The flow of concentrated suspensions of solid particles can be suddenly blocked by the formation of a percolated network of frictional contacts above a critical value of the applied stress. Suspensions of magnetic particles coated with a superplastifier molecule were shown to produce a strong jamming transition. We find that, for these suspensions with an abrupt discontinuous shear thickening, a model using the divergence of the viscosity at a volume fraction that depends on the applied stress does not well describe the observed behaviour both below and above the critical stress. At a constant applied stress above the critical one, we have a stick–slip behaviour of the shear rate whose period can be predicted and scaled as the square root of the relaxation time of the frictional contacts. The application of a small magnetic field allows us to continuously decrease the critical shear rate, and it appears that the yield stress induced by the magnetic field does not contribute to the jamming transition. Finally, it is shown that this jamming transition also appears in the extrusion of a suspension through a die, but with a much slower dynamics than in the case of stress imposed on a rotational geometry. This article is part of the theme issue ‘Heterogeneous materials: metastable and non-ergodic internal structures’.