How do I get rid of a large ants nest permanently?

I just dug up my lawn prior to laying a new lawn and garden. Below is a 12mx10m ants nest! How do I get rid of it permanently before laying new lawn and garden? If I put down ant killer, it'll kill these, but they'll presumably be back soon... Ideally, I'd like to avoid using chemicals, and anything that will damage the garden / other animals.