: 2.358 μm for x = 0.00, 2.292 μm for x = 0.05, 2.087 μm for x = 0.10, and 1.994 μm for x = 0.15.

Fig. 1 SEM images of all samples: (a) x = 0.00, (b) x = 0.05, (c) x = 0.10 and (d) x = 0.15.

Fig. 2 Size-distribution histograms of La_0.8Na_0.2−x□_xMnO₃: (a) x = 0.00, (b) x = 0.05, (c) x = 0.10 and (d) x = 0.15.

3.2. Chemical analysis

The percentages of Mn³⁺ and Mn⁴⁺ ions in our La_0.8³⁺Na_0.2−x⁺□_x⁰(Mn_0.6−x³⁺Mn_0.4+x⁴⁺)O₃²⁻ samples were determined using a conventional chemical technique. Initially, we dissolved the sample powder in oxalic acid dihydrate (H₂C₂O₄·2H₂O) and concentrated sulfuric acid (H₂SO₄). The resulting solutions were subsequently titrated with potassium permanganate (KMnO₄). Table 1 depicts a comparison of the theoretical and experimental results of the Mn³⁺ and Mn⁴⁺ contents. The obtained data indicate that the experimental concentrations of manganese ions were very close to the theoretical values. Ultimately, it is noteworthy that our samples were prepared in air, ensuring they were stoichiometric in oxygen.

Table 1 Chemical analysis results for La_0.8Na_0.2−x□_xMnO₃ samples with 0.00 ≤ x ≤ 0.15

x	Theoretical content		Experimental content
	Mn^3+ (%)	Mn^4+ (%)	Mn^3+ (%)	Mn^4+ (%)
0.00	60	40	62.14	37.86
0.05	55	45	56.02	43.98
0.10	50	50	51.17	48.83
0.15	45	55	45.84	54.16

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3.3. Structural properties

The X-ray diffraction pattern analysis confirmed the structural integrity and phase purity of our compounds. The X-ray diffraction patterns at room temperature for the La_0.8Na_0.2−x□_xMnO₃ (0.00 ≤ x ≤ 0.15) compounds are depicted in Fig. 3(a), which indicate that all the samples exhibited a consistent perovskite structure with identical peaks. These peaks were associated with the diffraction lines of the rhombohedral phase with the R3̄c space group. All the peaks accurately correlated with the 2θ values of 23.3°, 32.4°, 33.2°, 40.1°,40.8° 47°, 59°, 69.4°, and 77.9° indicating the 012, 110, 104, 113, 202, 024, 214, 220, and 134 crystalline planes, respectively.

Fig. 3 XRD patterns of La_0.8Na_0.2−x□_xMnO₃ compounds. The peaks were indexed to the R3̄c space group. The inset displays a deviation of the peaks toward lower angles for the most intense peaks (Bragg reflections 110 and 104) (a). Experimental XRD diagram and Rietveld refinement for La_0.8Na_0.05□_0.15MnO₃ (b).

Also, with the increase in vacancy content, the patterns showed a slight shift of the most intense peak toward smaller 2θ values (inset of Fig. 3(a)), suggesting that the vacancy had a larger ionic radius than Na. The displacement of the diffraction peaks toward smaller angles indicated that the cell parameters of the samples increased as the vacancy rate increased. The Rietveld technique produced satisfactory agreement factors and lattice parameters when refining the data using FULLPROF software.⁵² An example of the XRD pattern refinement for the x = 0.15 sample is shown in Fig. 3 (b). The refinement results (see the ESI†), as summarized in Table 2, indicated there was a slight increase in both the cell parameter and unit cell volume with the rising vacancy content.

Table 2 Refinement results for the XRD experimental patterns

Vacancy content	x		0.00	0.05	0.10	0.15
La0.8Na0.2−x□xMnO3 (rhombohedral), R3̄c	Lattice parameters	a = b (Å)	5.412(6)	5.427(5)	5.440(1)	5.448(7)
		c (Å)	13.132(4)	13.145(3)	13.153(2)	13.16(5)
	Unit cell volume (Å^3)		55.531	55.892	56.185	56.415
	dMn–O (Å)		1.9250	1.9336	1.9374	1.9404
	θMn–O–Mn (°)		164.5877	162.7587	162.5934	162.4338
	Rwp (%)		5.20	5.36	6.14	4.68
	Rp (%)		5.04	4.68	5.02	4.49
	Rf (%)		2.18	2.24	1.18	1.81
	χ^2 (%)		3.41	4.13	2.74	2.11
Mn3O4 (tetragonal), I41/amd	Lattice parameters	a = b (Å)	5.734(6)	5.731(8)	5.731(5)	5.739(4)
		c (Å)	9.467(9)	9.458(7)	9.453(5)	9.455(2)
	%		0.08	0.11	0.08	0.16

