Is it permissible to mortgage land to someone so that they may exploit it and take its full produce in exchange for a sum of money until it is repaid, and what is the legitimate form of mortgaging in Islamic law?

Pledging is permissible, based on the Almighty's saying: ﴿فَرِهَانٌ مَقْبُوضَةٌ﴾ (then a pledge in hand). So, if you borrow an amount and pledge land or a car, that is permissible. However, it is not permissible for the mortgagee to exploit the pledge beyond his right; the produce belongs to you. The mortgagee can exploit the pledge by renting it out, and the rent is deducted from the debt, or he can hand it over to you, and you rent it to him, and the rent is deducted from the debt. As for exploiting it in exchange for giving you time (to repay), this is a loan that draws benefit and is not permissible; it is usury. If the land is exploited without rent, it is not permissible because it is a benefit obtained in exchange for the loan, and this is usury.