They are called Micas. Some names for Micas are called, Muscovite, Biotite, and Phlogopite.

Many types of mica are known: biotite, lepidolite, muscovite, phlogopite, zinnwaldite, clintonite, illite, phengite.

Many minerals have "cleavage" that causes them to split on flat cleavage planes. Such minerals include micas (muscovite, biotite. phlogopite), calcite, gypsum, and feldspars. Cleavage is the result of the minerals' crystal structure that has weaker chemical bonds aligned in planes.

. The commercially important micas are muscovite and phlogopite, which are used in a variety of applications. Mica's value is based on several of its unique physical properties. The crystalline structure of mica forms layers that can be split or delaminated into thin sheets usually causing foliation in rocks. These sheets are chemically inert, dielectric, elastic, flexible, hydrophilic, insulating, lightweight, platy, reflective, refractive, resilient, and range in opacity from transparent to opaque

Muscovite and Phlogopite, along with Biotite and Lepidolite and many others are all minerals that cleave into thin sheets with a fair amount of flexibility. However, these minerals are all part of the silicate mineral group known as Micas. Slate can also be cleaved into thin sheets which are slightly flexible, but which are quite brittle. Graphite may also be expanded by chemical treatments to yield a flexible sheet known as graphite foil with interesting electrical and thermal properties.