The XRD pattern of La_0.67Ca_0.33MnO₃ samples, sintered at different temperatures are shown in Fig. 1. The XRD data have been analyzed with the Rietveld refinement technique and the materials were found to crystallize in Pbnm space group. It is also clear from the analysis that the samples are single phase with no detectable impurity. The Mn-O-Mn bond angle and Mn-O bond length obtained from the Rietveld refinement are presented in Table 1. The average particle sizes of the materials were estimated using peak broadening 10 through the Scherrer formula, <S> = Kλ/βcosθ, where <S> average crysttallite size in Ǻ, K is a constant (shape factor; 0.89), λ is the Cu Kα wavelength and β is the corrected full-width-half-maxima of XRD peaks of the sample. SiO₂ was used to correct the intrinsic width associated with the equipment. The calculated average crystallite size values are given in Table 1. It is clear from the table that the crystallite sizes are found to increase with increasing sintering temperature.

AC susceptibility measurements of all the samples have been carried out as a function of temperature (Fig. 2) and based on these results, the ferro to paramagnetic transition temperatures (T_C) were obtained and are given in Table 2. It is clear from the table that T_C values decrease with increasing sintering temperature thereby indicating that T_C is decreasing with increasing particle size. The observed behavior may be explained following the work by Dutta et al. 14; According to these authors, the magnetic and transport properties of the perovskite manganites are strongly coupled and are very sensitive to Mn-O-Mn bond angle and Mn-O bond length. It has been found that a decrease in magnetization and an increase in resistivity occur as we decrease the particle size, due to broken Mn-O-Mn bonds at the surface of smaller particles that hamper exchange interaction and degrade connectivity for electron conduction, but in this case it seems that the spin interaction increases and the connectivity improves as we decrease the particle size. The decrease in particle size results increase in Mn-O-Mn bond angle and decrease in Mn-O bond length. Therefore magnetization increases and T_C enhances with decreasing particle size. It is also clearly evident from Table 1 that the bond angles are found to be almost constant, while the bond lengths decrease continuously with decreasing particle size of the material. In view of these arguments and explanations, it is reasonable to understand that there is a continuous decrease in the values of T_C with a continuous increasing sintering temperature.

The metal insulator transition temperature (T_P) and peak resistivity (ρ_Peak) obtained from electrical resistivity measurements are given in Table 2. It is interesting to note that T_P values are found to increase with increasing sintering temperature from 145 to 195 K, while ρ_Peak values are decreasing. In view of these observations, one can understand that there is a tremendous influence of crystallite size on various properties mentioned, and that the observed behavior may be explained on the basis of a qualitative model. According to this model, it has been assumed that in the case of sol-gel prepared samples of the present investigation, when the grain size of the material is decreased, a non-magnetic surface layer having nanocrystalline size would be created around the grain. This may increase the residual resistivity of the material, which in turn decreases the density of Ferromagnetic Metallic (FMM) particles. Therefore, lowering of T_P and enhancement of electrical resistivity at a given temperature (ρ_T) are expected. Finally, the shifting of T_P towards the low temperature region could be due to the loss of long-range ferromagnetic order in the sample 15.

It can also be seen that a difference between T_C and T_P is observed and it is has been calculated ΔT (T_C ~ T_P) for each material and given in Table 2. The ΔT values are found to decrease from a large value of 108 to 24 K as the sintering temperature increases continuously and in fact, a similar difference between T_C and T_P has been reported earlier 14. The observed difference between the two transition temperatures may be explained as outlined here. It is well known that two contributions are responsible for the transport properties among CMR materials. One of them is intrinsic and might have originated from the double exchange (DE) interaction between the neighboring Mn ions, while the other one is extrinsic and is due to spin-polarized tunneling between ferromagnetic grains through an insulating grain boundary (GB) barrier. According to DE model, the metal-insulator transition always occurs in the vicinity of T_C. However, in the case of granular samples with a large number of GBs, the influence of interfaces and boundaries should be taken into account. Further, as the GB is similar to the amorphous state, the magnetic configuration on the grain surface is more disordered than in the core. In such a situation, the occurrence of anti-ferromagnetic insulating regions on the grain boundary may not modify the magnetic transition temperature, T_C. However, the phenomenon may influence the metal-insulator (electrical) transition, T_P thereby shifting it to lower temperatures 16.

