The Physical Properties of Submicron and Nano-Grained La_0.7Sr_0.3MnO₃ and Nd_0.7Sr_0.3MnO₃ Synthesised by Sol–Gel and Solid-State Reaction Methods

Abstract

La_0.7Sr_0.3MnO₃ (LSMO) and Nd_0.7Sr_0.3MnO₃ (NSMO) possess excellent colossal magnetoresistance (CMR). However, research work on the neodymium-based system is limited to date. A comparative study between LSMO and NSMO prepared by sol–gel and solid-state reaction methods was undertaken to assess their structural, microstructural, magnetic, electrical, and magneto-transport properties. X-ray diffraction and structure refinement showed the formation of a single-phase composition. Sol–gel-synthesised NSMO was revealed to be a sample with single crystallite grains and exhibited intriguing magnetic and electrical transport behaviours. Magnetic characterisation highlighted that Curie temperature (T_C) decreases with the grain size. Strong suppression of the metal–insulator transition temperature (T_MI) was observed and attributed to the magnetically disordered grain surface and distortion of the MnO₆ octahedra. The electrical resistivity in the metallic region was fitted with theoretical models, and the conduction mechanism could be explained by the grain/domain boundary, electron–electron, and electron–magnon scattering process. The increase in the scattering process was ascribed to the morphology changes. Enhancement of low-field magnetoresistance (LFMR) was observed in nano-grained samples. The obtained results show that the grain size and its distribution, as well as the crystallite formation, strongly affect the physical properties of hole-doped manganites.

1. Introduction

Research on perovskite manganites has been carried out since the 1950s and almost reached a saturated point thereafter. Nevertheless, the discovery of the colossal magnetoresistance (CMR) of this material has once again positioned it as an excellent candidate for memory recording applications and magnetic field sensors. The hole-doped perovskite manganites with the general formula of RE_1−xA_xMnO₃, where RE is a rare earth ion (RE = La, Nd, Pr) and A is a divalent alkaline earth metal ion (B = Ba, Sr, Ca), have been investigated extensively due to the correlation between spin, charge, orbital, and lattice degrees of freedom [1,2,3]. Besides CMR, doped manganites have been discovered with some other intriguing properties, such as ferromagnetic–paramagnetic transition, metal–insulator transition, magnetocaloric effect (MCE), and charge order state [4,5,6,7,8]. A double exchange (DE) mechanism between pairs of Mn³⁺ and Mn⁴⁺ has been proposed to understand the interactions of charge and spin in manganites [9]. However, the CMR phenomenon cannot be explained alone by the DE mechanism. Some other interactions should also be considered, such as the Jahn–Teller (JT) polaron and phase separation. The CMR effects can be grouped into two categories, namely intrinsic and extrinsic MR [10]. The intrinsic MR is only expressive at a high magnetic field, while the latter is significantly greater in low magnetic fields (<0.2 T) [11]. The properties of hole-doped manganites can be controlled through the choice of dopants and their quantity. The doping concentration of divalent alkaline earth cation is normally selected in the range of 0.3 ≤ x ≤ 0.4, as this range lead to a high value of Curie temperature (T_C) and is more appealing for modern devices. Besides the cation ratio, the oxygen stoichiometric is also crucial in deciding the electrical and magnetic properties of manganites [12,13,14].

At present, there are several well-established methods, such as solid-state reaction [15,16,17], co-precipitation [18], sol–gel [17,19,20,21], microemulsion [22], pyrophoric reaction [23,24,25], hydrothermal [26], and combustion [27,28], that have been utilised to synthesise different grain distributions in manganites. The solid-state reaction method is commonly applied to prepare the manganites. The mixing of starting materials is done by a grinding or ball-milling technique. This process is essential prior to the heat treatment for obtaining a homogeneous composition. The solid-state reaction can be done without a sophisticated setup but it is not efficient. It requires multiple repetitions of the milling and heating cycles to obtain powders with the desired phase and chemical compositions. Therefore, another low-cost method (sol–gel) has been employed by researchers to tackle this shortcoming. Sol–gel synthesis is a bottom-up approach that allows the precursors to mix in liquid medium at the molecular level, thereby resulting in lower processing temperature compared to the solid-state reaction method. Furthermore, the sol–gel method also permits better stoichiometry, shorter heating time, and smaller particle size [29,30].

