  Recently we have reported on the magnetization dynamics of a single CrO$_2$
grain studied by micro Hall magnetometry (P. Das \textit{et al.}, Appl. Phys.
Lett. \textbf{97} 042507, 2010). For the external magnetic field applied along
the grain's easy magnetization direction, the magnetization reversal takes
place through a series of Barkhausen jumps. Supported by micromagnetic
simulations, the ground state of the grain was found to correspond to a flux
closure configuration with a single cross-tie domain wall. Here, we report an
analysis of the Barkhausen jumps, which were observed in the hysteresis loops
for the external field applied along both the easy and hard magnetization
directions. We find that the magnetization reversal takes place through only a
few configuration paths in the free-energy landscape, pointing to a high purity
of the sample. The distinctly different statistics of the Barkhausen jumps for
the two field directions is discussed.
