Losses in ferrites: single-crystal studies

Abstract

A simple experiment on ferromagnetic resonance absorption in single crystals of ferrites is described, and the method of deducing physically significant parameters of the ferrite from the results of such experiments is derived. Results at 24000Mc/s, and the parameters deduced from them in this way, are given for (NiO)o-75(FeO)o-25Fe203 and for (NiO) 0 .95(FeO)o-05Fe 2 0 3 . The results indicate that the presence of divalent iron gives rise to an important loss mechanism. Another experiment is described in which the motion of an individual ferromagnetic domain boundary is observed in a single crystal, and results of such an experiment on (NiO)o-75(FeO)o-2sFe203 at various temperatures are given. They indicate that the damping of domainwall motion in this material increases by a large factor (100 or more) as the temperature decreases from 300 to 77° K. An elementary thermodynamical calculation is given which describes both types of experimental results in terms of a torque relaxation. Elastic-constant and conductivity measurements which yield relevant results are also discussed briefly. LIST OF PRINCIPAL SYMBOLS/ = Angular momentum of ferromagnetic electrons per unit volume. M = Magnetic moment per unit volume. H = Magnetic field. y = Gyromagnetic ratio (y = MIX). A = Damping parameter. iV*, N£ = Demagnetizing factors used in representing effective field of magnetocrystalline anisotropy on M. W a = Magnetocrystalline anisotropy energy. K\ = Magnetocrystalline anisotropy energy constant. «i» «2» a 3 -Direction cosines of magnetization with respect to cubic axes. fi(0) = Angular dependence of the effect of magnetocrystalline anisotropy on ferromagnetic resonance field in (110) plane of a cubic crystal. z = Displacement of ferromagnetic domain wall, i, z = First and second time derivatives of z. m w = Mass of ferromagnetic domain wall. j8 = Viscous damping constant of ferromagnetic domain wall. a = Stiffness of ferromagnetic domain wall. M s = Saturation magnetization of a magnetic material. <D = Magnetic flux. w w = Dimension of a ferromagnetic domain wall. N = Number of turns per centimetre. / = Electric current, abamp. 8 = Angular position of M. v = Velocity of a ferromagnetic domain wall. A = Exchange energy constant. W = Free energy. T = Torque. T = Relaxation time. w = Work. E = Activation energy. Mr. Gait is with Bell Telephone Laboratories, Inc., New Jersey, U.S.A. a = Parameter which measures relaxing component of magnetic field energy. l x , l y = Parameters which relate applied field to torque acting on M in precessional motion in an anisotropic ferromagnetic material.