I guess it's an augemented fourth because it contains a half step more than a perfect fourth; [from a source] but in a minor scale it isn't allowed: an augmented fourth is IV degree.
Any A to any D is some kind of 4th since the distance in letter names is that of a 4th. Since A to D is a perfect 4th, making the interval bigger by one semitone from A to D♯ makes this interval an augmented 4th.
For more information about naming intervals in general, please see one of the many questions on the site addressing this:
Depends on which note is the lower. From D# to A, one has D#,E,F,G,A (with 5 letters) the interval is a diminished fifth. Going from A to D# one has A,B,C,D# and 4 letters so it's an augmented fourth.
I've always referred to that interval as the Tritone and folks seem to know what I'm talking about. Augmented fourth or diminished fifth offer an explanation of how we arrive at this result, but I know it as a Tritone interval, am I wrong?