Barkhausen statistics from a single domain wall in thin films studied with ballistic Hall magnetometry

The movement of a micron-size section of an individual domain wall in a uniaxial garnet film was studied using ballistic Hall micromagnetometry. The wall propagated in characteristic Barkhausen jumps, with the distribution in jump size $S$, following the power-law relation, $D(S)\ensuremath{\propto}{S}^{\ensuremath{-}\ensuremath{\tau}}$. In addition to reporting on the suitability of employing this alternative technique, we discuss the measurements taken of the scaling exponent $\ensuremath{\tau}$, for a single domain wall in a two-dimensional sample with magnetization perpendicular to the surface, and low pinning center concentration. This exponent was found to be $1.14\ifmmode\pm\else\textpm\fi{}0.05$ at both liquid helium and liquid nitrogen temperatures.