Reliable evaluation of magnetic properties of nanoparticle systems

Abstract

We obtain magnetic properties of magnesioferrite nanoparticles grew in a magnesiowstite crystalline matrix by analyzing the temperature dependence of the coercive field and the magnetization behavior. We introduce a modelling scheme to evaluate those properties in which the input variables are estimated from experimental data. The core of the method relies in sampling for nearby values in order to reach the optimal one that yields the smallest difference between calculated and experimental data. This procedure is efficient and our results match with the ones found in the literature. Thus, our method paves the way for a robust characterization of superparamagnetic nanoparticle materials.

Equilibrium properties of assembly of interacting superparamagnetic nanoparticles

“…It is important that in a superparamagnetic assembly the relaxation to a thermodynamically equilibrium occurs for a finite observation time. The fundamental physical quantity of a superparamagnetic assembly is the equilibrium magnetization, M eq = M eq (H 0 ,T), which can be easily measured experimentally [23][24][25][26][27][28][29]. Theoretically, this value can be determined on the basis of the Gibbs principle [14][15][16][17][18][19][20][21], as the derivative of the assembly's free energy with respect to the applied magnetic field.…”

“…Unfortunately, in a number of recent experimental works (see, for example, Refs. [26][27][28][29], the experimental data for the equilibrium assembly magnetization are described by a weighted sum of Langevin functions. In this way the particle size distribution is taken into account, whereas the influence of the magnetic anisotropy energy is completely ignored.…”

“…The Langevin law for equilibrium assembly magnetization is given in standard textbooks [20,21]. It is often used in the analysis of the experimental data [22][23][24][25][26][27][28][29]. However, it is important to recall that in the simplest Langevin approximation [19] both the magnetic anisotropy energy and the energy of the magneto-dipole interaction of the nanoparticles are neglected.…”

“…It is worth noting that in contrast to the theoretical problem mentioned, the measurement of the equilibrium magnetization and magnetic susceptibility of interacting assembly of superparamagnetic nanoparticles is a routine experimental task that can be performed using standard equipment [22][23][24][25][26][27][28][29]. In an attempt to improve theoretical understanding in this work the equilibrium magnetization of an assembly of interacting superparamagnetic nanoparticles uniformly distributed in a rigid nonmagnetic matrix is calculated by solving the stochastic Landau -Lifshitz (LL) equation [56][57][58][59][60].…”

“…In a classical paper 19 , Langevin used Gibbs principle 20,21 to calculate the equilibrium magnetization of a non-interacting assembly of freely rotating magnetic dipoles. The Langevin law for equilibrium assembly magnetization is often used in the analysis of the experimental data [22][23][24][25][26][27][28][29] . However, it is important to recall that in the simplest Langevin approximation 19 , both the magnetic anisotropy energy and the energy of the magneto-dipole interaction of NPs are neglected.…”