Barkhausen noise in metallic glasses with strong local anisotropy: Model and theory

We discuss a model metallic glass in which Barkhausen noise can be studied in exquisite detail, free of thermal effects and of the rate of ramping of the magnetic field. In this model the mechanism of the jumps in magnetic moment that cause the Barkhausen noise can be fully understood as consecutive instabilities where an eigenvalue of the Hessian matrix hits zero, leading to a magnetization jump Δm which is simultaneous with a stress and energy changes Δσ and ΔU respectively. Due to a large effect of local anisotropy, in this model Barkhausen noise is not due to movements of magnetic domain boundaries across pinning sites. There are no fractal domains, no self-organized criticality and no exact scaling behavior. We present a careful numerical analysis of the statistical properties of the phenomenon, and show that with every care taken this analysis is tricky, and easily misleading. Without a guiding theory it is almost impossible to get the right answer for the statistics of Barkhausen noise. We therefore present an analytic theory that culminates in a probability distribution function that is in excellent agreement with the simulations.