Theory of the Wiedemann Effect

Abstract

As regards the classical problem of the Wiedemann effect in ferromagnetic polycrystalline substances, no satisfactory theory has yet been proposed except Fromy's theory for the case of thin-walled tube specimens. In a simple way, a general expression is derived for the Wiedemann effect or for the torsion angle per unit length, θ_r of a cylindrical layer of the radius _r in the case of a cylindrical rod of ferromagnetic substance, fixed at its one end and magnetized by a longitudinal magnetic field, H_l, parallel to, and by a circular magnetic field, H_cr, around, the rod axis. When the elastic energy is negligible as compared with the magnetic field energy as in normal ferromagnetics, the general expression is reduced to
θ_r=(2/r){λ_l(H_r) -λ_t(H_r)}(H_tH_cr/H_r²),
where Hr=(H_l²-H_cr²)^1/2 and λ_l(H_r) and λ_t(H_r) are, respectively, the longitudinal and transverse magnetostrictions accompanied with H_r. This expression is rewritten, for the surface of a rod of the radius a, as
θ_a=(2/a){λ_l(H_a)-λ_t (H_a)}(H_lH_ca/H_a²),
which holds also for a thin-walled tube and is the expression derived already by Fromy. This expression is further reduced to
θ_a=(3/a)•λ_l(H_a)•(H_lH_ca/H_a²),
if the volume magnetostriction is considered negligible as in normal ferromagnetics. It is shown that the above expressions can explain, completely qualitatively and to a considerable extent quantitatively, all of the available experimental facts concerning the Wiedemann effect.