Ezaami et al. studied the critical behaviour of La_0.6Ca_0.2Sr_0.1MnO₃ samples synthesised by sol–gel and solid-state reaction, and the particle variation has been identified as the leading cause of the property changes [31]. Reduction in the particle size was also discovered by Arun et al. when they prepared Nd_0.67Sr_0.33MnO₃ samples by different synthesis routes (sol–gel and solid-state reaction) [17]. They suggested that the particle size reduction had resulted in the increase in effective grain boundaries and surface over volume ratio, as well as the formation of disorders (structural and magnetic) at the grain surfaces. According to the literature, the physical properties, such as magnetic and electrical behaviours, of manganites strongly depend on the particle size. Besides the synthesis route, particle size can also be tuned by varying the sintering temperatures, as demonstrated by Ng et al. [20]. The grain size of Pr_0.67Sr_0.33MnO₃ samples was in the range of 46–245 nm when sintered at different temperatures (600 to 1000 °C). Both grain and crystallite sizes were observed to increase with the sintering temperature due to the congregation effect. Moreover, particle variation could be accomplished by employing different water-to-surfactant ratios in the microemulsion method [22]. Hintze et al. reported that the T_C of La_1−xSr_xMnO₃ was reduced significantly (22%) when particle size decreased to ~25 nm with respect to bulk crystals. Due to the unique physical properties of the hole-doped manganites, nano-sized particles often possess physical properties that are dramatically different from the corresponding bulk properties. Hence, manipulation of the particle size of manganites is expected to give rise to rich functionalities.

The large bandwidth manganite La_0.7Sr_0.3MnO₃ (LSMO) has been extensively studied among the hole-doped perovskite manganites because it exhibits high values of MR (%) and T_C [32,33]. To date, the study of the neodymium-based system is still limited and less attention has been paid to Nd_0.7Sr_0.3MnO₃ (NSMO), though it is excellent in terms of CMR, accompanied by a T_C close to room temperature [34]. Both LSMO and NSMO present a rich phase diagram in the manganite family but there are no studies that report and compare both compounds in detail. Consequently, this paper aims to investigate the structural, microstructural, magnetic, electrical, and magneto-transport properties of LSMO and NSMO. To produce different grain and crystallite sizes, manganite samples in this work were synthesised by sol–gel and solid-state reaction methods.

2. Materials and Methods

The LSMO and NSMO samples were prepared using sol–gel (SG) and solid-state reaction (SS) methods to modify the particle size. The samples will hereafter be denoted as LSSG, LSSS, NSSG, and NSSS. A similar sol–gel preparation procedure has been reported in our previous works [20,35]. The stoichiometric amounts of La (NO₃)₃·6H₂O (Alfa Aesar, Heysham, UK; 99.99%), N₂O₆Sr (Alfa Aesar, Heysham, UK; 99.97%), and Mn (NO₃)₂·4H₂O (Sigma-Aldrich, St. Louis, MO, USA; ≥97%) were used as the precursors to synthesise LSSG. Lanthanum (III) nitrate hexahydrate was replaced with Nd (NO₃)₃·6H₂O (Sigma-Aldrich St. Louis, MO, USA; 99.9%) to prepare NSSG. LSSG and NSSG were sintered at 700 °C in air atmosphere to obtain the nanocrystalline compounds. On the other hand, the starting materials for the solid-state reaction method were La₂O₃ (Alfa Aesar, Heysham, UK; 99.9%), Nd₂O₃ (Sigma-Aldrich, St. Louis, MO, USA; 99.9%), SrCO₃ (Sigma-Aldrich, St. Louis, MO, USA; ≥99.9%), and MnCO₃ (Sigma-Aldrich, St. Louis, MO, USA; ≥99.9%). The stoichiometric ratios of related materials were well mixed by the ball-milling technique with analytical-grade acetone for 24 h before the drying process in the oven at 70 °C (24 h). The dried powder was later calcined at 900 °C for 12 h. Lastly, the powder was pelletised and sintered at 1100 °C for 24 h to produce LSSS and NSSS. Both heat treatment processes were carried out in an air atmosphere.

