They do little damage to plants themselves, except by disturbing soil around plant roots and depositing it on the surface during their nest building activities. This can be a nuisance especially on lawns where small mounds of soil are more obvious & unsightly.
An alternative method to using chemicals is biological control.
Parasitic nematodes (roundworms) are available through mail order. You mix them with water and apply to the soil – they then destroy the ant larvae.
They must be applied to moist, warmer soil (at least 10C) on a cloudy day or in the evening. Find out more about them here.