Magnetic irreversibility and saturation criteria in ultrasmall bi-magnetic nanoparticles

Ultrasmall magnetic particles are notorious for exhibiting a magnetization increase even at quite intense applied fields, behavior which can be interpreted as a non-saturation of the magnetic disordered shell even if the nanoparticle magnetization is reversible. In this work we study two kinds of ultrasmall core@shell nanoparticles (3 nm) with contrasting core anisotropy, composed of MnFe2O4 and CoFe2O4 cores covered by a thin maghemite layer. In order to investigate the saturation criterion associated to the closure of major loops (in contrast to minor loops), we use several procedures to determine, at moderate fields, if the effective anisotropy energy barrier is overcome or not. Firstly, we carefully evaluate the closure field of the hysteresis loop, interpreted as the effective anisotropy field, correspondent to two different contributions. One, arising from the nanoparticle core, is related to the coercivity and the other one is associated to pinned spins of the nanoparticle shell. Secondly, the ZFC-FC magnetization measurements taken at different fields give us information about both the anisotropy energy barrier distribution and the thermal dependence of effective anisotropy field. Thirdly, forced minor loops are performed, measured after either ZFC or FC processes, to counter-check the effective magnetic anisotropy at low temperature of both samples. Finally, we perform major hysteresis loop calculations in order to better understand the magnetization processes involved. To go further, we propose in this study a procedure to extract information about the two contributions which composes the effective magnetic anisotropy field.