Abstract
In this paper, we investigate the quantum size effects on Eu2MnHfO6 (EMHO) nanoparticles (NPs) synthesized
via sol–gel and annealed at 500, 800, and 1000 ◦C. XRD confirmed a cubic Fd3‾m structure across all samples,
with NP sizes increasing from 7.4 nm to 23.8 nm. Smaller NPs displayed features of quantum dots (QD) and
weakened Mn/Hf–O–Mn/Hf bonding due to broken surface coordination, as seen in FTIR spectra. Magnetic
measurements revealed size-dependent behaviour: smaller NPs exhibited surface-driven phenomena like
blocking temperature (TB) and surface spin effects (TSE), while larger NPs (23.8 nm) showed bulk-like superexchange
interactions with distinct N´eel (TN) and Curie (TC) temperatures. Local magnetic inhomogeneities
indicating a Griffiths phase (GP) were found in the smallest and largest particles, overlapping with TC. These
novel results underscore how surface-to-volume ratios influence magnetic transitions, supporting a modified
Curie–Weiss law that distinguishes surface and volume effects with coordination variations in MNPs.