Self-Similar Barkhausen Noise in Magnetic Domain Wall Motion

A model for domain wall motion in ferromagnets is analyzed. Long-range magnetic dipolar interactions are shown to give rise to self-similar dynamics when the external magnetic field is increased adiabatically. The power spectrum of the resultant Barkhausen noise is of the form $1/{\omega }^{\alpha }$, where $\alpha \approx 1.5$ can be estimated from the critical exponents for interface depinning in random media.