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In fact, we noted the existence of very low intensity peaks in the XRD patterns, which were associated with Mn₃O₄, as is frequently encountered in mixed-valence manganites. This Mn₃O₄ secondary phase had no significant effect on the stoichiometry of the materials, given its low concentration.⁵³ Furthermore, it is important to highlight that the introduction of sodium vacancies did not lead to any changes in the space group of the parent compound La_0.8Na_0.2MnO₃. The average crystallite size has been estimated using a variety of techniques, such as Scherrer's formula.^54,55 The following formula was utilized here to calculate the average crystallite size D_SC:

This formula makes it possible to extract the microstructural parameters of the diffraction peaks, but it only gives partial information. In this relationship, the broadening of the line characterized by the width at half maximum is linked to an effect of the size of the coherent diffraction domains (crystallite size). Applying Scherrer's formula, we calculated the size of the crystallites within our compounds, observing an increase as the vacancy rate (x) increased. The respective values for the four samples (x = 0.00, x = 0.05, x = 0.10, and x = 0.15) were 95, 108.2, 108.5, and 109.5 nm. The elemental volume increased as the vacancy rate rose, shifting from 55.5 Å to 56.5 Å when the vacancy rate increased from 0.00 to 0.15. To elucidate this variation, we took into account the following three factors:

• Variation in the average radius of B sites,

• Variation in the average radius of A sites,

• Variation of the Mn–O distance.

According to electrical neutrality, the La_0.8³⁺Na_0.2−x⁺□_x⁰(Mn_0.6−x³⁺Mn_0.4+x⁴⁺)O₃²⁻ compounds contain (0.6 − x) Mn³⁺ ions and (0.4 + x) Mn⁴⁺ ions per formula unit. By increasing the rate of vacancies x, there is a conversion of a fraction x of the manganese Mn³⁺ ions into Mn⁴⁺ ions, whose radius is smaller (r_Mn³⁺ = 0.65 Å and r_Mn⁴⁺ = 0.53 Å⁵⁶). Thus, the average ionic radius 〈r_B〉 of the cations occupying the B site was determined from the following relation:

〈r_B〉= (0.6 − x)r_Mn³⁺ + (0.4 + x)r_Mn⁴⁺ (3)

We observed that the variation in the average radius 〈r_B〉 of the cations at the B site decreased, unlike the volume V, which increased with the vacancy rate x. This reduction in 〈r_B〉 did not significantly affect the volume variation, as it did not exceed ∼2% in the best cases. To explain this evolution in volume, we studied the effect of a second parameter, namely the average ionic radius 〈r_A〉 of the cations occupying the A site. Thus, the creation of vacancies at the sodium site in the La_0.8Na_0.2−x□_xMnO₃ series could increase the average ionic radius of the A site (with r_La³⁺ = 1.216 Å and r_Na⁺ = 1.24 Å); therefore r_V > r_Na⁺. The creation of a vacancy in a monovalent or divalent site tends to increase the volume in relation to the vacancy rate x.⁵⁷ Khlifi et al.⁵⁷ showed, in the La_0.8Ca_0.2−x□_xMnO₃ series, that the vacancy would admit an r_V radius greater than that of calcium (r_Ca²⁺ = 1.18 Å), consequently resulting in an expansion of the unit cell volume. Whereas the formation of a vacancy in a trivalent site typically results in a reduction in volume.⁵⁸ Likewise, Skini et al.⁵⁸ showed that, in La_0.8−x□_xCa_0.2MnO₃ compounds, the radius of the vacancy r_V was smaller than r_La³⁺ = 1.216 Å. Then, r_Ca²⁺ ≤ r_V ≤ r_La³⁺, causing a decrease in volume.

