  Domain-wall dynamics and spatial fluctuations are closely related to each
other and to universal features of disordered systems. Experimentally measured
roughness exponents characterizing spatial fluctuations have been reported for
magnetic thin films, with values generally different from those predicted by
the equilibrium, depinning and thermal reference states. Here, we study the
roughness of domain walls in GdFeCo thin films over a large range of magnetic
field and temperature. Our analysis is performed in the framework of a model
considering length-scale crossovers between the reference states, which is
shown to bridge the differences between experimental results and theoretical
predictions. We also quantify for the first time the size of the depinning
avalanches below the depinning field at finite temperatures.
