Specific absorption rate in Zn-doted ferrites for self-controlled magnetic hyperthermia

In this paper, we study mixed ferrites nanoparticles with structure formula Me 1− x Zn x Fe 2 O 4 (Me = Co, Ni, Cu, Mn) appropriated for self-controlled magnetic hyperthermia (SMHT) for in vivo and in vitro applications. We discuss in details the influence of the size d , the Zn-ion concentration x on the magnetic characteristics: saturation magnetization M S , coercivity H C , effective anisotropy K eff and specific absorption rate ( SAR ). From a theoretical point of view we investigate monodispersed, non-interactive, single-domain spherical magnetic nanoparticles (MNPs). We propose a simple core–shell model with a constant thickness of the surface layer. We explain the behaviour of SAR as a function of size and dopping based on two thermal heating mechanisms: the mechanism leading to dynamic hysteresis loops of superparamagnetic origin and the heating mechanism via conventional metastable hysteresis. We investigate also a thermal heating efficiency based on the Zn-ion concentration. We show that whether SAR decreases (increases) when doping increases depends on whether the nanoparticle diameter d is smaller (larger) than the particle size d max for which SAR has a maximum value. The numerical results are in qualitative agreement with many experimental data. Graphical abstract