Nanocomposites and nanomaterials
 Critical behavior of ensembles of superparamagnetic nanoparticles with a variance of magnetic parameters
A. V. Bodnaruk1, S. M. Ryabchenko1,  M. M. Kulyk1, V. M. Kalita1,3 and A. I. Tovstolytkin2
1 Institute of Physics of NAS of Ukraine. Prospect Nauki, 46, Kyiv-03039, Ukraine. 
E-mail: andrew.bodnaruk@gmail.com
2 Institute of Magnetism of NAS of Ukraine and MES of Ukraine, 36-b Vernadsky Blvd., Kyiv 03142, Ukraine
3 National Technical University “Igor Sikorsky Kyiv Polytechnic Institute,” Prospekt Peremohy 37,03056 Kyiv, Ukraine
Magnetic nanoparticles have generated a new trend in the field of advanced materials, particularly due to their multiple technological and biomedical applications [1–2]. A magnetization of an ensemble of magnetic nanoparticles is complicated enough process especially in the region of a transition between superparamagnetic and paramagnetic states. The effects in this region may be approximately represented as a simultaneous realization of two different processes: a change of the magnetic moment of a separate particle with magnetic field (paraprocess for a separate particle) and alignment of the magnetic moments of the particles in their ensemble by the magnetic field (superparaprocess). These two processes are analyzed and the way to separate them are suggested. The procedure to account for these processes in the determination of the average magnetic moment of the particle from the magnetization curve of the particles ensemble is developed. 
	Fig. 1.  Calculated dependences of Sav(H,T)L(XL) (Sav – the average moment of a magnetic ion in the ensemble, L(XL) – the  Langevin function, XL=MH/kT, M = N·Sav) for the 1/H interval (in kOe-1) from 0.04 up to 1.2 for the model sample. The value of Sav(H,T)L(XL) was calculated for a model of nanogranule with N=104 magnetic ions with spin S=3/2, g=2 and with exchange interaction between nearest magnetic ions in the crystal lattice that leads to TC=300 K (in the mean field approximation). 	
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