Detailed dc and ac magnetic properties of chemically synthesized Nd0.4Sr0.6MnO3 with different particle size (down to 27 nm) have been studied in details. We have found ferromagnetic state in the nanoparticles, whereas, the bulk Nd0.4Sr0.6MnO3 is known to be an A-type antiferromagnet. A Griffiths-like phase has also been identified in the nanoparticles. Further, critical behavior of the nanoparticles has been studied around the second order ferromagnetic-paramagnetic transition region (|(T-TC)/TC|{pounds} 0.04) in terms of modified Arrott plot, Kouvel-Fisher plot and critical isotherm analysis. The estimated critical exponents (b,g,d) are quite different from those predicted according to three-dimensional mean-field, Heisenberg and Ising models. This signifies a quite unusual nature of the size-induced ferromagnetic state in Nd0.4Sr0.6MnO3. The nanoparticles are found to be interacting and do not behave like ideal superparamagnet. Interestingly, we find spin glass like slow relaxation of magnetization, aging and memory effect in the nanometric samples. These phenomena have been attributed to very broad distribution of relaxation time as well as to inter-particle interaction. Experimentally, we have found out that the dynamics of the nanoparticle systems can be best described by hierarchical model of spin glasses.
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