**7. Dependence of the g-factor with the crystallite size**

### **7.1 Detection of magnetic states transitions by g-factor**

The Landé g-factor is a dimensionless number calculated from the resonance field based on equation g = hν/μBHres. The curve of g-factor variation as a function of crystallite size can be subdivided into three parts (**Figure 8**). The first is with g values around 2.05, corresponding to the samples with crystallite sizes less than 24.5 nm. This value is slightly higher than that of the typical value of perovskite manganite materials in a paramagnetic state (g = 1.996) [46]. A strong increase in g-factor was observed in the intermediate region corresponding to the samples with crystallite sizes of 24.5 and 32 nm. In the last region, corresponding to the samples with larger crystallite sizes above 32 nm, the g-factor value continues to increase with a lower slope.

The observed slope changes coincide with those reported variations of the linewidth and other ESR spectrum parameters (line shape, LFMA, etc.). So, these changes reflect transitions of magnetic states, from superparamagnetism to ferromagnetism and from single-domain to multi-domain.

To confirm this hypothesis, magnetization measurements were recorded at 300 K and 360 K, collected in a vibrating sample magnetometer (VSM), for the three samples (a) LSr700-2 h (16 nm), (b) LSr700- 24 h (28 nm), and (c) LSr900- 15 h (55 nm), belonging to different regions (**Figure 9**).

At room temperature (300 K), the nonlinearity in magnetization curves confirms the ferromagnetic behavior of three samples, while the linearity of the magnetization curve recorded at 360 K reflects a typical paramagnetic character [32]. The magnetization for samples (a) reaches more than 90% of its experimental saturation (Ms) value just above 0.5 T. Moreover, the very small residual magnetization (Mr) considered to be negligible reflects the superparamagnetic character of this sample [63, 65]. The existence of a thick dead magnetic layer in the superparamagnetic state explains the decrease of the saturation magnetization [13, 17].

A magnetization/demagnetization curve of the samples (b, c) with hysteresis loops characterizes the materials in a ferromagnetic state. For sample (b) there is no complete saturation even in the vicinity of 5 T. This means that the magnetic moments are blocked and their alignment toward the applied field requires larger values; this characterizes single-domain ferromagnetic particles [13, 17] Moreover, magnetic remanence (Mr) practically equals 0.5 Ms.; this value is consistent with the model established by Stoner and Wohlfarth for single-domain ferromagnetic particles [66, 67].

Significant reduction in Ms. for the sample (a) compared to samples (b, c) is coherent with both ESR measurements (low factor g) and core-shell model [68]. The core-shell model assumes the formation of a magnetically dead layer of thickness t, which increases with size reduction and can be estimated using the following formula [48]:

**31**

**Figure 9.**

*and for sample of 16 nm recorded at 300 K and 360K.*

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

\_ Ms (nano) Ms (bulk) ) 1/3

(1)

d 2 (1 −

As a necessary condition for superparamagnetism, nanoparticles must be formed by small magnetic volumes without exchange interaction [68]. The previous formula shows a significant increase in the dead layer for sizes below 24.5 nm, which has favored superparamagnetism. ESR spectra for these compounds have similarities: narrow linewidth, symmetrical form, g-factor less than 2.08, and

*Magnetization/demagnetization curves of the samples with the crystallite sizes 28 and 55 nm recorded at 300 K.* 

where t is dead layer thickness and d is crystallite size.

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

*t* = \_

absence of LFMA.

**Figure 8.**

*The change of g-factor with crystallite size.*

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

\_Assum\_ and ESR Study of Transition\_ from supernovae to Superparamagnetism.\
1: http://dɛ.do1.org/a1.green/2/intechoopen.\
9999.

$$t = \frac{d}{2} \left(1 - \frac{\mathbf{M}\_{s\\_(nano)}}{\mathbf{M}\_{s\\_(bulk)}}\right)^{1/3} \tag{1}$$

where t is dead layer thickness and d is crystallite size.

As a necessary condition for superparamagnetism, nanoparticles must be formed by small magnetic volumes without exchange interaction [68]. The previous formula shows a significant increase in the dead layer for sizes below 24.5 nm, which has favored superparamagnetism. ESR spectra for these compounds have similarities: narrow linewidth, symmetrical form, g-factor less than 2.08, and absence of LFMA.

**Figure 8.** *The change of g-factor with crystallite size.*

*Smart Nanosystems for Biomedicine, Optoelectronics and Catalysis*

field is controlled principally by crystallite size.

**7. Dependence of the g-factor with the crystallite size**

**7.1 Detection of magnetic states transitions by g-factor**

magnetism and from single-domain to multi-domain.

15 h (55 nm), belonging to different regions (**Figure 9**).