The structural properties of the samples were characterised by an X-ray diffractometer (XRD, X’Pert Pro PW 3040, Malvern Panalytical, Malvern, UK) and their data were analysed by HighScore Plus software. Field emission scanning electron microscope (FESEM, JEOL 7600 F, JEOL, Tokyo, Japan) and transmission electron microscope (TEM, Talos L120C, Thermo Fisher Scientific, Waltham, MA, USA) were utilised to examine the sample’s morphology and grain size. The magnetic properties were studied using a vibrating sample magnetometer (VSM, Lakeshore 7407, Lake Shore Cryotronics, Westerviller, OH, USA) and AC susceptometer (ACS, CryonBIND T, CryoBIND, Zagred, Croatia). AC susceptibility was measured in a magnetic field of 5 Oe at 219 Hz. The temperature dependence of the electrical resistivity and magneto-transport (variable magnetic field up to 1 T) were assessed by standard four-point probe method using Hall effect measurement system (HMS, Lakeshore 7604, Lake Shore Cryotronics, Westerviller, OH, USA) in the temperature range of 80–300 K.

3. Results and Discussion

LSMO and NSMO samples were characterised by X-ray diffraction (XRD) analysis using CuK_α radiation at room temperature (300 K). Figure 1 shows the XRD patterns along with Rietveld refinement of LSSG, LSSS, NSSG, and NSSS. All samples were fully crystallised in single-phase by referring to the indexed peaks. LSSG and LSSS possessed a hexagonal crystal structure with the space group of R-3c (167) (ICSD reference code: 98-004-9739). Meanwhile, both NSSG and NSSS samples displayed a strong orientation towards the (121) direction with an orthorhombic crystal structure (ICSD reference code: 98-003-7439).

Goldschmidt’s tolerance factor, t_G, is an indicator of the formation of perovskite structures and researchers have been using it to verify the stability and distortion of manganite compounds [7,36,37]. The tolerance factor is defined as:

$$t_{\mathrm{G}=}\frac{r_{\mathrm{A}}+r_{\mathrm{O}}}{\sqrt{2}\left(r_{\mathrm{B}}+r_{\mathrm{O}}\right)}$$

(1)

where r_A, r_B, and r_O are the radii of A, B, and O sites in the perovskite structure (ABO₃). Hole-doped manganites have a stable perovskite structure if their t_G is in the range of 0.89–1.02 [37]. The radii of La³⁺, Nd³⁺, Sr²⁺, Mn³⁺, Mn⁴⁺, and O²⁻ are 1.30, 1.25, 1.40, 0.72, 0.67, and 1.28 Å, respectively. The tolerance factors of LSMO (0.930) and NSMO (0.917) perovskite compounds in this work are within the acceptable range and confirmed the stability of the perovskite structures.

The Rietveld refinement was carried out on the XRD patterns to determine the structural parameters. All diffraction patterns displayed good refinement, fitting with the calculated data by showing the low residual value of the weighted pattern, R_WP, and goodness of fit, χ², as shown in Figure 1. The lattice parameters, bond angles, and lengths of all samples are listed in

Table 1. Tolerance factor and structural parameters obtained from the Rietveld refinement of the XRD patterns for LSSG, LSSS, NSSG, and NSSS.

Sample Code	LSSG	LSSS	NSSG	NSSS
Sample	La0.7Sr0.3MnO3		Nd0.7Sr0.3MnO3
ICSD Reference Code	98-004-9739		98-003-7493
Crystal Structure	Hexagonal		Orthorhombic
Space Group	R-3c (167)		Pnma (62)
Tolerance Factor, tG	0.930		0.917
Lattice Parameter	-
a (Å)	5.486	5.505	5.437	5.450
b (Å)	5.486	5.505	7.670	7.700
c (Å)	13.381	13.366	5.480	5.466
Volume (Å3)	348.704	350.757	228.516	229.398
Bond Angle and Length	-	-	-	-
∠Mn-O1-Mn (°)	166.496	161.681	159.880	165.804
∠Mn-O2-Mn (°)	-	-	158.591	160.057
Mn-O1 (Å)	1.950	1.860	1.967	1.943
Mn-O2 (Å)	-	-	1.951	1.955

. It can be observed that the unit cell volume of LSMO is greater than NSMO. This increase can be linked to the larger ionic radius of La³⁺ (1.30 Å) compared to Nd³⁺ (1.25 Å). Moreover, changes were observed in Mn–O bond length and Mn–O–Mn bond angle when the samples were prepared by different methods. These changes indicate the distortion of the MnO₆ octahedra and could hamper the DE mechanism as well as the electrical behaviour.

