Famous for its spin-state puzzle, LaSrCoO$_4$ (Co$^{3+}$) is an intermediate between antiferromagnetic (AFM) La$_2$CoO$_4$ (Co$^{2+}$) and ferromagnetic (FM) Sr$_2$CoO$_4$ (Co$^{4+}$). The appearance of the Co$^{3+}$ valence state (not present in the end compounds) is intriguing because of the spin-state transitions associated with it. In this work, we report two magnetic transitions in LaSrCoO$_4$: (i) a transition at T $=$ T$_c$ $simeq$ 225 K, from the paramagnetic state to a state with an inhomogeneous long-range ferromagnetic (FM) order wherein finite FM clusters coexist with infinite FM matrix in the percolation sense, and (ii) the transition to the cluster spin glass (CSG) state at T $=$ T$_g$ $simeq$ 8 K. Finite FM clusters (which at low temperatures give rise to the cluster spin glass state) and infinite FM matrix are formed due to the spin-spin interactions brought about by the inhomogeneously distributed Co$^{3+}$ high spin (HS) and Co$^{3+}$ low spin (LS) ions. A firm support to the presence of an unconventional (inhomogeneous) ferromagnetic order comes from the anomalous values of the critical exponents $beta$, $gamma$ and $delta$ for the spontaneous magnetization, `zero-field magnetic susceptibility and the critical M - H isotherm, while the coexistence of HS Co$^{3+}$ and LS Co$^{3+}$ ions is confirmed by the results of the extended X-ray absorption fine structure spectroscopy.
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