  Barkhausen effect in ferromagnetic materials provides an excellent area for
investigating scaling phenomena found in disordered systems exhibiting
crackling noise. The critical dynamics is characterized by random pulses or
avalanches with scale-invariant properties, power-law distributions, and
universal features. However, the traditional Barkhausen avalanches statistics
may not be sufficient to fully characterize the complex temporal correlation of
the magnetic domain walls dynamics. Here we go beyond power laws and focus on
the multifractal scenario to quantify the temporal scaling characteristics of
Barkhausen avalanches in polycrystalline and amorphous ferromagnetic films with
thicknesses from $50$ nm to $1000$ nm. We show that the multifractal properties
are dependent on the film thickness, and insensitive to the structural
character of the materials. Further, we observe for the first time the collapse
of the multifractality in the domain walls dynamics as the thickness is
reduced, and the multifractal behavior gives place to a monofractal one over
the entire range of time scales. The reorganization in the temporal scaling
characteristics of Barkhausen avalanches is understood as an universal
restructuring associated to the dimensional transition, from three to
two-dimensional magnetization dynamics.