According to the structural refinement, we noticed that the Mn–O distance increased from 1.9250 Å to 1.9404 Å when the rate of vacancies in the A sites passed from 0.00 to 0.15. This variation in the Mn–O distance directly affected the cell parameters, which increased, and consequently the volume of the cell increased with the rate of vacancies in A sites increasing. In Fig. 4, we plotted the changes in both the Mn–O distance and the volume against the vacancy rate x. This graph vividly demonstrates there was an upward trend in the Mn–O distance, providing a clear explanation for the concurrent increase in volume as the vacancy rate x rose.

Fig. 4 Variation in the volume V and the distance d_Mn–O as a function of the x rate vacancy of La_0.8Na_0.2−x□_xMnO₃ compounds (x = 0.00, 0.05, 0.10 and 0.15).

3.4. Magnetic properties

The magnetic properties were investigated by measuring the temperature-dependent magnetization (M(T)) under an applied field of 0.05 T for the compounds La_0.8Na_0.2−x□_xMnO₃ with vacancy rates ranging from 0.00 to 0.15, as illustrated in Fig. 5(a)–(d). The findings revealed a transition from ferromagnetic to paramagnetic states for all the samples as the temperature increased.⁵⁹ Accordingly, it was evident that the magnetization declined as the sodium deficiency rate increased, attributable to the diminished presence of Mn³⁺ ions, distinguished by their elevated spin (S = 2), and the concomitant augmentation of Mn⁴⁺ ions (S = 3/2), as delineated by the equation La_0.8³⁺Na_0.2−x⁺□_x⁰(Mn_0.6−x³⁺Mn_0.4+x⁴⁺)O₃²⁻. Furthermore, there are two techniques available to identify the transition temperature (T_C) from the ferromagnetic to the paramagnetic state.

Fig. 5 Variation in the magnetization (M) and the inverse of the magnetic susceptibility vs. temperature of La_0.8Na_0.2−x□_xMnO₃ (x = 0.00 (a), 0.05 (b), 0.10 (c) and 0.15 (d)) compounds measured at an applied magnetic field of 0.05 T. Symbols are the experimental results and solid lines are the graphs fitted. The insets display the numerical derivation d²M/dT² as a function of temperature for all the samples.

Method I. Through numerical derivation (d²M/dT²), as shown in the insets of Fig. 5(a)–(d), whereby it is possible to precisely identify the transition's inflection point.

Method II. By determining the saturation magnetization and the Curie temperature T_C using the following equation as presented in Fig. 5(a)–(d):where ε, δ, and σ are constant parameters. The adjusted parameters obtained from the refinement of the magnetization as a function of temperature curve are illustrated in Table 3. The Curie temperature (T_C) delineating the transition between the paramagnetic and ferromagnetic phases exhibited a decrease from 336 K to 263 K as the sodium deficiency (x) increased from 0.00 to 0.15. These findings were in excellent accordance with those reported by Wali et al.⁵⁹ The reduction in T_C could be ascribed to several factors, notably a direct correlation with the bandwidth (W), which affects both the mobility of e_g electrons and the double-exchange (DE) interaction. Indeed, the introduction of a sodium vacancy in site A initiates a partial transformation of Mn³⁺ ions into Mn⁴⁺ ions, in accordance with the electronic formula La_0.8³⁺Na_0.2−x⁺□_x⁰(Mn_0.6−x³⁺Mn_0.4+x⁴⁺)O₃²⁻. As the vacancy rate escalated from 0.00 to 0.15, the number of tetravalent Mn⁴⁺ ions increased from 40% to 55%, while the number of trivalent Mn³⁺ ions decreased from 60% to 45%. This shift in the Mn³⁺/Mn⁴⁺ ratio led to a reduction in the average ionic radius of the B site. Furthermore, owing to electrostatic reasons, a vacancy possesses a non-zero radius, further modifying the average ionic radius of the A site. These dual effects explain the decrease in magnetization and the Curie temperature (T_C) as the vacancy rate increased. Additionally, this alteration in the Mn³⁺/Mn⁴⁺ ratio associated with sodium vacancies promoted an increase in the super-exchange interactions, thereby enhancing double exchange. It is evident that the magnetic properties of manganites are closely tied to the lengths and angles of the Mn–O–Mn bonds. The strength of the exchange interactions relies on both the bond distance and the bond angle. Consequently, reducing the angle and increasing the bond length weaken the Mn–Mn exchange interaction, resulting in a decrease in the Curie temperature (T_C) and magnetization.

