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

Temperature dependence of ac susceptibilities χ ′ and χ ″ are reported using frequencies f m = 0.1 , 1, 99, 499, and 997 Hz for nanoparticles of Ni dispersed in silica ( Ni / SiO 2 : 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 T B , as determined by peaks in χ ″ versus T data, are fit to the Vogel-Fulcher law based on the following equation: T B = T o + T a / ln ( f o / f m ) . Using the attempt frequency f o = 1.82 × 10 10 Hz , T a ( 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 T o ( representing the interparticle interaction ) = 0 , 0, 6.6(0.7), and 12.5(2.5) K respectively. The magnitudes of T a = K a V / k yield the anisotropy constant K a 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 ( f o / 2 π f m ) ] is checked and the calculated values of f o are consistent with experimental value of f o = 1.82 × 10 10 Hz .