Is the hadith about a man beating his wife with a siwak authentic?

There is no hadith stating that a wife should be beaten with a siwak. Rather, these are sayings of some scholars in interpreting the verse: (And those [wives] from whom you fear defiance, [first] advise them; then if they persist, forsake them in bed; and [finally], strike them. But if they obey you [thereafter], do not seek a way against them). It was narrated from Ata and Ibn Abbas that the striking should be with a siwak or similar object. This is the view of the Malikis and some Shafi’is and Hanbalis, that the discipline should be a non-violent striking with a siwak or similar object, not with a whip or stick, so that the intent is discipline, not harm.