They're part of the shinigami position. The size and style denote power and rank respectively, and only those in charge of their own territory have feathered ones.

[He searches as he speaks, bending over and pushing at anything that's big enough and isn't obviously either attached to something or buried deep. So far it's taking awhile, it's hard to tell what's under the sand.]

Lower ranking staff for the Reaper's Game have smaller, almost skeletal looking bat wings.