For modern hard drives the head actuator is linear motor made from permanent magnet(s) and solenoid. the arrangement is called voice coil, because it is mostly

For modern hard drives the head actuator is linear motor made from permanent magnet(s) and solenoid. the arrangement is called voice coil, because it is mostly the same thing as coil of an speaker (although the geometry is 90 degrees rotated such that it is flat instead of cylindrical)