Abstract: Griffiths-like phases (GP) are connected to disordered magnetic nanostructures. Here, we focus on the Giant Magnetocaloric compound Tb4.95La0.075Si2Ge2 with x = 0.075 where a re-entrant cluster-glass state (CGS) emerges at a characteristic freezing temperature TF-140 K within the GP (110-180 K), i.e. above the Curie temperature (TC). This unconventional magnetic state has been studied via temperature-dependent DC magnetization (5-300 K), time-dependent macroscopic AC susceptibility (80-200 K), including ageing and memory experiments, and magnetic small-angle neutron scattering (SANS), above TC (110-250 K). This approach allows to reveal the microscopic structure of the GP at the nanoscale in this system. AC susceptibility and DC magnetization confirm the presence of interacting short-range (< 2 nm) ferromagnetic (FM) clusters in the GP. The Langevin-like field dependence of the isothermal magnetization provides a quantitative assessment of the temperature dependence of the cluster size. Memory effects and ageing phenomena within GP are indicative of magnetically-frustrated states. Our results reveal that the dynamics is affected by the progressive coupling among CGS and GP towards the FM state. SANS correlation lengths between 1-5 nm above TF are determined from the calculated magnetic correlation function C(r), which is computed from the magnetic SANS intensity. A phenomenological model based on the formation of FM clusters with intercluster (FM) interactions within a PM matrix is proposed to explain the unusual re-entrant glassy behaviour in the PM state. These findings serve as another experimental reference for the global understanding of disordered magnetic compounds.

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