Do Abjure Enemy effects last only one turn?

I play the Oath of Vengeance paladin and have came across a problem.

There is the Channel Divinity: Abjure Enemy description, which states:

As an action, you present your holy symbol and speak a prayer of denunciation, using your Channel Divinity. Choose one creature within 60 feet of you that you can see. That creature must make a Wisdom saving throw, unless it is immune to being frightened. Fiends and undead have disadvantage on this saving throw.

On a failed save, the creature is frightened for 1 minute or until it takes any damage. While frightened, the creature’s speed is 0, and it can’t benefit from any bonus to its speed.

On a successful save, the creature’s speed is halved for 1 minute or until the creature takes any damage.

It sounds pretty good, but does anything forbid an abjured enemy from simply harming himself on his turn?