Why does magnetic locking happens? Well it happens in induction motor mainly due to its working principle. The stator coils in the motor is supplied by single/three phase AC supply. As a result of this supply, the stator coils develop their own respective magnetic polarity. Now, as the supply is time-varying, there is time-varying magnetic field also which induces emf in rotor conductors.
Brushed DC motors don’t have cogging because of their contruction and principle of operation.
Brushless DC motors have cogging torque.