Abjure means ‘to renounce on oath’
and to abjure one's country (or realm) is to swear to abandon it for ever. It is also used in the weakened sense ‘to renounce’
(He had abjured, he thought, all superstitions—Iris Murdoch, 1985)
By contrast, adjure means ‘to request earnestly’ with or (now) more frequently without an oath (They were all talking at once, adjuring each other to have fresh cups of tea). Neither word is in everyday use, but they are found in literature and can cause confusion when wrongly used.
(Are faculty members willing to abjure e-mail in communicating with their students and colleagues?—The Nation, 2002 [OEC]).