The shape instability of magnetic domain walls under current is investigated in a ferromagnetic (Ga,Mn)(As,P) film with perpendicular anisotropy. Domain wall motion is driven by the spin transfer torque mechanism. A current density gradient is found either to stabilize domains with walls perpendicular to current lines or to produce finger-like patterns, depending on the domain wall motion direction. The instability mechanism is shown to result from the non-adiabatic contribution of the spin transfer torque mechanism. ... These instabilities originate from a competition between the surface tension which tends to favor flat interfaces and a destabilizing interaction as a gradient of external driving force (temperature, gravitational field, magnetic field...) or as long range dipolar interactions 10,11 for quasi-two-dimensional systems 12 . A crucial point for understanding interface dynamics as well as domain pattern formation is to determine the parameters controlling the instabilities and their formation mechanism.In ferromagnetic systems, it was shown recently that domain walls (DWs) can be moved by a spin polarized current 13-16 through the so-called spin transfer torque (STT) [17][18][19][20] . This has motivated an intense research effort for elucidating the physics of STT and for potential application in spin-electronics 21,22 . The STT acts as a driving force proportional to the current density. As expected by analogy with the well studied field-driven dynamics, essentially two dynamical regimes are observed. At low drive, DWs move in the pinning-dependent creep regime. Above a depinning threshold, the dynamics corresponds to flow regimes limited by dissipation 16 . Current-driven DW dynamics is most generally studied in narrow tracks, where DWs remain stable over the track width. However, field and current-driven dynamics exhibit, in extended a) Electronic mail: vincent.jeudy@u-psud.fr geometry, quite different behavior. A magnetic field acts essentially as a magnetic pressure pushing DWs with an average uniform velocity. In contrast, the current-driven creep regime was found to result in the formation of triangular domain-shapes 23 . In the flow regime 24 , the DW velocity was shown to depend on the respective orientations of the DW and the current flow. Those observations suggest a complex interplay between the DW shape and dynamics, and the STT magnitude. In this frame, it is particularly interesting to characterize the shape stability of DW driven by current. To address this issue, we investigated DW motion under current in wide geometries where instabilities induced by current and/or dipolar interactions can develop and be visualized. We used a (Ga,Mn)(As,P) thin film with perpendicular magnetization, as in this material, a wide range of dynamical regimes can be accessed thanks to its extraordinary weak current density required to induce DW motion. To get a better understanding of the role of current induced motion on DW stability, we introduce, on purpose, a progressive current density gradient by p...