The best and most recent, Peter Jackson's "The Mongols and the Islamic World: From Conquest to Conversion," (Yale University Press, 2017) discusses both the initial interactions between the Mongols and Islam (from the invasion of the Kara Khitai to Chinggis' campaigns against the Khawrezmians) and discusses in detail the conversions of the Golden Horde, Chagatai Khanate and Ilkhanate through to the fourteenth century, with the lkhanate perhaps getting the most detail and the Chagatai Khanate covered rather sparingly, but that is sort of a given for Mongolian studies. It covers all the latest scholarship and discussions, the primary sources, the chronology and effectively every other concern you may have for this topic. I really can't recommend it enough if you are interested in this area. It is easily accessible, you literally may be able to find it at a local bookstore.

There is also the Cambridge History of Iran, Vol. 5. "The Saljuq and Mongol Periods," which covers this topic extensively, but focuses on the Ilkhanate and as it was released in 1968 or so, it is a little dated now, but is extremely detailed and worth a look: https://books.google.ca/books?id=16yHq5v3QZAC&lpg=PP1&pg=PA1&redir_esc=y#v=onepage&q&f=false

EDIT: grammer and spelling, clarity