Crackling noise: the Barkhausen effect

The term “crackling noise” refers to the signal that some disordered systems produce as a response to an external driving field smoothly changing in time. Due to the presence of disorder, crackling signals are extremely irregular, despite the steady increase of the external forcing. They are typically characterized by a sequence of pulses of very different sizes and durations, separated by quiescence intervals. Tiny events occur very frequently, while large ones are rare, with power laws probability distributions.

Systems that “crackle” are found in many different situations, and, remarkably, the corresponding signals often share some common characteristic features. Examples of crackling signals include the shear response of a granular media, the acoustic emission during martensitic phase transitions, the bursts of dislocations activity in plastic deformation, the dynamic of superconductors and superfluids, the fluctuations in the stock market, the dielectric polarization of ferroelectric materials, the acoustic emission in fractures, and the seismic activity in earthquakes. Crackling noise signals are expected to encode information on the physical process that generates them. Understanding the statistical properties of these jerky emissions, is therefore a step towards the understanding of the microscopic dynamics taking place in the system that crackles. Moreover, the fact that very diverse systems behave in a remarkably similar manner, suggests that some general basic principle may exist in the underlying physics.

Barkhausen noise (BN) is probably one of the fiirst crackling signals ever recorded. Indeed the Barkhausen effect has been known for almost a century: its first observation dates back in 1919, when Heinrich Barkhausen noticed that “iron produces a noise when magnetized: as the magnetomotive force is smoothly varied […] it generates irregular induction pulses in a coil wound around the sample that can be heard as a noise in a telephone”. As the magnetization reverses, the variations of the magnetic flux induce a voltage, that indirectly measures the changes in the magnetization of the sample. The signal recorded in correspondence to jumps in the magnetization, appears to be very irregular, no matter how smooth is the variation of the external field. In soft ferromagnetic materials the magnetization mainly reverses by domain wall displacement. Due to the presence of various types of disorder, like non–magnetic inclusions and dislocations, which act as pinning points, the wall movement is discontinuous. As the external field is smoothly increased, the magnetization changes in steps, in correspondence to jumps of the magnetic interface, or, in microscopic terms, in correspondence to avalanches of spin flips. The hysteresis loops is also discontinuous, and the signal, which is proportional to the derivative of the magnetization, plotted versus time, looks like a disordered series of pulses. The size and duration of magnetization events are power law distributed, and the distributions have been found to be universal in a large class of materials.