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The effect of particle size reduction on the magnetic correlations of Pr 0.4 Bi 0.2 Sr 0.4 MnO 3  nanoparticles prepared by  top-down  approach has been studied in detail. It was observed that as the milling time increases from 0 to 240 min, particle size decreases from 160 to 12 nm. Correspondingly it was observed that the ferromagnetic transition temperature ( T   C  ) drops (264 to 213 K) and saturation magnetization ( M   S  ) decreases (2.12–0.41    $${\upmu }_{\mathrm{B}}/\mathrm{f}.\mathrm{u}.$$  μ B / f . u . ) while coercivity ( H   C  ) shows a monotonous increase (0.18–1.5 kOe) as the particle size decreases due to increase in milling. The magnetic entropy change ( ΔS ) also decreases (2.41–0.24 J/kg-K) as particle size decreases indicating a strong correlation between magnetism and particle size. The metamagnetic M–H response of the bulk sample, which signifies the magnetic phase coexistence, is suppressed, and the nature of magnetic interactions demonstrates a transition from long range to short range. The observed characteristics emphasizes that with particle size reduction there is an increase in the surface disorder which can be explained by considering the core–shell model for the nanoparticles. Graphic abstract

Finite-size effects on the evolution of magnetic correlations and magnetocaloric properties of Pr0.4Bi0.2Sr0.4MnO3