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The magnetic properties and the effects of interparticle interaction on ithave been studied in nanoparticles of half doped Pr$_{0.5}$Sr$_{0.5}$MnO$_{3}$.Three samples consisting of nanoparticles of different average particle sizesare synthesized to render the variation in interparticle interaction. Thoughall the samples crystallize in the same structure to that of their bulkcompound, the low temperature ferromagnetic-antiferromagnetic transition, whichis present in bulk compound, is not evident in the nanoparticles. Linear aswell as nonlinear ac susceptibility coupled with dc magnetic measurements haveshown the superparamagnetic behavior of these nanoparticles where the blockingtemperature increases with the increasing particle size. Presence ofinterparticle interaction is confirmed from the temperature variation ofcoercive field and the analysis of frequency dependent ac susceptibility. Wehave identified the nature of this interaction to be of dipolar type, and showthat its strength decreases with the increasing particle size. The effect ofthis dipolar interaction on magnetic properties is intriguing as the compoundsexhibit crossover from de Almeida-Thouless to Gabay-Toulouse like criticallines on field-temperature plane above their respective interaction field. Inagreement with theoretical prediction, we infer that this crossover is inducedby the unidirectional anisotropy arising from interparticle interaction, andthis is confirmed from the presence of exchange bias phenomenon.

The interparticle interaction and crossover in critical lines on field-temperature plane in Pr$_{0.5}$Sr$_{0.5}$MnO$_{3}$ nanoparticles