Some AC relays have a shaded pole, like a motor, to eliminate chatter.
The end of the core, where it comes out of the coil and attracts the armature, is split , forming two smaller poles each with a D-shaped cross-section. A D-shaped piece of heavy copper (sort of like a copper washer) is wrapped around one of the two poles, forming a one-turn shorted secondary coil.
When you energize the relay with AC, the pole that isn't "shaded" by the copper D acts normally, producing a magnetic attraction of the armature that varys with the current in the main coil. But the changing magnetic field induces a current in the D, and that lags the current in the main coil by a quarter-cycle. The current in the D magnetizes the pole that passes through the D, and THAT pole's field, like the D's current, also lags by a quarter cycle.
So the field from the part of the core that goes through the D is strongest when the field from the part that bypasses it is reversing, and vice versa. The force on the armature is the sum of the magnitudes of the forces from both poles, and that sum is strong over the whole cycle and doesn't even vary a lot. With the armature pulled in strongly throughout each cycle the relay doesn't chatter or even hum much.