Yes, that kind of mineral exists in nature under the name fuchsite and it is just a colored form of the common mica found in some sands (original name: muscovite). The gree mica is actually a variety of muscovite very reach in chromium (usually between 1-5%). While the common mica is grey or silver, the fuchsite form has a very nice, bright green color.

The photo above is of a little stone gathered from a stone carving artist from northern Germany who opened a galery with artistic gardening ideas (photo wide: 8 mm). One of them included fuchsite as main element due to its warm color. When the stone is exposed to sunset light it shines even stronger than under normal light, which makes the stone very attractive for colored garden fans.