Is a woman permitted to seek divorce because she does not love her husband and is tempted by other men, or even if she is not tempted, she lives in sadness and depression from which she cannot free herself?

If a woman dislikes her husband and finds it impossible to live with him, she has the right to seek khul' (divorce initiated by the wife) by returning the mahr (dower) he gave her, especially if she fears for her religious commitment (fitnah in her religion). This is based on the Almighty's saying: "But if you fear that they will not uphold the limits of Allah, then there is no blame upon either of them concerning what she gives in return." It is sunnah for the husband to accept her request. Khul' is disliked if the situation is stable, but it is valid, based on the Prophet's (peace and blessings be upon him) saying: "Any woman who asks her husband for divorce without cause, the scent of Paradise will be forbidden to her."