We have chickens but no rat problem on our land. There are rats on neighbouring fields which I can't control because neighbours have bird feeders etc but as others have said chickens themselves don't attract rats, it's their food. If your neighbours will control that then the rat problem solves itself as they will go away to a new food source.
We used to have a terrible rat problem and at one point used poison. If anyone in your area has pets or children I would not consider doing that. Locked boxes don't make it safe. Rats carry it from the box to their nest and can drop it on the way. We had a pet eat it and die an agonising death. It could just as easily have been a child, whether ours or someone else's. You cannot control the rats dropping the poison once they pick it up. If you are going to kill them consider pets, wildlife and children and use safer methods such as shooting, terrier man and digging up the nest. However given the nest is not in your house and you know what's attracting them it should be easy enough to persuade them to move on.
What you need is proper rat proof feeders. Well your neighbours do anyway. The best ones are quite expensive, they are called grandpa's original feeders but they save money on feed as you aren't feeding the rats as well. Also all the feed should be kept in stainless steel bins not just in sacks in a shed ready for the rats to eat. Hopefully your neighbours are willing to discuss this seriously with you. As a minimum they should be putting their feeders away at night, if they insist on using the cheap plastic ones they need to go in the steel bins or in the neighbour's house.
We found during the chicken lockdown when our chickens were bored we gave them too many treats and they weren't eating them all, so the rats were coming out at night and finishing them off. Now we're much more cautious and give very limited treats, if any, so they are always finished before chicken bedtime.
Rats like sheltered secret runs and to travel around undisrupted, so the more you can rearrange your woodshed, tidy your garden, dig in their nest, dig your compost bin, clear any old rubbish and wood you may have laying around which shelters them (ideally get neighbours to do so too) - they will feel less safe and want to move on to live somewhere more secure.