A permanent magnet electric machine (PM machine) includes a rotor with rotatable magnets and a stator defining an air gap with the rotor. An actuator rotates the rotatable magnets at predetermined operating points through an angular distance sufficient for changing magnetic pole orientations of the rotatable magnets, and thus modifies magnetic flux linkage with stator windings across the air gap. Fixed magnets may be arranged around a circumference of the rotor. The actuator may be actively or passively driven. Flux-shunting elements are optionally disposed in the rotor to further modify the flux linkage. A gear set connected to torque transfer elements may be driven by the actuator to rotate the rotatable magnets. A vehicle includes drive wheels, a transmission, and the PM machine. A method controls magnetic flux linkage in the PM machine noted above.