It is not permissible to marry without a mahr (dowry)
Question

Is it permissible for a Muslim to give his daughter in marriage to a man for the sake of Allah, may He be exalted, and not take any mahr (dowry) for that?
Praise be to Allah.In marriage, it is essential that there should be some wealth, because Allah, may He be glorified and exalted, says (interpretation of the meaning):
{All women other than these are lawful for you, so that you may seek them with your wealth in honest wedlock, not fornication. When you consummate your marriage with them, give the dowries due to them} [an-Nisa’ 4:24].
And in the hadith of Sahl ibn Sa‘d, the soundness of which is agreed upon, the Prophet (blessings and peace of Allah be upon him) said to the man who proposed marriage to the woman who had offered herself in marriage to the Prophet (blessings and peace of Allah be upon him) [but he did not want to marry her]: “Look for something [to give as a dowry], even if it is a ring of iron.”
If a man marries without giving a dowry, the woman is entitled to a dowry like that of her peers.
It is permissible to marry with a commitment to teach the woman something of the Quran or hadith, or other types of beneficial knowledge, because the Prophet (blessings and peace of Allah be upon him) married the suitor mentioned above to the woman who had offered herself to him in marriage on the basis that he would teach her some surahs of the Quran, because he did not have any wealth.
The mahr is the woman’s right, then if she gives it up after that, and she is of sound mind, that is valid, because Allah, may He be glorified and exalted, says (interpretation of the meaning):
{And give the women [on marriage] their dowry graciously; but if they, of their own accord, choose to give up to you a part of it, you may enjoy it with a clear conscience} [An-Nisa’ 4:4]. End quote.
Shaykh ‘Abd al-‘Aziz ibn Baz (may Allah have mercy on him), Kitab ad-Da‘wah (2/210).