Vinca is a shade groundcover. Won't be happy in much sun - grows slowly and gets very chlorotic. Ajuga prefers some shade also but can tolerate a sunny position if adequately moist. But both can be pretty aggressive and that is a very small space that you already have a good many other plants in.

You don't indicate where you are located or what zone you are in but there are a number of spreading perennials that would serve your purpose yet not spread aggressively or smother/overgrow other plants. Not all of these will work in all zones but research and see what you like and what may work for you. Most are evergreen. And they are often planted as edging plants in perennial borders, with larger growing perennials, shrubs, etc. behind them. A few of these and some mulch and your soil should be adequately covered and offer a presentable look in winter.

Helianthemum nummularia - Sunrose
Iberis sempervirens - Candytuft
Cerastium tomentosum - Snow in Summer
Stachys byzantina - Lamb's ear
Veronica peduncularis 'Georgia Blue' - creeping veronica
Abrieta deltoides - Rockcress
Thymus citriodorus - Lime thyme
heaths and heathers
Lithodora diffusa