Hi Kar,
Mimosa (Albizia Julibrissen).
Beautiful as it may be, Mimosa is not a good neighbor to many native species of flora or fauna. It is irrefutably invasive and propagates freely from seed and also by sprouting new shoots from a dense spreading root structure.

Sciece Lesson Now.
Mimosa is allelopathic this means chemicals from the tree that wash down with rain suppress blooms in other plants and suppress seed germination of most species of plants. Mimosa may not be the greatest plant to have growing anywhere near blooming trees that fruit to sustain wildlife as yields can be compromised in the presence of this species.
In short, you are doing the only thing you can!
Hope this helps.
Bryan.