**5. Electronic magnetic resonance**

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multi-domain state to a magnetic single-domain state and then to the superparamagnetic state. The changes observed in the EMR and LFMA signal appear to be

*Variation depending on the crystallite size of: (a) resonance fields in the spectral zone of 3100–3700 G, (b) low* 

A zoom on the low-field spectral region (**Figure 5(b)**) shows that the intensity of LFMA gradually decreases with decreasing crystallite size and disappears from 27 nm. This microwave absorption, around zero fields, is a nonresonant absorption.

indicative of these magnetic state transitions.

*field microwave absorption and (c) linewidth ΔHpp [20].*

**4. Low-field microwave absorption**

**26**

**Figure 5.**

The peak-to-peak EMR linewidth ΔHpp is an important parameter in measuring magnetic property.

ΔHpp may be due to various factors, namely, magnetic anisotropy field (ΔHK), sample porosity (ΔHpor), demagnetization field (ΔHD), and eddy currents (ΔHeddy) [51]. In the polycrystalline particles, the crystallites are randomly oriented; in that case, the contribution of the magnetocrystalline anisotropy field is dominant and we can have the following approximation Hpp=HK [52].

Linewidth ΔHpp plotted as a function of the crystallite sizes shown in **Figure 5(c)** can be subdivided into three regions. The first part, corresponding to samples with crystallite sizes less than 24.5 nm, ΔHpp has a low value around 1000 G, and between 27 and 32 nm and ΔHpp greatly increases and goes through a maximum at 28 nm. Finally, for sizes greater than 32 nm, ΔHpp increases with a lower slope. This curve calls back the variation of coercivity (Hc) with the particle size, which is maximal for particles in a single-domain state [18].

The magnetocrystalline anisotropy energy in the superparamagnetic state is small and comparable to thermal energy. By random fluctuations of the magnetization due to thermal excitation, the directions of easy magnetization vanish. This is reflected in the low value of ΔHpp [53]. A narrow resonance line is considered as the fingerprint of superparamagnetism at high temperatures, where the energy barrier is dominated by thermal oscillations [54, 55]. Thus, particles smaller than 24.5 nm are in a superparamagnetic state.

Important resonance broadening occurring at superparamagnetic zone boundary indicate that the samples with crystallites size 27, 28, and 32 nm are singledomain ferromagnetic. In the particle formed by a single magnetic domain, the magnetocrystalline anisotropy energy is proportional to the magnetic volume (EB = K V, where K and V are the anisotropy constant and volume of the particle) [56]. In the single-domain region, energy barrier separating two directions of easy magnetization is high. The magnetization requests more energy to get itself aligned along the applied field. The angular dependence of the ΔHpp results in significant increases in linewidth [42].

In the multi-domain state, application in the measurement of weak magnetic field can easily move the magnetic domain walls. The magnetization vectors approach the direction of the applied field, thus leading to reduce ΔHpp. Thus, the decrease of ΔHpp in addition to the appearance of the absorption at low field confirms multi-domain state of samples higher size 32 nm.

These results are comparable to the overall results obtained with samples of analogous compositions [35, 57]. In particular, Sujoy R. et al. reported an exponential increase of the magnetic core between 8 and 22 nm [18], favoring the transition from superparamagnetic state to the single-domain ferromagnetic state.

In addition to the intrinsic causes of line broadening due to the change of magnetic state, extrinsic causes related to the size and shape of the magnetic particles are to be considered. Nanocrystalline powders are formed by several crystallites bonded together to form a wide variety of sizes and shapes that have different magnetic properties [58, 59]. "Crystallite size" is not synonymous with "particle size"; X-ray diffraction is sensitive to the size of crystallite inside the particles.

To study the effect of particle sizes on the line shape, ESR measurements have been performed for two populations with diverse particle size selected by magnetic separation from the sample LSr900- 15 h (55 nm).
