Spin-glass-like complex susceptibility of frozen magnetic fluids

The complex magnetic susceptibility chi=chi'-i chi " of different kinds of magnetic fluids (MFs) was measured as a function of temperature T from 6 to 300 K in a weak ac field of 1 Oe for frequencies ranging from f=0.1 to 1000 Hz. A prominent peak appears in both chi' and chi " as a function of T in the frozen state of the MF in which cluster formation of the colloidal particles is difficult, whereas no peak appears in the frozen state of other MFs in which clusters form easily. The peak temperature T-p2 of chi " depends on f following the Vogel-Fulcher (VF) law, i.e., f=f(0)exp[-E-sg/k(B)(T-p2-T-0)], where f(0) and E-sg are positive constants and T-0 is a function of the particles' volume fraction phi. The VF law only holds for 0.0007 less than or equal to phi less than or equal to 0.104, where an empirical power law of T-0 proportional to phi(0.41) holds. There is another kind of peak in the loss factor tan delta=chi "/chi' as a function of T, which means the existence of a magnetic after effect. This peak temperature T-p4 is far less than T-p2 and shown as an Arrhenius-type dependence on f with the exception of a MnZn ferrite particle MF.