Magnetic moment arrangments in (a) paramagnetic, (b) ferromagnetic, (c) ferrimagnetic, (d) antiferromagnetic, and (e) superparamagnetic materials.  

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... materials have a small, positive susceptibility. In paramagnetic phase, a weak field-induced magnetization appears due to uncoupled magnetic moments m aligned partially as in Fig.1a. Materials such as O2, NO, Cr and Mn are paramagnetic [16]. ...

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... atomic moments couple to each other and align cooperatively in the absence of an applied magnetic field characterize ferromagnetic, antiferromagnetic, and ferrimagnetic materials (see Fig.1) [14,16]. ...

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... a temperature below TC, the magnetic moments are aligned, while above Curie temperature material losing magnetic ordering and behave as paramagnetic phase. In this temperature range for T > T C , susceptibility depends on temperature in the same way as Curie law described before by Eq. (5) with a slight modification expressed by law that is called Curie-Weiss law (see Fig.1b and Eq. ...

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... magnetization is called remnant magnetization Mr. In ferrimagnetic materials, the magnetic moments are aligned antiparallel to each other as in antiferromagnetic ordering. However, the magnitude of the magnetic moment in one direction is different than the magnetic moment in the opposite direction as shown in Fig.1c. As a result, the net magnetic moment remains in the absence of the applied magnetic field. ...

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... see that the energy value we have got from Eq. (14) for magnetic nanoparticle with radius R = 1 cm is significantly larger than for R = 10 nm suggesting that a larger nanoparticle has to have a multi-domain configuration to lower its single-domain configuration energy. There is preferable flux closure configuration represented in Fig.10a when the anisotropy energy is low. ...

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... will discuss two different types of crystallographic configurations of magnetic nanoparticles in the following section [17]. Fig.10b shows the model of a cubic crystallographic arrangement in magnetic nanoparticle. ...

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... A is the exchange energy constant. For body-centered cubic (Fe) as in Fig.10b, we can calculate the critical radius of the magnetic nanoparticle by using the fact that at this critical size the energy of the multi-domain configuration is equal to the energy of single-domain configuration when multi-domain structure makes a transition to the single-domain configuration. ...

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... the uniaxial crystallographic symmetry, the domain structure is represented by domains in which the magnetizations are directed antiparallel to each other as in Fig.10c. There is only one easy magnetization axis and two different alignments. ...

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... is quantified by material constants α, β, and KS, respectively. Ferromagnetic nanoparticles of MnBi with high anisotropy KV were chosen to see how RC2 changes with β at KS = 0 for α = 0 nm, 10 nm, 100 nm (Fig.18). close to the surface decreases and so Curie temperature. ...

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... addition, ferromagnetic nanoparticles of MnBi with high anisotropy KV were chosen to see how RC2 changes with α at KS = 0 for β = 0 nm, 10 nm, 100 nm (Fig.19). Figure 19. ...

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... addition, ferromagnetic nanoparticles of MnBi with high anisotropy KV were chosen to see how RC2 changes with α at KS = 0 for β = 0 nm, 10 nm, 100 nm (Fig.19). Figure 19. The effect of α on the critical radius RC2 between single-and multi-domain configurations of MnBi nanoparticles when β = 0 nm, 10 nm, 100 nm, and KS = 0. ...

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... Fig.19, the critical radius RC2 for MnBi nanoparticles with a high volume anisotropy, K V = 10 6 J/m 3 , increases with increasing value of α which is related to decrease of the saturation magnetization close to the surface of the nanoparticles. As we previously discussed, the interaction between magnetic moments (spins) close to the surface decreases and so saturation magnetization. ...

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... ferromagnetic nanoparticles of MnBi with high anisotropy KV = 10 6 J/m 3 were chosen to see how RC2 changes with KS at α = 0 and β = 0 ( Fig.20), and at β = 10 nm, α = 0 nm, 10 nm, 100 nm (Fig.21), and at α = 10 nm, β = 0 nm, 10 nm, 100 nm (Fig.21). R C2 vs. K S of MnBi nanoparticles for α = 10 nm β=0 β=10 nm β=100 nm chosen from a plot represented in Fig.18 results in the value of β = 213 nm. ...

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... experimental result of the critical size RC1 between single-domain structure and superparamagnetic phase can be predicted to be smaller than the theoretical size RC10 = 2.93 nm due to the surface effect. From Fig.31 tell that the size of the superparamagnetic limit of iron experimentally is equal to RC1 = 4.75 nm, which is less than theoretical value of 8.1 nm which can be due to surface anisotropy KS (see Fig. 32). ...