*3.3. Morphology*

To understand the morphology of the samples, we performed FESEM with EDX and obtained the results, as shown in Figure 5. The images in Figure 5 reveal that the surface of the sample is non-homogeneous and the grains are agglomerated. The particles are also observed as non-spherical in shape. According to the image, the grain size of all samples are in the range of ~3.7 μm to ~5.6 μm, respectively. The grain sizes observed by FESEM are larger than those calculated by the Debye–Scherer formula. This can be explained by the fact that each particle observed by FESEM is formed by several crystallized grains. The results of EDX plot matches with a standard peak position of Nd, Bi, Mn and O from the previous study [19]. The EDX spectrum confirms the homogeneity of the samples.

**Figure 5.** Field emission scanning electron microscopy (FESEM) micrograph and EDX spectra of Nd1−<sup>x</sup>BixMnO3 (**a**) x = 0 (**b**) x = 0.25 and (**c**) x = 0.5.

## *3.4. AC Susceptibility Measurement*

Figure 6 shows the temperature dependence of the AC susceptibility of the Nd1−<sup>x</sup>BixMnO3 system on the real part χ' with the inset dχ'/dT versus the temperature range of 30–300 K. For x = 0 and x = 0.25, a definite and sharp peak was observed at 70 K and 72 K, respectively, associated to the ordering temperature of Mn spins [22]. The observed cusp depicts the PM to AFM transition, which is consistent with the results from previous studies [5,8,23]. For x = 0.50, two sharp peaks were observed, which were at 42 K and 57 K, respectively. The existence of two peaks indicates the magnetic inhomogeneity that may be induced by Bi substitution [12]. The TC was determined using the minimum, while TN was determined using the maximum point of differentiation, as shown in the inset of the graph in Figure 6. In the figure, all the three compounds exhibit a strong AFM with a competing weak FM, where TN and TC decreased with Bi substitution. The decreasing value of TC shows the weakening of the FM behavior due to the Bi substitution. Temperature dependence of inverse susceptibility, 1/χ', for all samples is plotted in Figure 7. The experimental data were fitted by using Curie–Weiss (C–W) equation, χ = C/(T − <sup>θ</sup>), where C is Curie constant and θ is Curie–Weiss temperature. The red line is the best fit for C–W law in the paramagnetic region. The inverse susceptibility curve follows the C–W law at the higher temperature and starts to deviate from the linear fitting of C–W law at the lower temperature above TC, which shows the existence of Griffiths phase (GP) in the samples [24,25]. The deviation shows that the C–W law is inapplicable in the temperature range between TC and Griffiths temperature, TG (TC < T < TG). This anomaly indicates the possible existence of ferromagnetic cluster within the paramagnetic region in the system which would enhance the total magnetic susceptibility of the samples [24–27]. The temperature ranges of Griffiths phase normalized with TC were evaluated using the equation GP = (TG − TC)/TC and were found to increase as the substitution of Bi increased. The increasing values were due to an increase of magnetic inhomogeneity near TC. Therefore, the substitution of Bi in Nd1−<sup>x</sup>BixMnO3 system could enhance the appearance of Griffiths phase [24]. The values of TC, TN, TG and GP are summarized in Table 3.

**Figure 6.** AC magnetic susceptibility against temperature curves for Nd1−<sup>x</sup>BixMnO3.

**Table 3.** Parameters obtained from AC magnetic susceptibility studies of Nd1−<sup>x</sup>BixMnO3 samples.


**Figure 7.** Temperature dependence of inverse susceptibility spectra of Nd1−<sup>x</sup>BixMnO3 (**a**) x = 0, (**b**) x = 0.25 and (**c**) x = 0.5.
