  In this paper, we perform a detailed study of the scaling properties of a
ferromagnetic thin film model. Recently, interest has increased in the scaling
properties of the magnetic domain wall (MDW) motion in disordered media when an
external driving field is present. We consider a (1+1)-dimensional model, based
on evolution rules, able to describe the MDW avalanches. The global interface
width of this model shows Family-Vicsek scaling with roughness exponent
$\zeta\simeq 1.585$ and growth exponent $\beta\simeq 0.975$. In contrast, this
model shows scaling anomalies in the interface local properties characteristic
of other systems with depinning transition of the MDW, e.g. quenched
Edwards-Wilkinson (QEW) equation and random-field Ising model (RFIM) with
driving. We show that, at the depinning transition, the saturated average
velocity $v_\mathrm{sat}\sim f^\theta$ vanished very slowly (with $\theta\simeq
0.037$) when the reduced force $f=p/p_\mathrm{c}-1\to 0^{+}$. The simulation
results show that this model verifies all accepted scaling relations which
relate the global exponents and the correlation length (or time) exponents,
valid in systems with depinning transition. Using the interface tilting method,
we show that the model, close to the depinning transition, exhibits a
nonlinearity similar to the one included in the Kardar-Parisi-Zhang (KPZ)
equation. The nonlinear coefficient $\lambda\sim f^{-\phi}$ with $\phi\simeq
-1.118$, which implies that $\lambda\to 0$ as the depinning transition is
approached, a similar qualitatively behaviour to the driven RFIM. We conclude
this work by discussing the main features of the model and the prospects opened
by it.
