Is swearing by one's head an oath or a covenant, and is expiation obligatory if it is broken?

It is not permissible to swear by other than Allah, and it is a form of polytheism (shirk), based on the Prophet's (peace and blessings be upon him) saying: "Whoever swears by other than Allah has disbelieved or committed shirk." This includes swearing by a person's life, head, or honor. An oath sworn by other than Allah is not binding and does not require expiation (kaffarah) according to most scholars. Whoever swears by their head has committed a forbidden act, and they must repent, feel remorse, and resolve not to return to it. There is no expiation required if they fail to fulfill what they swore by.