ac susceptibility studies of magnetic relaxation in nanoparticles of Ni dispersed in silica

Abstract

Temperature dependence of ac susceptibilities χ′ and χ″ are reported using frequencies fm=0.1, 1, 99, 499, and 997 Hz for nanoparticles of Ni dispersed in silica (Ni/SiO2:15/85) with the mean sizes D=3.8, 11.7, 15, and 21 nm (σ≃0.2 nm), as determined by transmission electron microscopy. The blocking temperatures TB, as determined by peaks in χ″ versus T data, are fit to the Vogel–Fulcher law based on the following equation: TB=To+Ta/ln(fo/fm). Using the attempt frequency fo=1.82×1010 Hz, Ta (K)=310 (21), 954(17), 1334(14), and 1405(47) are determined for D=3.8, 11.7, 15, and 21 nm, respectively, along with To (representing the interparticle interaction)=0, 0, 6.6(0.7), and 12.5(2.5) K respectively. The magnitudes of Ta=KaV/k yield the anisotropy constant Ka increasing with decreasing D (or volume V) due to contributions from surface anisotropy. The validity of the theoretical result χ″=C∂(χ′T)/∂T with C≃π/[2 ln(fo/2πfm)] is checked and the calculated values of fo are consistent with experimental value of fo=1.82×1010 Hz.