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Probing the magnetic state by linear and non linear ac magnetic susceptibility measurements in under doped manganite Nd0.8Sr0.2MnO3

We have thoroughly investigated the entire magnetic states of under doped ferromagnetic insulating manganite Nd0.8Sr0.2MnO3 through temperature dependent linear and non linear complex ac magnetic susceptibility measurements. This ferromagnetic insulating manganite is found to have frequency independent ferromagnetic to paramagnetic transition temperature at around 140 K. At around 90 K (\approx T_f) the sample shows a second frequency dependent re - entrant magnetic transition as explored through complex ac susceptibility measurements. Non linear ac susceptibility measurements (higher harmonics of ac susceptibility) have also been performed (with and without the superposition of a dc magnetic field) to further investigate the origin of this frequency dependence (dynamic behavior at this re-entrant magnetic transition). Divergence of 3rd order susceptibility in the limit of zero exciting field indicates a spin glass like freezing phenomena. However, large value of spin relaxation time (?0= 10-8 s) and small value of coercivity (~22 Oe) obtained at low temperature (below T_f) from critical slowing down model and dc magnetic measurements, respectively, are in contrast with what generally observed in a canonical spin glass (?0 = 10-12 - 10-14 s and very large value of coercivity below freezing temperature). We have attributed our observation to the formation of finite size ferromagnetic clusters which are formed as consequence of intrinsic separation and undergo cluster glass like freezing below certain temperature in this under doped manganite. The results are supported by the electronic - and magneto - transport data.