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 MnCo
₂
O
₄
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
/
t
₀
) in which the magnitude of
M
(
t
) strongly depends on the wait-time spend at temperatures below
TF
.