A critical examination of magnetic states of   La$_{0.5}$Ba$_{0.5}$CoO$_3$: non-Griffiths phase and interacting   ferromagnetic-clusters
  We report detailed dc magnetization, linear and non-linear ac susceptibility measurements on the hole doped disordered cobaltite La$_{0.5}$Ba$_{0.5}$CoO$_3$. Our results show that the magnetically ordered state of the system consists of coexisting non-ferromagnetic phases along with percolating ferromagnetic-clusters. The percolating ferromagnetic-clusters possibly undergo a 3D Hisenberg like magnetic ordering at the Curie temperature of 202(3) K. In between 202 and 220 K, the linear and non-linear ac susceptibility measurements show the presence of magnetic correlations even when the spontaneous magnetization is zero which indicates the presence of preformed short range magnetic-clusters. The characteristics of these short range magnetic-clusters that exist above Curie temperature are quite distinct than that of Griffiths phase e.g the inverse dc susceptibility exhibits an field independent upward deviation, and the second harmonic of ac susceptibility is non-negative. Below Curie temperature the system exhibit spin-glass like features such as irreversibility in the field cooled and zero field cooled magnetization and frequency dependence in the peak of ac susceptibility. The presence of a spin or cluster -glass like state is ruled out by the absence of field divergence in third harmonic of ac susceptibility and zero field cooled memory. This indicates that the observed spin-glass like features are possibility due to progressive thermal blocking of ferromagnetic-clusters which is further confirmed by the Wohlfarth's model of superparamagnetism. The frequency dependence of the peak of ac susceptibility obeys the Vogel-Fulcher law with $\tau_0\approx 10^{-9}$ s. This together with the existence of an AT line in H-T space indicates the existence of significant inter-cluster interaction among these ferromagnetic-clusters. 
Devendra Kumar and A. Banerjee
cond-mat.str-el