From Figure 1, the peak broadening can be observed in the samples synthesised by the sol–gel method, which suggests the larger value of the full width at half maximum (FWHM). The FWHM and average crystallite size of all samples are summarised in

Table 2. FWHM, crystallite size, grain size, T_C, T_MI, and magnetoresistance (MR) at 1 T for LSMO and NSMO samples.

Sample	FWHM (°)	Average Crystallite Size D (nm)	Average Grain Size GS (nm)	Curie Temperature, TC (K)	Metal–Insulator Temperature, TMI (K)	MR at 1 T (%)
						80 K	TMI
LSSG	0.417	22.6	44.4	>300	238	21.0	7.1
LSSS	0.115	127.4	699.9	>300	>300	19.2	−
NSSG	0.434	21.6	26.5	255	150	25.2	17.8
NSSS	0.163	73.3	607.5	270	244	19.5	27.7

. The average crystallite size, D, was calculated by Scherrer’s equation [38]:

$$D=\frac{0.9\mathsf{\lambda }}{\mathsf{\beta }\cos \mathsf{\theta }}$$

(2)

where β = β_sample − β_instrumental, β is the line broadening at half of the maximum intensity (FWHM), λ is the X-ray wavelength (1.5406 Å), and θ is the position of the most intense diffraction peak. NSSG obtained the highest FWHM value and has the smallest crystallite size (21.6 nm). Another sample (LSSG) prepared by the sol–gel method also exhibits much smaller crystallite size (22.6 nm) as compared to the samples synthesised by the solid-state reaction method (LSSS and NSSS). The peak broadening (larger FWHM) is ascribed to the non-uniform lattice strain that comes from the nanocrystalline nature of the sample [39].

Figure 2 depicts the grain size distribution histograms and FESEM micrographs of the internal section for LSMO and NSMO samples. All samples showed a uniform grain size distribution and were composed of grains with an irregular shape. As the solid-state reaction samples were sintered at a higher temperature (1100 °C), LSSS and NSSS possessed a more compact and dense morphology compared to the sol–gel samples (LSSG and NSSG) sintered at lower temperatures. It was found that the grain size of samples prepared by the sol–gel method was in the nanometre range (26–45 nm), and the solid-state reaction method produced grains in submicron size (608–700 nm). These outcomes are in good agreement with the reported works [31,40].

TEM analysis was carried out to further validate the formation of the nanostructured particles in NSSG as it had the smallest grain size (26.46 nm) among all samples. Figure 3 reveals that the grain size of NSSG was in the range of 12–36 nm, with 23.22 nm as the mean grain size. The histogram shown in Figure 3 reflects the local grain distribution and it is comparable to the corresponding FESEM result. The selected area electron diffraction pattern (SAED) shown in Figure 3 confirms the polycrystalline nature of NSSG. The plane orientations such as (101), (121), and (022) were identified to corroborate with the XRD peaks. Furthermore, the lattice fringe observed was applied to the (101) plane, which had a d-spacing of 0.390 nm. A grain normally consists of several crystallites that are arranged in a similar orientation. The grain and crystallite sizes will be increased with the sintering temperature due to the congregation effect [20]. However, single-crystallite grains can be formed when samples are sintered at low temperatures [35] and this was witnessed in our NSSG sample. Furthermore, LSSG was found to have two crystallites in a single grain when referring to the data given in Table 2. As a result, manganite compounds with single (NSSG), double (LSSG), and multiple crystallites (LSSS and NSSS) in a single grain were synthesised and observed in this study.

