Frequency dependence of hysteresis curves in ´non-conducting´ magnetic materials

The problem of modeling the frequency dependence of hysteresis in magnetic materials is approached in a new way. The DC magnetization curve, or hysteresis loop, is assumed to be the equilibrium position for the bulk magnetization. All microscopic processes which occur under the action of a time-varying field can be averaged to give a time dependent displacement from the equilibrium, ΔM. The case where eddy current effects do not play a significant role is examined. It is shown that ΔM obeys a damped simple harmonic motion equation. This means that the time dependence of the displacement magnetization ΔM is the Laplace transform of the field waveform. This enables the time dependence of the magnetization to be modeled, once the DC hysteresis curve is known, with only two additional materials parameters: relaxation time and natural frequency