How deep of a barrier do I need to contain Maximillian sunflowers?

I'm planting a patch of Maximillian sunflowers near a neighbor's fence, and want to put in a root barrier to contain them on my side. (And keep their grass on their side.) How deep do you think I should go?

In my experience Maximilian sunflowers do not spread but remain in nice distinct clumps.

In my experience of wild sunflowers they spread by seed and don't survive mowing.  If your neighbor has a grass lawn that they mow, neither of you will need to take any extra steps, to control the sunflowers.

Now controlling the grass is a different matter.  Let me know if you discover an effective barrier for grass roots.  I control mine by persistent pulling, but they can travel several feet underground. It's a garden task force that never really ends.