Dynamic Magnetic Properties of NiFe$_{2}$O $_{4}$ Nanoparticles Embedded in SiO$_{2}$ Matrix

NiFe
₂
O
₄
nanoparticles with average sizes of 3.5(plusmn0.4) nm, 5.0(plusmn0.5) nm, and 19(plusmn1.1) nm embedded in the SiO
₂
matrix were prepared by the sol-gel method. Size and temperature dependence of magnetic relaxation of the ferrite nanoparticles were studied. A classical logarithmic distribution function was considered to analyze the thermally activated relaxation phenomenon in the nanocomposites, but it cannot describe the behavior within the whole range of temperatures and times. An alternative more general approach called
T
ln(
t
/tau
₀
) scaling was used to generate master curves which allows one to extrapolate the relaxation behavior at times that are experimentally inaccessible. The mean energy barrier as well as the width, sigma of the energy distribution curves can also be estimated from this study. These results are in good agreement with those obtained from ac and dc susceptibility measurements.