Use wood and branches that have been prepared by machinery such as a chipper or shredder as soil covering. It will keep the soil protected in many ways – see here for more information. Different plants, shrubs or trees will create a different end materiel, some will be mostly wood (bramble/hazel) ranging through to leafy and green (elder/conifer). Additionally, properties in the cells of wood will help prevent weed seeds from germinating (see: lignin – https://en.wikipedia.org/wiki/Lignin). When it is very woody, mix it in with some green material. A mature erbal border will also be a good source of material, after they finish flowering.
A Garden Shredder
A Row of Broad Beans on Left and Potatoes on Right, Reggy for a Covering