Motor braking occurs when the motor is used as a generator and the power it develops is dissipated as heat. The dc magnet is the fixed field of the generator.
Sometimes for small motors, the input to the motor is simply connected to a dc source, usually a full or half-wave rectified input of the mains.
In a three phase motor, reversing the phases momentarily can also be used as a brake. The currents are fairly high during this procedure. For a single phase motor, 'reversing the polarity' will simply cause it to spin up again.
For a mechanical clutch, the use of ac or dc is irrelevant except that the solenoid or actuator is designed for either ac or dc.
An experiment striking enough to take it home and show your kids is to get a NdFeBa magnet about 0.5 x 0.5 in, and drop it down a 2 or 3 foot length of extruded aluminum tubing or square pipe. The magnet pushes itself away from the walls of the pipe, and takes about 15-30 seconds to fall through. In square pipe, the sides act like a kaleidoscope which adds to the visual effect. This is an example of magnetic braking.
DspDad