The best ground cover depends on climate, soil type, and the angle of the slope the tree is on. When deciding on a ground cover, consider the compatibility with the existing trees on the slope, soil retention ability, maintenance, requirements, and local invasive species laws.
One option is using native plants and grasses because they are deep-rooted and adapted to local conditions. Creeping juniper is shade-tolerant, drought-tolerant, and forms a dense mat.
Periwinkle is fast-growing and tolerates many climates, while bugleweed is low-growing, and spreads quickly. Sedum is drought-resistant and works well on rocky slopes, while cotoneaster is a woody ground cover with good erosion control.
Creeping phlox is a pretty flowering option for full-sun slopes, and for shaded moist slopes, consider using moss.