The magnetic behaviour behind the divalent/monovalent ion-doped perovskite manganites is the existence of Mn³⁺/Mn⁴⁺ pair that leads to magnetic coupling as well as the DE interaction [41]. Vibrating sample magnetometer (VSM) measurement was carried out to characterise the magnetic properties, and the field dependence magnetisation measurement (M-H curve) at room temperature (300 K) for LSSS and NSSS is shown in Figure 4. A soft ferromagnetic hysteresis loop was observed on the LSSS, which indicates that the Curie temperature (T_C) of LSMO was above room temperature. Its T_C was reported in the range of 350–370 K by Souza et al., who studied the particle reduction (bulk to ~20 nm) of La_0.7Sr_0.3MnO₃ [33]. Nevertheless, NSSS behaves as a paramagnetic curve in the M-H graph. The T_C was verified by AC susceptometer measurement in the range of 80–320 K. As the temperature increases, the magnitude of susceptibility demonstrates a rapid drop until it reaches a minimum value (close to 0), and this transition is called ferromagnetic (FM)–paramagnetic (PM) transition. The Tc was identified from the inflection point of dχ’/dT versus temperature plot. There was no drop in AC susceptibility in the LSSG and LSSS measurements (Figure 4), with an χ’ value that was much higher than 0, which further confirms the ferromagnetic behaviour of LSSS observed in VSM analysis. Therefore, the transition of LSMO compounds was clearly above room temperature, which was beyond the range of our ACS measurement. For NSSG and NSSS, the Tc was observed at 255 and 270 K, respectively, as depicted in Figure 4. In Table 2, the results show that T_C decreases as the grain size decreases. This behaviour can be attributed to the loss of long-range ferromagnetic ordering and the presence of magnetically disordered grain boundary layers in sol–gel-synthesised samples [20,40,42]. The existence of this layer can be explained by the core-shell model. It is also known as a magnetically dead layer, where the magnetic interactions are modified by the defects, vacancies, stress, and broken bonds, whereas the core is dominated by the DE interaction and promotes the ferromagnetic interaction like a bulk counterpart [43,44]. The thickness/portion of the dead layer with random spin orientation increases with the decrease in grain size. Hence, the NSSG, which is smaller in grain size, has lower T_C compared to NSSS. Furthermore, the reduction in T_C was also correlated with the changes in the structural parameters of NSMO samples as listed in Table 1. It can be observed that the increase in Mn–O bond length and the decrease in Mn–O–Mn bond angle weakened the DE coupling and hence reduced the T_C [22]. The observed broader dχ’/dT peak minimum in NSSS is the result of the broad grain size distribution, as shown by the corresponding FESEM analysis [36]. In other words, the width of the FM–PM transition relies on the grain size distribution. The same outcome was also reported by Ng et al. when investigating the grain size reduction of Pr_0.67Sr_0.33MnO₃ [20]. In conclusion, we can deduce that the T_C and FM–PM transition are influenced by the grain distribution and its morphological properties.

The electrical transport behaviour of mixed-valence manganites is another fundamental characteristic after magnetism, as these two properties are essential in determining a high-efficiency, workable device. The electrical resistivity is contributed by the grains and inter-grain boundaries as they act as the scattering region for the electron transport [45,46,47,48]. Figure 5 depicts the resistivity as a function of temperature (ρ vs T) for all samples under a magnetic field of 0 and 1 T. The resistivity displayed by NSMO is much higher because it is an intermediate-bandwidth manganite and possesses lower electron mobility compared to LSMO [28]. In addition, there is a noticeable difference in resistivity between the samples produced by sol–gel and solid-state reaction methods. The nanocrystalline samples achieved resistivity in the order of a few magnitudes higher than the sub-micron-sized samples. This significant rise can be attributed to the drastic increase in effective grain boundaries in the samples with nano-sized grains. As reported by Arun et al., the potential barrier developed at the grain boundary layers localised the e_g electrons at Mn atom and restricted their flow in the DE mechanism [40]. Besides the influence of the grain boundaries, the loosely packed grains (high porosity) in nanocrystalline samples also notably reduced the electron mobility, where the electron was insufficient to move through the grains.

