Superparamagnetism of Ferromagnetic Nanoparticles

3 Theoretical Description of Primary Nanoferroics. Comparison of the Theory... 

The aforementioned features are illustrated in Figs. 2.35, 2.36, 2.37, 2.38, 2.39, 2.40, and 2.41. The description of the abovementioned properties should compulsory account for distribution of particle sizes. For that purpose the distribution function P(v) has to be introduced. Here v = V7V, Vm = 7t J /6 is the maximal volume of a particle and dm is its maximal diameter. 

Ai T Tiy (recollect that is blocking temperature) the influence of anisotropy energy on magnetization M(H,T) can be neglected. In this case the analysis can be carried out on the base of Langevin function L(x) = l/tanh(x) — l/x so that the magnetization can be written as 

The Hamiltonian // of a nanoparticle with magnetic moment jjLp in a magnetic field H with respect to anisotropy energy with uniaxial constant Ea can be written as 

Here /o(j) = f dt Qxp(y cost) is modified Bessel function of zero order ji 0 

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