On the low-field, low-frequency susceptibility of magnetic fluids

Abstract

A formula is derived for the complex, frequency-dependent, low-field relative susceptibility of a magnetic fluid which takes account of magnetic fluctuations of the intraparticle Neel-type and those induced by the rotational Brownian motion of the particles.

Suitability of water based magnetic fluid with CoFe2O4 particles in hyperthermia

“…Therefore, as the mean magnetic grain radius is much greater than 3.1 nm, the dominant mechanism of magnetisation of this magnetic fluid is the Brown mechanism [2,3].…”

“…The second mechanisms (Ne´el process) involves rotations of the magnetic moment inside the grains and can take place even when the grain movement is blocked, for example in the frozen liquid. The relaxation times of the above processes are described by [2,3]:…”

“…DE ¼ KV m is the energy barrier to moment reversal, t o is the time constant ($1 ns), and K is the anisotropy constant. When both mechanisms act simultaneously, the effective magnetic relaxation time t eff of the magnetic fluid is given by [3]:…”

Characteristic times of relaxation peaks of magnetic fluids

“…For a system with a single relaxation time, t, the frequency dependence of the complex magnetic susceptibility, w(o) ¼ w 0 (o)Àiw 00 (o), obeys the Debye equation [13] wðoÞ ¼ w 1 þ wð0Þ À w 1 1 þ iot (15) where w N is the high-frequency susceptibility, w(0) is the static susceptibility, o is the angular frequency and i ¼ OÀ1. As results from Eq.…”

“…Due to the fact that t eff À1 ¼ /t j À1 S, t eff is a measure of the average fastest relaxation time in a system. Using the autocorrelation function method and assuming that the Ne´el and Brownian relaxation processes are statistically independent, Scaife [15] derived a formula for the effective relaxation time, which is of the same form as Eq. (29).…”