Most of the perovskite manganites are paramagnetic insulators at room temperature and display an increase in resistivity with a decrease in temperature [7,20,40,46]. The increase in resistivity will reach a peak maximum known as metal–insulator transition temperature (T_MI). The T_MI was recorded by LSSG, NSSG, and NSSS in this study. The resistivity curves (80–300 K) shown by the LSMO samples agree with the previous study [42] indicating that the nanocrystalline samples (LSSG) exhibit metal–insulator transition below room temperature, which is absent in the bulk compound (LSSS). The strong suppression of the T_MI was observed in NSMO as the particle was reduced to nano-size. This could be due to the enhanced scattering of the charge carriers through the higher density of magnetic disorder in effective grain boundary layers for nano-sized samples. Enhancement of grain boundaries in nano-grained samples also reduces the DE interaction between Mn³⁺ and Mn⁴⁺ and leads to an increase in resistivity [17]. In addition, the increase in Mn–O bond length and the decrease in Mn–O–Mn bond angle in the NSSG sample caused a decrease in bandwidth and electron mobility, thereby resulting in a decline in the DE interaction [49,50]. T_MI was observed to shift towards high temperatures under the applied magnetic field, as depicted in Figure 5. This is because the magnetic field delocalised the charge carriers (e_g electrons at Mn atom) and aligned the magnetic spins in manganite compounds. Hence, the resistivity is decreased when electrons move through DE coupling, resulting in a shift in T_MI.

To understand the nature of different scattering mechanisms responsible for the conduction in the metallic region (T < T_MI), the electrical resistivity results were fitted with the equation below [42,51,52,53]:

$$\mathsf{\rho }\left(T\right)={\mathsf{\rho }}_0+{\mathsf{\rho }}_2{T}^2+{\mathsf{\rho }}_{4.5}{T}^{4.5}$$

(3)

where ${\mathsf{\rho }}_0$, ${\mathsf{\rho }}_2{T}^2,$ and ${\mathsf{\rho }}_{4.5}{T}^{4.5}$ represent the grain/domain boundary effect, electron–electron scattering, and electron–magnon scattering process in the ferromagnetic region, respectively. The experimental data were fitted to the theoretical models (solid lines) as shown in Figure 5. The good match between them is evidenced by the obtained regression coefficient, R² values (close to 100%). The obtained parameters for all the samples are given in

Table 3. Parameters obtained corresponding to the best fit of the experimental data based on Equation (3) from LSMO and NSMO compounds.

Sample	H (T)	ρο (Ω cm)	ρ2 (Ω cm K−2)	ρ4.5 (Ω cm K−4.5)	R2
LSSG	0	2.463	7.12 × 10−5	−4.00 × 10−1	0.999
	1	1.854	7.53× 10−5	−3.89 × 10−1	0.999
LSSS	0	4.79 × 10−3	1.91 × 10−7	−5.47 × 10−1	0.999
	1	3.77 × 10−3	1.95 × 10−7	−5.21 × 10−1	0.999
NSSG	0	1819	0.232	−2.85 × 10−7	0.999
	1	1293	0.192	−2.08 × 10−7	0.999
NSSS	0	8.30 × 10−2	8.18 × 10−6	3.79 × 10−12	0.999
	1	5.33 × 10−2	8.43 × 10−6	1.89 × 10−12	0.999

. The residual resistivity due to the grain/domain boundary (${\mathsf{\rho }}_0$) is greatest among all parameters, which indicates that it plays a dominant role in the metallic region conduction. It was observed that ${\mathsf{\rho }}_0$ decreases under an applied magnetic field and this can be attributed to the increase in domain, size thus reducing the value of ${\mathsf{\rho }}_0$ [20]. On the other hand, the electron–magnon scattering (${\mathsf{\rho }}_{4.5}$) interaction was small in our study as it originated from the induced spin inhomogeneity [51]. As shown by the tolerance factor, LSMO and NSMO compounds are stable perovskite structures and exhibit less electron spin fluctuation. As seen in Table 3, the fitting parameters ${\mathsf{\rho }}_0$ and ${\mathsf{\rho }}_2$ decrease with the increase in particle size and this is associated with the decrease in the grain boundaries [52]. The parameters obtained by NSSG are much higher compared to LSSG, evidencing the increase in Mn–O bond length and the decrease in Mn–O–Mn bond angle in NSSG. Concurrently, this results in an increase in the scattering process and reduces the strength of the DE mechanism.

