Quantum size effects on magnetism in Eu2MnHfO6 nanoparticles: Role of surface-to-volume ratio, magnetic blocking, and magnetic phase transitions

• Size-controlled magnetism: EMHO nanoparticles show a transition from surface-dominated to bulk-like magnetic behaviour as size increases from 7.9 nm to 23.8 nm. • Broken surface coordination: FTIR confirms disrupted Mn/Hf–O–Mn/Hf bonding in < 20 nm nanoparticles, indicating reduced coordination and quantum confinement. • Magnetic transition crossover: Small NPs exhibit surface spin effects (T SE , T B ), while larger ones reveal distinct T N and T C from bulk-like super-exchange. • Griffiths phase at both size extremes: Magnetic inhomogeneities associated with a Griffiths phase appear in both the smallest and largest particles. • Modified Curie–Weiss model proposed: A new model separates surface and volume magnetic contributions, reflecting coordination and shape dependence. In this paper, we investigate the quantum size effects on Eu 2 MnHfO 6 (EMHO) nanoparticles (NPs) synthesized via sol–gel and annealed at 500, 800, and 1000 °C. XRD confirmed a cubic Fd 3̅ 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 (T B ) and surface spin effects (T SE ), while larger NPs (23.8 nm) showed bulk-like super-exchange interactions with distinct Néel (T N ) and Curie (T C ) temperatures. Local magnetic inhomogeneities indicating a Griffiths phase (GP) were found in the smallest and largest particles, overlapping with T C . 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.