moose have been killed with a .22LR rimfire, which proves only that it's possible.
in a somewhat like manner, a .40 for deer will depend solely on the shooter behind the gun's sights and trigger, hunting experience, gun proficiency, hunting ethics (if any), and what a less than 100 grain ball ballistics are at what distance, in what venue, and under what conditions. what'd i leave out?
these things are also true for a .50, or .62, rifle or smoothie, etc. - a far lesser caliber is just somewhat more, er, limiting?