Factor Group Analysis on the Deformed Pyrochlore-Structure Hydroxyl Transition Metal Halides

Factor group analysis on the deformed pyrochlore-structure hydroxyl transition metal halides M2(OH)3X (M = Co, Fe and Mn; X = Cl, Br and I) with the crystal symmetry ≡ D3d5 of space group No. 166 for their infrared (IR) and Raman spectroscopic studies are, for the fist time to the best of our knowledge, reported. Through a standard factor group analysis, we predict that there are 17 IR active normal modes (7A2u+ 10Eu) and 12 Raman active modes (5A1g + 7Eg), caused by five atomic site groups [HOM3], [OM3], [MO4X2], [ClM3] and [MO6], where the black body letters represent the site atoms. In addition we figure out all the atomic displacement patterns of 12 Raman active normal modes, and point out these results are completely same as those of the famous geometric frustration material Herbertsmithite ZnCu3(OH)6Cl2.