Scaling laws and approximate expressions for the dynamic magnetic susceptibility of Brownian nanoparticles


We present simplified expressions for the out-of-phase component of the dynamic susceptibility chi '' of lognormal-sized magnetic nanoparticles under Brownian rotation. These expressions are based on transforming the general integral functions used for chi '' in the convolution of gaussian functions. chi '' can thus be expressed as a sum of gaussians with parameters directly related to those of the size distribution and to the saturation magnetization. The gaussian fit of chi ''(omega) (where w is the ac field frequency) is a simpler way to determine these structural and magnetic parameters as it avoids fitting chi ''(omega) to an integral function. The expressions derived for chi '' suggest that chi '' T data collapses in a omega eta(T)/T scale (where T is the temperature and eta the fluids viscosity), which is confirmed by numerical calculations. We also discuss the limits of validity of these approximations in real systems where both Neel and Brownian relaxation mechanisms coexist and we present further approximations for the relation of omega(chi) with the average volume (being omega(chi) the frequency at which chi '' is maximum). The omega eta(T)/T scale can be used to qualitatively evaluate the dominance of the Brownian relaxation mechanism. (C) 2011 Elsevier B.V. All rights reserved.



subject category

Materials Science; Physics


Silva, NJO

our authors


The author acknowledges S.S. Braga and R. Duarte for critical reading the manuscript. The author also acknowledges CSIC for a I3P contract and FCT for Ciencia 2008 program.

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