A timepiece escapement mechanism includes a stopper between a resonator and an escape wheel set. The wheel set includes a magnetized track with an angular period of travel over which its magnetic characteristics are repeated. The stopper includes a magnetized or ferromagnetic pole shoe that is mobile in a transverse direction relative to the direction of travel of an element of a surface of the track. The pole shoe or the track creates a magnetic field in a pole gap between the pole shoe and the surface. The pole shoe is opposite a magnetic field barrier on the track just before each transverse motion of the stopper commanded by the periodic action of this resonator. The stopper is multistable and arranged to occupy at least two stable positions.