Relaxational Behavior of Fine Magnetic Particles

Abstract

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 v>vc and zero for v<vc, 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.