What is the religious ruling and expiation for an oath after the husband said to his wife, "By divorce, I did not say such and such," in response to her accusation, and her refusal of intimacy after she asked him to retract his oath?

If a divorce oath (talaq (definition)) is sworn believing it to be true, then the divorce does not occur, even if reality differs from the belief. However, if it is sworn intentionally as a lie, the fatwa (definition) we follow is that the divorce does occur, and no expiation is required. Sheikh al-Islam Ibn Taymiyyah, however, holds that such an oath does not cause divorce nor does it require expiation. If a revocable divorce (talaq raj'i) occurs, the husband has the right to take his wife back during her waiting period ('iddah (definition)), and she may not refuse to respond to his marital call unless there is a valid excuse. The lawful oath is by Allah Almighty.