Memory Effects and Relaxation Dynamics of ${\rm MnCo}_{2}{\rm O}_{4}$ Nanocrystallites

We present a detailed analysis of the time decay of magnetization (M) and ac-magnetic susceptibility (χ_ac)of hexagonal-shaped MnCo₂O₄ nanocrystals of average size 28 nm. The temperature (T) and magnetic field (H) dependence of the magnetization measurements reveal that even in the ferromagnetic state these nanocrystals do not exhibit conventional long-range ordering. The Curie temperature TC=176.4 K and the Hopkinson peak TH=146 K are found to be lower than those of the bulk values 184 and 175 K, respectively. Such a major decrease in TC and TH accounted for by the effect of finite-size scaling that has been thought to change the critical ordering temperatures. The dynamical properties studied by χ_ac (T ) measurements suggest the existence of a spin-glass phase for T ≤ TF(=165 K) associated with the magnetic frustration of spins in the nanocrystals. The presence of glassy magnetic state is supported by the frequency (f) dependent studies of χ_ac(T) and H^2/3 dependence of TF in the intermediate-field region (50 Oe ≤ H ≤ 1000 Oe). Various measurement protocols including temperature quenching, step-field and wait-time dependence have been used to investigate the relaxation dynamics both in MZFC and in M_FC for T ≤ TF, which show prominent memory and aging effects and supports the spin-glass state that established below TF. The magnetic viscosity (S) and microscopic spin-flip time (τ) were deduced from the time (t) dependence of M_ZFC using the expression M(t,T)=M(0,T)+S ln(1+t/t₀) in which the magnitude of M(t) strongly depends on the wait-time spend at temperatures below TF.