Achieving a noninteracting magnetic nanoparticle system through direct control of interparticle spacing

Abstract

Monodisperse magnetite (Fe3O4) nanoparticles (NPs) were synthesized and coated using a SiO2 shell with controlled thickness ranging from 3.0 to 20.0 nm. The temperature-dependent zero-field-cooled (ZFC) and field-cooled (FC) magnetizations of the 7.5 nm Fe3O4 NPs with systematically increasing interparticle spacing were studied using the continuous and intermittent cooling protocol. The experimental evidence from dc magnetization and simulated ZFC/FC curves reveal that the increasing interparticle spacing modulated the collective magnetic behavior by effectively lowering the interparticle dipolar coupling, and for 7.5 nm Fe3O4 NPs a noninteracting particle system formed with interparticle spacing above 31.5 nm.

Magnetic susceptibility curves of a nanoparticle assembly, I: Theoretical model and analytical expressions for a single magnetic anisotropy energy

“…Comparison with the ''two states model'': temperature and width of the crossover A quite crude model, that we shall call the ''two states model'' or ATM (abrupt transition model), is widely used in the literature [8][9][10][11][12][13] when dealing with superparamagnetic nanoparticles. It corresponds to the case of an extremely abrupt transition: particles are either fully blocked (constant magnetic moment), or purely superparamagnetic (magnetic moment varying as 1/T [31]).…”

“…Experimental curves are often just qualitatively analyzed, the only point of interest being the value of T max . When a fit of the entire curve is considered, the crude model proposed by Wohlfarth [8] with an abrupt blocked to superparamagnetic transition is always used [9][10][11][12][13]. In this model, a particle is supposed to be blocked (its magnetic moment does not change with T) as long as the temperature is below its blocking temperature T B , and superparamagnetic (the macrospin switching is so frequent that the equilibrium value of the magnetic moment is observed) for T 4T B .…”

Magnetic susceptibility curves of a nanoparticle assembly II. Simulation and analysis of ZFC/FC curves in the case of a magnetic anisotropy energy distribution

“…We can then write M 0 ¼ M eq (T X ): there is no discontinuity in the FC curve. Using T eff instead of T X , as it is the case in the literature [2][3][4][8][9][10][11][12][13], would result either in a discontinuity, or a wrong low temperature limit for the FC curve.…”

“…The analysis has been however performed only in the framework of the two states model [3][4][5][6][7], and unfortunately using a wrong expression for the ZFC curve [3,4,6] (this question is addressed further). This model (again, with often a wrong expression of the curves) is also the only one used, up to now, when a quantitative analysis is performed, using a fit of the ZFC curve and sometimes additionally of the FC curve [8,3,4,[9][10][11][12][13].…”

Comment on “Nano-particle magnetism with a dispersion of particle sizes” [J. Appl. Phys. 112, 103915 (2012)]

“…" We perfectly agree that the two formulations using either the particle size distribution qðVÞ or the "volume weighted distribution" f(V) are equivalent 7 [it can be seen directly by setting f ðVÞ ¼ VqðVÞ= V ]. Unfortunately, the fact is that many authors 9 did not notice in the original paper 10 the important difference between f(V) and the particle size distribution qðVÞ. The consequence is an erroneous interpretation of experimental data, and this was what we wanted to point out in our article.…”