Abstract: Collective behaviors in which the magnetic response depends not only on the individual constituents but also on their interactions are an area of active research. We have produced a paradigmatic system where DC magnetron sputtered FexAg100?x (x?=?15, 35) nanogranular films exhibit a crossover between a superspin glass (SSG) state and a superferromagnetism (SFM), where direct exchange interactions overcome the frustration. The systems have been studied by non-linear susceptibility (NLS) and small angle neutron scattering (SANS). The NLS measurements were carried out between 2 and 300?K, in the absence of a biasing magnetic field, with frequencies spanning two decades. These measurements shed light on the complex nature of the interactions and the intricate relationship between direct exchange and long range magnetic interactions. The use of SANS allows us to estimate qualitatively the lengthscale of the magnetic correlations, and therefore identify a clear difference between the collective ?supermagnetic? states (i.e., SSG and SFM) while establishing links between the structure and the magnetic interactions.

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