Planting under Magnolia

I have a Magnolia macrophylla in my garden. As time goes by the roots are becoming more and more apparent and there is less and less grass underneath the tree. I assume that this is because the tree is soaking up all the moisture.

Has anyone got any ideas what I could do with this quite large patch around the tree? Would it be better to give up on grass altogether in this area? In that case, what could I plant there given that there is not much earth between roots to plant anything in?

Any suggestions would be very welcome. Thanks!