  Anomalous diffusion and L\'evy flights, which are characterized by the
occurrence of random discrete jumps of all scales, have been observed in a
plethora of natural and engineered systems, ranging from the motion of
molecules to climate signals. Mathematicians have recently unveiled mechanisms
to generate anomalous diffusion, both stochastically and deterministically.
However, there exists to the best of our knowledge no explicit example of a
spatially extended system which exhibits anomalous diffusion without being
explicitly driven by L\'evy noise. We show here that the
Landau-Lifshitz-Gilbert equation, a stochastic partial differential equation
(SPDE), despite only driven by Gaussian white noise, exhibits superdiffusive
behaviour. The anomalous diffusion is an entirely emergent behaviour and
manifests itself in jumps in the location of its travelling front solution.
Using a collective coordinate approach we reduce the SPDE to a set of
stochastic differential equations (SDEs) driven by Gaussian white noise. This
allows us to identify the mechanism giving rise to the anomalous diffusion as
random widening events of the front interface.
