Question: What is the ruling on one who swears by other than Allah Almighty to divorce his wife?

Swearing by other than Allah, such as by the Prophet, or the Kaaba, or someone's head, is polytheism (shirk). The one who swears by it is not bound by anything, nor is there any expiation, because it is an invalid oath. As for swearing by divorce, such as saying: "If you speak to so-and-so, then you are divorced," if the intention behind it is to prevent or encourage an action, there is a difference of opinion among scholars. The preponderant view is that the divorce does not occur, and expiation is required. This is the choice of Sheikh al-Islam Ibn Taymiyyah and Sheikh Ibn Baz.