Random magnetic anisotropy driven transitions in layered perovskite LaSrCoO$_4$

Attempts to unravel the nature of magnetic ordering in LaSrCoO$_4$ (Co$^{3+}$), a compound intermediate between antiferromagnetic (AFM) La$_2$CoO$_4$ (Co$^{2+}$) and ferromagnetic (FM) Sr$_2$CoO$_4$ (Co$^{4+}$), have met with a limited success so far. In this report, the results of a thorough investigation of dc magnetization and ac susceptibility (ACS) in single-phase LaSrCoO$_4$ provide clinching evidence for a thermodynamic paramagnetic (PM) - ferromagnetic (FM) phase transition at T$_{c}$ = 220.5 K, followed at lower temperature (T$_{g}$ = 7.7 K) by a transition to the cluster spin glass (CSG) state. Analysis of the low-field Arrott plot isotherms, in the critical region near T$_{c}$, in terms of the Aharony-Pytte scaling equation of state clearly establishes that the PM-FM transition is basically driven by random magnetic anisotropy (RMA). For temperatures below $\approx$ 30 K, large enough RMA destroys long-range FM order by breaking up the infinite FM network into FM clusters of finite size and leads to the formation of a CSG state at temperatures T $\lesssim$ 8 K by promoting freezing of finite FM clusters in random orientations. Increasing strength of the single-ion magnetocrystalline anisotropy (and hence RMA) with decreasing temperature is taken to reflect an increase in the number of low-spin (LS) Co$^{3+}$ ions at the expense of that of high-spin (HS) Co$^{3+}$ ions. At intermediate temperatures (30 K $\lesssim T \lesssim$ 180 K), spin dynamics has contributions from the infinite FM network (fast relaxation governed by a single anisotropy energy barrier) and finite FM clusters (extremely slow stretched exponential relaxation due to hierarchical energy barriers).