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 ${\mathrm{v>v}}_c$ and zero for ${\mathrm{v<v}}_c$ , where $v_c$ 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 $\mathrm{v\hspace{0.17em}=\hspace{0.17em}c\hspace{0.17em}}\exp \mathrm{(-W/kT)}$ ; $W$ is the same in both theories, but in the new theory ${\text{c\hspace{0.17em}=\hspace{0.17em}(γ′/2)(vJ}}_s{H}_c^3{\text{/2πkT)}}^{\frac{1}{2}}$ . Here $H_c\mathrm{\hspace{0.17em}=\hspace{0.17em}}\mathrm{critical}\hspace{0.17em}\mathrm{field}\hspace{0.17em}\mathrm{for}\hspace{0.17em}\mathrm{static}\hspace{0.17em}\mathrm{reversal}$ , $J_s\mathrm{\hspace{0.17em}=\hspace{0.17em}}\mathrm{spontaneous}\hspace{0.17em}\mathrm{magnetization}$ , ${\text{γ′\hspace{0.17em}=\hspace{0.17em}(2ηJ}}_s{\mathrm{)[(\eta J}}_s{)}^2{\text{+1/γ}}^2{]}^{\text{−1}}$ , $\mathrm{\gamma \hspace{0.17em}=\hspace{0.17em}(}\mathrm{magnetic}\hspace{0.17em}\mathrm{moment}\mathrm{)/(}\mathrm{angular}\hspace{0.17em}\mathrm{momentum})$ , $\mathrm{\eta \hspace{0.17em}=\hspace{0.17em}}\mathrm{coefficient}\hspace{0.17em}\mathrm{in}\hspace{0.17em}\mathrm{the}\hspace{0.17em}\mathrm{damping}\hspace{0.17em}\mathrm{torque}\mathrm{\hspace{0.17em}-\eta }\mathbf{M}\mathrm{\times (d}\mathbf{M}\mathrm{/dt)}$ in Gilbert's equation of motion. The new values of $\mathrm{v/T}$ vs time constant do not differ seriously from Néel's.