Table 3 Aharoni fitting parameters

x	MSat (emu g^−1)	T^theoC (K)	T^expC (K)
0.00	26.91	335.65	336
0.05	23.67	320.68	320
0.10	21.97	296.98	297
0.15	19.76	266.61	263

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Moreover, to understand the magnetic behavior within the paramagnetic range, we investigated the temperature dependence of the inverse magnetic susceptibility (χ) for all the samples, as depicted in Fig. 5(a)–(d). It is evident that the 1/χ dependence of the temperature follows the Curie–Weiss law: , where the Curie constant and Weiss temperature are represented by C and θ_W, respectively. The data's linear paramagnetic region can be used to obtain the Curie–Weiss parameters C and θ_W. Moreover, we calculated the experimental effective moment (μ^exp_eff), which is defined as: ,⁶⁰ where N is the Avogadro number, μ_B is the Bohr magneton, and k_B is the Boltzmann constant. We found the μ^exp_eff values were 5.634, 4.775, 5.203, and 5.830 respectively. Assuming the orbital contribution to be quenched in both Mn³⁺ and Mn⁴⁺, the theoretical paramagnetic effective moment (μ^th_eff) can be expressed as , where g = 2 represents the gyromagnetic factor and S is the spin of the cation. Therefore, the theoretical values were μ^th_eff = 4.90 μ_B for Mn³⁺ and μ^th_eff = 3.87 μ_B for Mn⁴⁺. Taking into account the rigid coupling of Mn³⁺ and Mn⁴⁺, the calculated effective paramagnetic moment per formula unit can be written as:

The theoretical values of the effective paramagnetic moments μ^th_eff were calculated for all samples as 4.516, 4.465, 4.415, and 4.363 μ_B for x = 0.00, 0.05, 0.10, and 0.15, respectively. However, the experimental measurements of the effective paramagnetic moments surpassed the corresponding theoretical values. This discrepancy indicated the presence of Mn⁴⁺ and Mn³⁺ clusters,⁶¹ suggesting that in the paramagnetic state, the individual magnetic spins were not isolated; instead, they formed small groups, revealing the existence of ferromagnetic correlations within the paramagnetic phase. In Table 4, we report the Curie constant (C), the Weiss temperature (θ_W), as well as the theoretical (μ^th_eff) and experimental (μ^exp_eff) moments. In the table, positive values of θ_W could be observed, confirming the ferromagnetic characteristics of all the samples. Additionally, these values exhibited a decreasing trend with increasing x, mirroring the behavior of the Curie temperature (T_C).

Table 4 Transition temperature (T_C), Curie constant (C), Curie–Weiss temperature (θ_W), theoretical (μ^th_eff) and experimental (μ^exp_eff) moments as a function of the x content for La_0.8Na_0.2−x□_xMnO₃ samples

x	TC (K)	C (K uem mol^−1)	θW (K)	μ^theff (μB)	μ^expeff (μB)
0.00	336	3.968	338.024	4.516	5.634
0.05	320	2.850	323.888	4.465	4.775
0.10	297	3.384	300.159	4.415	5.203
0.15	263	4.248	260.064	4.363	5.830

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3.5. Electrical properties

Fig. 6 shows the electrical AC-conductivity spectrum for the parent compound La_0.8Na_0.2MnO₃. A frequency-independent region could be clearly observed at low frequencies. Such a frequency range is associated with the DC-conductivity, as depicted in Fig. 6. Funke⁶² explained the electrical transport in such a regime by the long-range translational motion. Here, σ_AC remained constant as the frequency increased until reaching the hopping frequency. Such a characteristic frequency is defined by the frequency at which the conductivity changes the slope. Beyond this frequency, the electrical conductivity increased with the frequency increasing. Such an observation suggests the possibility of the presence of different electrical transport mechanisms, which has been widely studied using the Pike model⁶³ and detected in several amorphous and perovskite materials.^{17–20,26,27,29,64–70} As indicated in Fig. 6, σ_AC showed a significant increase with two linear slopes. Thus, such a result leads to the fact that this spectrum presented two frequency exponents. Accordingly, the frequency dependence of AC-conductivity was governed by Jonscher's double power law:^71–73

σ_AC = σ_DC + A₁ω^s₁ + A₂ω^s₂ (6)

where σ_DC is the DC-conductivity, A₁ and A₂ are constants, s₁ and s₂ are the frequency exponents, and A₁ω^s₁ and A₂ω^s₂ are the intermediate- and high-frequency responses of the AC-conductivity σ_AC, respectively. Such a result was detected for all the studied samples (Fig. 7(a)). In fact, the frequency increase led to an increase in the crystal vibration, which contributed to releasing the trapped charge carriers. Equally, it can create new conduction sites. In this case, the inter-sites distance was decreased, presenting a short-range translational motion at intermediate and high frequencies.