Magnetoresistance measurements were carried out in the presence of different magnetic fields viz; 1, 3, 5 and 7 T. A typical plot of variation of electrical resistivity with temperature in the case of LC-9 at different field runs is shown in Fig 3. It can be seen from the figure that the resistivity is found to decrease with increasing magnetic field and that T_P shifts towards higher temperatures and that as a matter of fact, T_P values are found to change from 160–185 K when the field changes from 0–7 T. This may be due to the fact that the applied magnetic field induces delocalization of charge carriers, which in turn might suppress the resistivity and also cause local ordering of the magnetic spins. Due to this ordering, the ferromagnetic metallic (FMM) state may suppress the paramagnetic insulating (PMI) regime. As a result, the conduction electrons (e¹_g) are completely polarized inside the magnetic domains and are easily transferred between the pairs of Mn³⁺ (t³_2g e¹_g : S = 2) and Mn⁴⁺(t³_2g e^o_g : S = 3/2) via oxygen and hence the peak temperature (T_P) shifts to high temperature side with application of magnetic field 17. In fact a similar explanation was given earlier 18.

Further, the percentage of MR of all the materials (except LC-11) of the present investigation has been calculated in the vicinity of T_C by using the well-known relation,

MR% = {[ρ₍₀₎ - ρ_(H)]/ρ₍₀₎} × 100

The calculated MR values are found to remain constant (Table 2) with increasing sintering temperature. The variation percentage of MR of LC-9 with temperature is also shown in the inset of the Fig. 3 and one may note from the figure that the percentage of MR values is found to be very high in the vicinity of T_C.

The electrical resistivity data (T<T_P) of samples of the present investigation are found to fit well with the equation

ρ = ρ₀ + ρ_2.5 T^2.5

Here the term ρ₀ represents the resistivity due to grain/domain boundary effects, while the second term, ρ_2.5T^2.5 represents the resistivity due to electron-magnon scattering process in ferromagnetic phase 17.

The conduction mechanism of manganites at high temperatures (T > T_P) is explained by adiabatic small polaron hopping mechanism and the equation is given by

ρ = ρ_αT exp (E_P/k_BT)

where ρ_α is residual resistivity, while E_P is the activation energy, ρ_α = 2k_B/3ne²a²v, here k_B is Boltzmann's constant, e is the electronic charge, n is the number of charge carriers, a is site – to – site hopping distance and v is the longitudinal optical phonon frequency. The activation energy values, calculated from the best-fit parameters are given in Table 3.

Thermoelectric power (TEP) measurements were carried out over a temperature range 77–300 K and Seebeck coefficient (S) values have been computed at different temperatures. The variation of S with temperature for all the samples is shown in Fig 4 and it can be seen that the magnitude of S decreases with increasing sintering temperature. It is also clear from the figure that in the case of LC-8, LC-9 and LC-10 samples the sign of S is positive through out the temperature range of investigation, while in the case of LC-11, thermopower changes from a positive to a negative value. It means that the samples with lower particle size (20, 30 and 35 nm) exhibit a positive S value, while those with higher crystallite size (45 nm) exhibit both negative and positive values. The observed behaviour may be explained as follows. The positive sign exhibited by LC-8, LC-9 and LC-10 materials might be attributed to holes which are excited from the valence band (VB) into the impurity band, while in the case of LC-11 sample, the change in sign may be attributed to the orbital degeneracy of the e_g band. According to this model, the orbital degree of freedom of the e_g band may play an important role. It is well known that e_g band consists of degenerate 3d orbital (i.e., d_3z²_-r² and d_x²_-y²) and may split into upper and lower bands by an order of J_H 19. If the lower (spin-up) band, splits further into two bands in the FM state, then the lowest band is filled, the dopants may introduce holes thereby showing positive S values while the lowest band is empty; it shows negative (electron-like) values. Therefore, one may conclude that there may be a possibility of changing sign from positive to negative with varying particle size 20.

Close observation of S versus T plots shows that as the temperature decreases from 300 to 77 K, the values of S increases thereby attaining a maximum value in the vicinity of magnetic transition temperature (T_C) designated as T_S. The obtained T_S values from S vs. T plots are included in the Table 2. Further, T_S values and the magnitude of S at T_S increase with increasing particle size. In the ferromagnetic metallic part (T < T_P), a broad peak is found to develop and increase with increased particle size. In fact, similar behaviour was reported earlier in Pr-based manganites 2122. The observed broad peak may be explained on the basis of the spin-wave theory. According to this theory, in ferromagnets and antiferromagnets, electrons are scattered by spin waves, giving rise to the electron-magnon scattering effect. In a manner similar to the scattering of phonons resulting in phonon drag effects, the electron-magnon interaction also produces a magnon drag effect. As the magnon drag effect is approximately proportional to the magnon specific heat, one may expect the variation of S with temperature as T^3/2 for ferromagnetic materials 22. In view of these arguments, one may conclude that the observed broad peaks may be attributed to the magnon drag effect which increases with increase in particle size.