However, the resonance frequency remains constant, equal to Hres = 2920 G for the three samples. This can be explained in terms of the same internal field, which is directly related to the crystallite size without exchange interaction between adjacent crystallite. Autocombustion synthesis gives voluminous powders of high specific surfaces, with a structure of "sponge" form [62, 63]. These structures weaken the exchange interactions between the crystallites. In addition to this, the formation of a magnetically dead layer, which increases in thickness with decreasing crystallite size, prevents crystallite-crystallite interactions [34, 62, 64]. Thus, the resonance

The Landé g-factor is a dimensionless number calculated from the resonance field

based on equation g = hν/μBHres. The curve of g-factor variation as a function of crystallite size can be subdivided into three parts (**Figure 8**). The first is with g values around 2.05, corresponding to the samples with crystallite sizes less than 24.5 nm. This value is slightly higher than that of the typical value of perovskite manganite materials in a paramagnetic state (g = 1.996) [46]. A strong increase in g-factor was observed in the intermediate region corresponding to the samples with crystallite sizes of 24.5 and 32 nm. In the last region, corresponding to the samples with larger crystallite sizes

The observed slope changes coincide with those reported variations of the linewidth and other ESR spectrum parameters (line shape, LFMA, etc.). So, these changes reflect transitions of magnetic states, from superparamagnetism to ferro-

To confirm this hypothesis, magnetization measurements were recorded at 300 K and 360 K, collected in a vibrating sample magnetometer (VSM), for the three samples (a) LSr700-2 h (16 nm), (b) LSr700- 24 h (28 nm), and (c) LSr900-

At room temperature (300 K), the nonlinearity in magnetization curves confirms the ferromagnetic behavior of three samples, while the linearity of the magnetization curve recorded at 360 K reflects a typical paramagnetic character [32]. The magnetization for samples (a) reaches more than 90% of its experimental saturation (Ms) value just above 0.5 T. Moreover, the very small residual magnetization (Mr) considered to be negligible reflects the superparamagnetic character of this sample [63, 65]. The existence of a thick dead magnetic layer in the superparamagnetic state explains the decrease of the saturation magnetization [13, 17]. A magnetization/demagnetization curve of the samples (b, c) with hysteresis loops characterizes the materials in a ferromagnetic state. For sample (b) there is no complete saturation even in the vicinity of 5 T. This means that the magnetic moments are blocked and their alignment toward the applied field requires larger values; this characterizes single-domain ferromagnetic particles [13, 17] Moreover, magnetic remanence (Mr) practically equals 0.5 Ms.; this value is consistent with the model established by Stoner and Wohlfarth for single-domain ferromagnetic

Significant reduction in Ms. for the sample (a) compared to samples (b, c) is coherent with both ESR measurements (low factor g) and core-shell model [68]. The core-shell model assumes the formation of a magnetically dead layer of thickness t, which increases with size reduction and can be estimated using the following

above 32 nm, the g-factor value continues to increase with a lower slope.

**30**

particles [66, 67].

formula [48]:

#### **Figure 9.**

*Magnetization/demagnetization curves of the samples with the crystallite sizes 28 and 55 nm recorded at 300 K. and for sample of 16 nm recorded at 300 K and 360K.*

The increase in the magnetic volume due to a sharp decrease in the thickness of the dead layer between 24.5 and 32 nm breaks the superparamagnetism. The system evolves toward the single-domain state, which results in a significant increase of the g-factor and ∆Hpp. Beyond 32 nm, nanoparticles change into a multi-domain state. This passage is confirmed by the asymmetrical EMR signal and the appearance of the LFMA.

These results are similar to those of the literature for manganite with the perovskite structure of similar composition [18, 35, 58].

#### **7.2 Superparamagnetic crystallite with multicore**

In **Figure 8**, we notice that in the powders with crystallite size less than 24.5 nm (superparamagnetic region), the value of the factor g is practically constant. This suggests that the magnetic core size is invariant regardless of crystallite size.

To rely on the core-shell model with a single magnetic core, in order that the magnetic core keeps the same volume, the thickness of the dead layer must increase with increasing crystallite size. This hypothesis is in contradiction with the literature which reveals that the thickness of the shell decreases [18, 34, 48]. To explain these experimental data, we resorted to the phenomena of magnetic phase separation, which is a usual phenomenon observed in manganites [69, 70]. The competition between several interactions in perovskite manganites means that there are only small energy differences between the different possible phases of the system. As a result, the perovskite manganite oxide is magnetically inhomogeneous, consisting of different spatial regions with different magnetic orders.

Phase separation leads to the formation of a nanometer-sized ferromagnetic droplet cloud ranging from tens of nanometers to several hundred nanometers [71, 72]. In particular, La1−xSrxMnO3 manganites tend to form mixed phases near the paramagnetic-ferromagnetic phase transition [65, 73]. In this case, transition from the single-domain to the superparamagnetic state is not due to increasing the thickness of the dead layer but to the subdivision of the magnetic volume in small volumes. Thus, the superparamagnetic particles are formed by a paramagnetic volume containing several distinct magnetic cores that we have called superparagmanetic multicore crystallite.

The multicore superparamagnetic state has a comparable magnetic structure with multicore magnetic particles (MCP)that have been shown to be promising for a wide range of biomedical applications, in particular in magnetic hyperthermia treatment and magnetic resonance imaging [74, 75]. So, we can conclude that control of crystallite size in the synthesis of manganites allows a controlled change of magnetism in these compounds.
