In addition to the commercially available ant compounds that you can use against ants in the garden, when there are a few nests, it can be useful to dig them out with a pair of spades and place them in innocuous places, or, where it is not possible to relocate them, to destroy them with boiling water. This is really easy to do in a wheelbarrow.
Another tried-and-tested solution is over-watering the nests locally very intensively so that the animals drown. When they have definitely been killed, re-lay the lawn in the relevant area. Do this either by seeding the area or by cutting some lawn from a suitable location and using this to patch up the damaged area.
As I have given this advice publicly, I must point out that you may only carry out these actions for ant species that are not protected (cf. www.ameisenschutzwarte.de/rechtliches
). The black garden ant (Lasius niger), which I suspect is your "culprit", is not, to my knowledge, a protected species. But that is a diagnosis made without actually having seen the problem!