A machine (1) having a rotor (11) including permanent magnets (PM) and field coils (EC). The magnets are housed in first axial recesses (E1) distributed within a circumferential portion of the magnetic body, thus defining circumferential polar sections. The coils are housed in second axial recesses (E2) distributed within an intermediate portion of the magnetic body. The circumferential polar section includes a third recess (E3), and a portion of the magnetic body forming a bridge having a height of around 0.7 mm to around 2 mm is retained between an apex of the recess and an outer pole face.