Nano-particle magnetism with a dispersion of particle sizes

In this paper, different definitions of the distribution functions that can be used to account for the magnetization of dispersed nano-particle systems are discussed. The volume and number weighted distributions are both found to be equally valid for the representation of distribution functions in nanoparticle magnetic systems. This study also shows that the room temperature magnetization curve M(H) of a superparamagnetic system is sensitive to the particle size distribution parameters and, that for a non-interacting system, these parameters can be unambiguously determined. Furthermore, the temperature variation of the initial susceptibility chi(T) for a dispersion of particle sizes is also examined using both the exact and the critical approaches. The critical approach is found to be a reasonable and valid approximation, since the discrepancy in the calculated chi(T) curves between the exact and the approximated form of the function exp(-t(m)/tau) was found to be very small. For a dispersion of anisotropy energies, both approaches adequately describe the unblocking process of the particle magnetic moments within the system when the temperature is increased. In this study, the distribution of the critical transition temperatures that can be obtained from the temperature variation of the initial susceptibility is also examined. For different definitions of the distribution functions, the retrieved distributions from the experimental data are bound to be different. Furthermore, the calculated temperature variation of the initial susceptibility is found to be sensitive to the constant value of the frequency factor f(0) used in the calculations. The discrepancy in calculating the chi(T) curve using an improper value of f(0) is larger than that discrepancy arising from the step-like approximation of exp(-t(m)/tau). Thus, the f(0) value has to be calculated using the physical parameters of the system and not just taken as a constant value between 10(9) and 10(11) Hz. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4766817]