Power spectrum of Barkhausen noise in simple materials

Abstract

The term ``Barkhausen noise'' employed herein does not have its customary meaning. In the present work, the flux in the sample is caused to vary linearly with time. Consequently Barkhausen noise appears as noise in the magnetomotive force (mmf) required to accomplish this. It is this mmf noise that is analyzed here. The general expression for the power spectral density, G(f), predicted by the spring model of hysteresis, is derived. This is then specialized to the case of an exponential distribution function. The method used to compare experiment with theory is outlined. The raw data consist of 2048 values of mmf voltage digitally sampled over a period of 37.12 sec. Smoothed power spectra were obtained by processing the time data with a digital inverse filter. Comparison of theory with experiment involves the determination of two parameters: S′Z, which is adjustable for best fit and N, which is not adjustable. The quality of the agreement between theory and experiment is measured in two ways: (i) comparison of experimental and theoretical spectra after choosing the parameter S′Z for best fit; (ii) comparison of parameter values so determined with values determined by other means. It is found that (within the experimental uncertainty due to the finite size of data set) the agreement between the predictions of the spring model and experimental spectra is quite good. This confirms the results of previous work on the autocorrelation function of Barkhausen noise. It is concluded that the spring model not only accurately describes the average shapes of hysteresis loops of simple materials, but also accurately describes statistical fluctuations from the average. These fluctuations are due to fluctuations in the number and strengths of the defects with which a wall interacts.