If one said to his companion, "By Allah, I will not speak to you," does he owe an expiation for breaking an oath?

If the oath was with intention, then it is binding and requires expiation upon speaking with the companion. If it was without intention, then it is a vain oath (laghw) from which nothing is required. It is preferable for him to expiate for his oath and speak with his companion, for the Prophet, peace and blessings be upon him, said: "If any of you takes an oath and then sees something better than it, let him expiate for it and do that which is better."