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.
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