Hello mechanics! I've been trying to solve my handlebar creaking issue here and have had trouble finding info by searching the forum. I found one thread from back in 2002 that is exactly like my problem. The folks replying all say to grease the stem and handlebar prior to clamping it down.
That is the fix for a stem that develops a squeek from the stem contact the inside of the steerer tube. Often this is most noticble when we get out of the saddle and really put some twisting and side to side stress on the handle bars.
Pull the stem from the steerer tube.
Using any grease (automotive or other) put a coating over the portion of the stem that is inserted into the steerer tube.
If there's any rust on the outside of the stem, it's a good idead to clean it up with some emory cloth first.
There's also a chance that it's actually broken. I had a lovely Cinelli XA stem once and I couldn't for the life of me track down the creaking. I finally decided it had to be breaking, took the whole cockpit apart, stripped down the bars, and popped out the little flying C badge on the stem before I found a small hairline crack radiating outward from the countersunk hole for said badge.