Fig. 6 Frequency dependence of electrical conductivity at room temperature for the parent compound La_0.8Na_0.2MnO₃.

Fig. 7 Conductivity spectra of La_0.8Na_0.2−x□_xMnO₃ (x = 0.05, 0.10 and 0.15) compounds (a). Evolution of DC-conductivity with the deficiency amount (b).

The conductivity spectra of the La_0.8Na_0.2−x□_xMnO₃ (x = 0.05, 0.10, 0.15) compounds are displayed in Fig. 7(a). At low frequencies, the conductivity showed a slight decrease with the deficiency ratio increasing from x = 0.05 to x = 0.10 (Fig. 7(a) and (b)). Then, a significant decrease in the conductivity values was observed when the deficiency ratio increased for x = 0.15. Various studies have reported that the transport properties in manganites are mainly controlled by the Mn³⁺–O²⁻–Mn⁴⁺ network and thus the Mn³⁺/Mn⁴⁺ concentration.^17–19 Such a concentration can be modified by the bond length Mn–O, the bond angle Mn–O–Mn, the unit cell volume, the average grain size, and the oxygen vacancies.^{17–20,26,74} In our case, the decrease in the conductivity values could be explained by the decrease in the grain size (Fig. 1(a)–(d)), which prevented the double-exchange interactions. Indeed, the SEM micrographs showed a decrease in the average grain size with increasing the deficiency rate (2.358, 2.292, 2.087, and 1.994 μm respectively for x = 0.00, 0.05, 0.10, and 0.15) (Fig. 1(a)–(d)). In the literature,^{17,29,75–79} it has been frequently proved in manganites that the grain boundaries are more resistive than the grains. This could be due to the non-stoichiometric distribution of oxygen and the existence of dangling bonds in the grain boundaries region.⁸⁰ These factors can lead to charge trapping and an increase in the barrier width, which would hamper the DE interactions in the Mn³⁺–O²⁻–Mn⁴⁺ chain. Therefore, the decrease in the conductor region (grains) leads then to an increase in the resistive region (grain boundaries) and the reduction of the grains connectivity when the deficiency ratio increases. Fig. 8 confirmed the significant increase in the grain boundary resistance for x = 0.15; whereas, such resistance values were very close for x = 0.05 and x = 0.10. Thus, the electrical conductivity decrease was an expected result (Fig. 7(a) and (b)).

Fig. 8 Evolution of the grain boundary resistance with the deficiency amount.

4. Conclusion

Deficient La_0.8Na_0.2−x□_xMnO₃ (x = 0.00, 0.05, 0.10, and 0.15) manganites were successfully prepared via a solid-state reaction. The phase formation of the synthesized samples was confirmed using X-ray diffraction diagrams. The scanning electron microscopy analysis revealed there was a decrease in the average grain size. The evolution of magnetization (measured under an applied field of 0.05 T) with temperature indicated the presence of a ferromagnetic–paramagnetic transition for all the compounds. The transition temperature T_C was found to decrease when the deficiency ratio increased. Measurements of the effective paramagnetic moments revealed the existence of ferromagnetic correlations within the paramagnetic phase. However, the electrical conductivity spectra showed the coexistence of two frequency slopes mirroring the presence of Jonscher's double power law. As the deficiency amount increased, a significant decrease in the conductivity values was obviously detected. Such an experimental result could be related to the decrease in the grain size. The significant increase in the grain boundary resistance for x = 0.15 confirmed the grain size effect on the transport properties. Eventually, it was observed that the Curie temperature for x = 0.10 was close to room temperature (T_C = 297 K). Such a result indicates that the 10% deficiency sample may be a promising candidate for several technological applications.

Ethical approval

This article does not contain any studies involving animal or human participants performed by any of the authors.

Data availability

The data included in this manuscript are available and can be discussed (or shared), on request from the corresponding author.

Author contributions

All the authors have accepted full responsibility for the content of this manuscript and have given their approval to its submission.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This study is supported by the Tunisian Ministry of Higher Education and Scientific Research.

References

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ra03519d

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