Answer: There are many plants you could use ranging from the traditional groundcovers such as English ivy, Ajuga, Pachysandra and Vinca minor (periwinkle) to perennials such as creeping thyme, small sedums and hostas, smaller daylilies (Hemerocallis), golden moneywort (Lysimachia nummumlaria "Aurea"), creeping phlox (phlox subulata), Blue Fescue (Festuca ovina glauca), Daylilies (Hemerocallis spp.) - especially smaller re-blooming varieties such as 'Happy Returns' or 'Rosy Returns', 'Nikko' Slender Deutzia (Deutzia Gracilis 'Nikko'), Junipers: (Juniperus horizontalis, Juniperus procumbens 'Nana'), Lily Turf (Liriope muscari), Creeping Phlox (Phlox subulata),
'Gro-low' Fragrant Sumac (Rhus aromatica "Grow-low'), 'Green Mound' Alpine Currant (Ribes alpinum 'Green Mound'), Sedum (Sedum spp. & cultivars, especially 'Vera Jamison,' Sedum spurium Sedum repestre 'Angelina'), Japanese spirea (Spirea japonica 'Little Princess' or 'Magic Carpet'), 'Crispa' Cutleaf Stephanandra (Stephanandra incisa 'Crispa'), Spreading English Yew (Taxus baccata 'Repandens').
Your selection will depend on several factors such as amount of sun and what time of day it is sunny, soil type and average soil moisture levels, wind exposure, and the amount of water moving on the slope as well as whether or not you want flowering, or prefer an evergreen, and so on. I would suggest you work with your local professionally trained nursery staff to analyze the growing conditions where you need to plant this and identify plants that would thrive there, then select the one(s) you like best from among those. Good luck with your project!
Q&A Library Searching Tips