Natural mica crystals have been characterized for use as reflectors for an ultracold neutron source using Bragg scattering of cold (400 m/s) neutrons from a moving mica reflector, recently installed at the Los Alamos neutron science center (LANSCE). In particular, the triotahedral Mg-rich mica phlogopite has been obtained in large sheets. The structure factor for the first-order Bragg reflection is a factor of four larger than for muscovite, the first variety of mica examined. The observed peak reflectivity for a phlogopite of 0.25 mm thickness is about 8.2% at 1.9 Å, with a mosaic spread of about 0.3° FWHM, in good agreement with the ideally imperfect crystal model. This can be extrapolated to a reflectivity of about 63% at the 17.4 Å operating wavelength of the ultracold neutron source. Improvements are possible by obtaining Fe-rich mica, which should be almost as effective as the alternative approach of using synthetic perfluorinated mica.