**4. Low-field microwave absorption**

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.

**27**

*Synthesis and ESR Study of Transition from Ferromagnetism to Superparamagnetism…*

In ferromagnetic materials, magnetic domains are in a fragile state of equilibrium, and the Bloch wall which is a narrow transition region at the boundary between magnetic domains moves with very low applied fields. In fact, LFMA is associated with dynamics of the magnetic domains in material [49]. The existence of this absorption at room temperature is an indication of the ferromagnetic state of the material used to detect magnetic order. For bulk samples, the LFMA signal is used to determine the Curie temperature of ferromagnetic compounds [23, 50]. Above 28 nm the existence of LFMA shows that these compounds are in a magnetic multi-domain state and a flat response for compounds with smaller size shows that they are in a single-domain state. According to Montiel et al., the absence of LFMA signal in the ferromagnetic compounds is a good indication of superparamagnetic state in the samples [21, 22]. By size reduction, the nanocrystalline passes from a particle with several magnetic domains to a monodomain particle; the latter is either in a single-domain state or in a superparamagnetic state. Low-field absorp-

Particles belonging to the single-domain state are characterized by maximum magnetocrystalline anisotropy energy; consequently the direction of magnetization is "frozen.' This characteristic has an effect on the linewidth of resonant absorption; a comparative analysis can reveal the critical size of changes in magnetic states.

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

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

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

Important resonance broadening occurring at superparamagnetic zone bound-

ary 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

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].

*DOI: http://dx.doi.org/10.5772/intechopen.89951*

tion cannot determine the intermediate state.

**5. Electronic magnetic resonance**

24.5 nm are in a superparamagnetic state.

increases in linewidth [42].

magnetic property.

*Synthesis and ESR Study of Transition from Ferromagnetism to Superparamagnetism… DOI: http://dx.doi.org/10.5772/intechopen.89951*

In ferromagnetic materials, magnetic domains are in a fragile state of equilibrium, and the Bloch wall which is a narrow transition region at the boundary between magnetic domains moves with very low applied fields. In fact, LFMA is associated with dynamics of the magnetic domains in material [49]. The existence of this absorption at room temperature is an indication of the ferromagnetic state of the material used to detect magnetic order. For bulk samples, the LFMA signal is used to determine the Curie temperature of ferromagnetic compounds [23, 50]. Above 28 nm the existence of LFMA shows that these compounds are in a magnetic multi-domain state and a flat response for compounds with smaller size shows that they are in a single-domain state. According to Montiel et al., the absence of LFMA signal in the ferromagnetic compounds is a good indication of superparamagnetic state in the samples [21, 22]. By size reduction, the nanocrystalline passes from a particle with several magnetic domains to a monodomain particle; the latter is either in a single-domain state or in a superparamagnetic state. Low-field absorption cannot determine the intermediate state.

Particles belonging to the single-domain state are characterized by maximum magnetocrystalline anisotropy energy; consequently the direction of magnetization is "frozen.' This characteristic has an effect on the linewidth of resonant absorption; a comparative analysis can reveal the critical size of changes in magnetic states.
