Non-equilibrium spin dynamics of the frustrated trication spinel ZnMnCoO₄ in the hierarchical free-energy framework

Short-range spin correlations, memory and rejuvenation effects have been reported in the trication oxispinel ZnMnCoO₄whose low-temperature spin dynamics, triggered by magnetic frustration (fr∼6), could be better explained by the 'phenomenological' hierarchical free-energy model than the short-range droplet theory. Accordingly, the aging mechanism of the system had an asymmetric memory response to the positive and negative thermal cycles within the cluster-glass state (T<32.6 K) and demonstrated a hierarchical organization of the phase space where its metastable energy states undergo continuous splitting with decreasing temperature. An attempt to reproduce the time evolution of the isothermal remanent magnetization in the system led to an investigation of various relaxation models featuring semi-logarithmic, algebraic, fractional or stretched-exponential tails. Nevertheless, Weron's probabilistic relaxation model (here, the fractal characterβ∼0.4, the hierarchical constraintk>0, and the order parameterq(T∼0.12TSG) = 1.88) based on a purely stochastic approach, was best suited for understanding the slow spin dynamics of the cluster-glass phase in the entire temporal range. A comprehensive picture of the magnetic phase map was developed for the system, aided by magnetometry techniques and heat-capacity studies.