Effects of size distribution on hysteresis losses of magnetic nanoparticles for hyperthermia

For understanding hysteresis losses of magnetic nanoparticles to be used for magnetic particle hyperthermia the effect of size distribution on the dependence of hysteresis losses on magnetic field amplitude is studied on the basis of a phenomenological model in the size range from superparamagnetism to magnetic multi-domains-roughly 10 up to 100 nm. Relying on experimental data for the size dependence of coercivity, an empirical expression for the dependence of hysteresis loss on field amplitude and particle size is derived for hypothetical monodisperse particle ensembles. Considering experimentally observable size distributions, the dependence of loss on distribution parameters-mean particle size and variance-is studied. There, field amplitude is taken into account as an important parameter, which for technical and biomedical reasons in hyperthermia equipment is restricted. Experimental results for different particle types with mean diameter of 30 nm may be well reproduced theoretically if a small loss contribution of Rayleigh type is taken into account. Results show that the Stoner-Wohlfarth model for single domain magnetization reversal via homogeneous rotation cannot explain experimental observations. In particular, in magnetosomes which are distinguished by nearly ideal crystallographic shapes and narrow size distribution large friction-like losses occur even for small field amplitude. Parameters of the high frequency field for hyperthermia (amplitude and frequency) as well as of the size distribution of applied particles are discussed with respect to attaining maximum specific heating power.