Understanding magnetic interparticle interactions within a single hydrodynamic volume of polydispersed magnetic nanoparticles and the resulting nonlinear magnetization properties is critical for their implementation in magnetic theranostics. However, in general, the field-dependent static and dynamic magnetization measurements may only highlight polydispersity effects including magnetic moment and size distributions. Therefore, as a complement to such typical analysis of hysteretic magnetization curves, we spectroscopically examined the complex magnetization harmonics of magnetic nanoclusters either dispersed in a liquid medium or immobilized by a hydrocolloid polymer, later to emphasize the harmonic characteristics for different core sizes. In the case of superparamagnetic nanoclusters with a 4-nm primary size, particularly, we correlated the negative quadrature components of the third-harmonic susceptibility with an insignificant cluster rotation induced by the oscillatory field. Moreover, the field-dependent in-phase components appear to be frequency-independent, suggesting a weak damping effect on the moment dynamics. The characteristic of the Néel time constant further supports this argument by showing a smaller dependence on the applied dc bias field, in comparison to that of larger cores. These findings show that the complex harmonic components of the magnetization are important attributes to the interacting cores of a magnetic nanocluster.
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