Relaxational Behavior of Fine Magnetic Particles

Weil and others have used the temperature variation of remanence and a formula of Néel's to determine volume-distribution curves for a powder of single-domain particles. The basic principle is that the time constant for spontaneous reversal of the magnetization, through thermal agitation, is effectively infinite for particle volume vvc and zero for vvc, where vc varies with absolute temperature T. Néel's derivation is open to criticism, in that the gyromagnetic properties of the particles are taken into account only up to a certain point in the argument and are thereafter ignored. A new formula has been derived by adaptation of a method of Kramers to angular coordinates and to a gyroscopic equation of motion. Like Néel's theory, this gives for the mean rate of transition between orientations a formula of the form v = c exp(−W/kT); W is the same in both theories, but in the new theory c = (γ′/2)(vJsHc3/2πkT)12. Here Hc = critical field for static reversal, Js = spontaneous magnetization, γ′ = (2ηJs)(ηJs)2+1/γ2−1, γ = (magnetic moment)/(angular momentum), η = coefficient in the damping torque −ηM×(dM/dt) in Gilbert's equation of motion. The new values of v/T vs time constant do not differ seriously from Néel's.