your only option is to install an underground barrier and then kill all the plants in your yard.

The depth of the underground barrier should be determined by digging down to see how far down the roots are and then go twice as deep. Forget about arbitrary depth advice some websites will offer, you have to go with what is actually occurring in your yard. Double the depth to be safe.

Round up on the leaves should take care of the roots, but it may need to be applied a few times to completely eliminate them.

I've got a large raspberry patch on one side of my garden and another large strawberry patch on the backside of my garden and have tried a lot of options to contain the runners to no avail. I have resorted over the years to accepting the manual removal as a part of the joy of the crop. Now for you, it's too bad they're your neighbors. I would consider requesting a rezoning in order to procure the delicious raspberries, or consider some sort of "export tax" since the raspberries are clearly obtaining their nutrition from your side of the fence...say around harvest time. Maybe all of the reruns of the Sopranos has clouded my judgement, though.

And here --I can't get berries to grow to save my life. LOL! I told my brother I wanted to try blackberries again this year and he asked incredulously, "You mean those things we work so hard to kill?"

Ah... when life gives you raspberries, make jam!

(just kidding. justaguy's answer would be mine too.)