Figure 6 illustrates the magnetoresistance, MR, as a function of the external applied magnetic field up to 1 T in the variation of temperature for LSSG, LSSS, NSSG, and NSSS. The MR can be calculated using the equation below:

$$\mathrm{MR}(\%)=\frac{{\mathsf{\rho }}_{\mathrm{H}}-{\mathsf{\rho }}_{\mathrm{O}}}{{\mathsf{\rho }}_{\mathrm{O}}}\times 100$$

(4)

where ${\mathsf{\rho }}_{\mathrm{O}}$ and ${\mathsf{\rho }}_{\mathrm{H}}$ are the resistivities without and with an applied magnetic field, respectively. It can be observed that the MR curves show two distinct regions as the magnetic field increases. The plot at the lower magnetic field (<0.2 T), better known as low-field magnetoresistance (LFMR), exhibits a steeper slope and it is more pronounced at low temperatures. This effect is attributed to the spin-polarised tunnelling across the grain boundaries. The disorder spins in manganites will align when the magnetic field begins to apply and it leads to the enhancement of electron hopping, thus resulting in a steep decrease in resistivity in the low-field region [54,55]. The other part of the plot is intrinsic MR and it is the result of the suppression from spin fluctuations, where the spins are aligned parallel to the magnetic field and exhibit high MR values near the T_MI or T_C. The MR (1 T) at 80 K for the samples LSSG, LSSS, NSSG, and NSSS was observed as 21.0%, 19.2%, 25.2%, and 19.5%, respectively. Figure 7 depicts the temperature dependence of MR for manganite samples at 0.2 and 1 T. The MR of LSMO increases monotonically with the decrease in temperature and it is comparable with the results reported earlier [42,56]. Enhancement of LFMR was observed in LSSG and NSSG, as shown in Figure 7a. Moreover, NSSS recorded the highest MR (27.7%) near the T_MI and this is attributed to the increase in disordered magnetic spin fluctuations at the high-temperature range [35]. Therefore, we can conclude that NSSS is dominated by intrinsic MR accompanied by weak extrinsic MR.

It is vital to understand the correlation between the microstructural, magnetic, electrical, and magneto-transport properties of manganite compounds. Therefore, the relationship between χ’, ρ, and MR as a function of temperature for NSMO samples is illustrated in Figure 8. The magnitude of susceptibility and resistivity have been normalised for ease of viewing. NSSS recorded T_C and T_MI values close to room temperature, signifying the strong correlation between magnetic and electrical properties. A significant drop in MR was also observed in the vicinity of T_MI with the increase in the applied magnetic field. Nevertheless, this is not seen on the NSSG sample, where it is mainly attributed to its single crystallite grains and extrinsic MR arising from the spin-polarised tunnelling. The DE interaction is also greatly suppressed and caused a shift in T_MI towards lower temperatures compared to NSSS. The values of T_C and T_MI are usually close to each other, as demonstrated by the bulk sample (NSSS), but these temperatures might behave differently in the nanocrystalline sample (NSSG). This is because the electrical properties greatly depend on the morphological properties (grain size and grain boundary) while the magnetic behaviour is a cumulative result of the intrinsic properties [28,35]. All characterisation results gathered here clearly indicate that LSMO and NSMO are promising candidates for magnetic field sensors and can be tuned easily by varying the particle size to suit different applications.

4. Conclusions

In summary, we have investigated the grain size effect on the structural, microstructural, magnetic, electrical, and magneto-transport properties of LSMO and NSMO. The XRD analysis showed that all samples are fully crystallised in single-phase. According to Rietveld refinement, the unit cell volume of LSMO is greater than NSMO. This is because the ionic radius of La³⁺ (1.30 Å) is larger than Nd³⁺ (1.25 Å). The differences in Mn–O bond length and Mn–O–Mn bond angle indicate the distortion of the MnO₆ octahedra when the samples were prepared by different methods. All samples exhibited a uniform grain size distribution with irregularly shaped grains. NSSG had the smallest grain size (26.46 nm) and appeared to be a sample with single crystallite grains. The T_C of LSMO was observed above room temperature, as evident from the magnetic studies. For NSSG and NSSS, the T_C was observed at 255 and 270 K, respectively. From the results obtained by ACS, it can be deduced that the T_C and FM–PM transition are influenced by the grain size and its distribution. The metal–insulator transition was recorded below 300 K for LSSG but it was absent in LSSS. The strong suppression of the T_MI was observed in NSMO as the particle size declined. The MR of LSMO samples increased monotonically with the decrease in temperature. NSSS recorded the highest MR (27.7%) near the T_MI, which could be attributed to the increase in disordered magnetic spin fluctuations in the high-temperature range. Overall, this work has shown that the physical properties of manganites are strongly influenced by their grain and crystallite sizes.