Borax mixed with syrup (sugar dissolved in warm water works just fine for this) has been the best killing bait I'd ever used with ants of all kinds. You have to really experiment to get the ratio right, if you aren't sure - try Terro Liquid Ant Baits which is exactly that but premixed with the correct ratios. You will suddenly see a LOT of ant activity at first - you know they're working then - but then just as suddenly the activity will disappear after a couple days or weeks. Do not let the liquid run out until they stop taking it (they will only stop taking it after they have all died, they love this stuff and swarm it as soon as they know it's there).
Do not ever put the bait stations touching any part of the mounds, rather near it. They can sense that stuff a good bit away but if it touches their hill at all, they'll view it as a threat and not something to eat and share with their queen or larvae. They make a version of the bait dispenser that can be staked to the ground but really it's as simple as keeping the stations anywhere birds wont reach them too, or just in a tupperware with holes drilled in just big enough for ants to get inside. It's pretty safe.
Do not spray insecticides of course. That's the biggest concern to avoid with poultry since sprays stay in the environment uncontrolled. It also makes it so baits wont work because the ants can smell/taste the spray instead. It will only make them move and become a problem to somewhere else in your pasture.