Experimental evidence of exchange forces between nanoparticles in a superparamagnetic system

Abstract

Although interacting superparamagnetic systems have been widely explored, in most of cases the correlations are only assigned to the dipolar interactions. Here we perform a systematic investigation of the properties of superparamagnetic MgFe2O4 nanoparticles, a system having characteristics that led us to the belief they are associated with the existence of exchange interactions into the system. We first confirm our sample does consist of pure MgFe2O4 nanoparticles, having average size of ∽12 nm and superparamagnetic behavior at room temperature with irreversibility temperature of 250 K. Nevertheless, we reveal the magnetic response is not well described by the Langevin function, even taking into account the size distribution of the nanoparticles. In order to address the reasons for such deviation from the non-interacting behavior of a superparamagnetic system, we focus our attention on equilibrium and dynamic magnetization measurements, and yet consider a theoretical approach in the context of the mean-field approximation, in which the effects of interactions into the sample are investigated. From the results, we find a positive value of 243 K for the parameter Θ associated to the mean field. Such condition imposes the existence of magnetizing effects due to interactions in the system, which according to Weiss' mean field theory are a fingerprint of the presence of exchange forces between nanoparticles.

The Nature of Ferromagnetism in a System of Self-Ordered α-FeSi2 Nanorods on a Si(111)-4° Vicinal Surface: Experiment and Theory

“…Such loops with inflection are typical of systems with two magnetic phases having different saturation fields. According to the AFM analysis ( Figure 1 a), NRs with significantly different lengths and heights, and consequently, different volumes, were observed, and their sizes were characteristic of the superparamagnetic state [ 42 , 43 ]. In such systems, the height of the energy barrier separating two stable states along the easy axis of a single-domain nanoparticle is determined by the value of uniaxial effective anisotropy K eff (magnetocrystalline anisotropy, shape anisotropy, or their combination) and the nanoparticle volume V [ 44 ]: E b = K eff V …”

“…After obtaining the FORC curves, they were processed using the do FORC software package [ 36 ], in accordance with the formula for ρ ( H a , H b ) reported in [ 33 ]. Subsequently, a square grid was built with different averaging coefficients n (50 and 100) for ρ ( H a , H b ), taking into account the method of numerical estimation of the optimal value of n [ 43 ]. Figure 5 a shows a FORC diagram with an averaging factor of n = 100 and a set of FORC curves (inset) along with the value of the second derivative ρ which is in color [ 33 ].…”