I will let you in a little secret I buy a 24" metal magnet bar and hang up my files,I must have so many that I lost count! Metal should never touch othet metal,but each file close to the tang does not have any teeth to get damaged that is the place I hang them on the magnet.
If you go to a store or on line you can buy them I think 12" long,24" long or even longer in length. If money is an issue you can build a small wood cabinet or build a butcher block type holder for all of your files.