Parameterization of magnetic nanoparticles mathematical model using evolutionary algorithms

In this paper, the evolutionary algorithms approach is applied to the parameterization of a mathematical model describing the Mossbauer spectra of nanogranular (or nanoparticle) magnetic systems. These systems exhibit physical properties very different from bulk specimens being of great interest for material science and its use as biosensors, magneto sensors, data storage, and magnetic fluids. The purpose of this work is to compare the performance between the Differential Evolution and the Evolutionary Strategies algorithms to optimize the model parameters which best fit the experimental Mossbauer spectra of nanoscale magnetic particles. Spectra of two samples (α‐iron foil and NiFe 2 O 4 nanoparticles) were recorded, at room temperature, by a conventional Mossbauer spectrometer using a scintillation detector in transmission geometry with a  57 Co/Rh source. Fits to Mossbauer spectra were done using spin hamiltonians to describe both the electronic and nuclear interactions; a model of superparamagnetic relaxation of two levels (spin ½) and stochastic theory; a lognormal particle size distribution function as well as a dependency of the magnetic transition temperature and the anisotropy constant on particle diameter. The evolutionary algorithms have been implemented using Python programming language. For comparison, the two algorithms obey the termination criterion of 6,000 evaluations of the objective function. The results presented show the efficiency of these algorithms in the optimization of the parameters and on the fits of the spectra.