I find
Chinese Tallow Tree (Triadica sebifera) popping up on occasion but I just yank them before they get to a large size. Cutting them down will not completely eradicate them, because they send up new shoots from the roots.
This site offers information and says to apply a herbicide to the base in late summer or early fall but apparently just one application won't work.
http://www.texasinvasives.org/... This site says that continued monitoring and control are necessary because of their ability to re-sprout following top kill:
http://www.fs.fed.us/database/...
You might try calling your County Agricultural Extension office or Forestry Service to see if they'd have suggestions regarding your neighbors field. It seems like a waste of time if they remain on his property because they will continue to spread and spread and spread.