I made an edge for the ajuga with some fairly deep wood chip mulch. The ajuga put out a few feelers over the wood chips, but didn't go further after it didn't find any hospitable soil. It spreads along the top of the soil, rooting where its stems touch the ground. If the stems touch down in a bad spot, it won't root.
BTw, the cultivar shown at the top of the thread might be one of the dark-leaved hybrids. The one I planted at my daughter's house (in Utah) had something about "Licorice" in the name as I recall. Even in spring its leaves were that dark color. It has quite deep purple flowers, too. There's a light green variegated one, too. (and probably many more since I last looked at it)
