I've seen my FIL put a small, very small, dab of super glue on the part of the key he had out, insert in the key hole, wait a few seconds and then pull the broken piece out.
If you don't have the other half of the key, try a small dowel or similar sized key with the glue.
Of I shouldn't need to say, but if you put too much glue on and it oozes out, you risk gluing up your lock.