Mimosa is a non-native invasive plant, the seeds are wind blown and spread fairly quickly. I would not recommend using at all. My neighbor up the hill has one or more mature, and just about any bare soil in my yard maybe 500 feet away is subject to the seed sprouts.
Black locust used to be planted for its nitrogen fixing capability, but it’s thorny. Some use clover. There may be some other native legumes, like partridge pea that I don’t remember.
If I was going with a non-native invasive, which I still suggest not to use, would be Sericea lespedeza. Some of our pine stands on eroded piedmont soils, really responded to the nitrogen fixation, and it goes pretty dormant in a closed canopy, but re-emerges when harvesting and opening the area to sunlight. Sericea is still commonly used along road construction or maintenance activities, so it’s probably not going away, but it’s persistent.
