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We investigate the second-order phase transitions in non-magnetic wurtzite ZnO and magnetic doped with cobalt. Using reformulated Landau-Lifshitz theory of second-order phase transitions and our computer program, we have found all possible lower space group symmetries of ZnO and ZnO doped with Co as well as symmetries of vibration modes which may cause structural phase transitions. We interpret the Raman phonon modes of magnetic doped ZnO according to corepresentations of the magnetic space group P6'₃m'c (ZnO magnetic). Some experimental techniques like X-ray diffraction, reflectivities and Raman spectroscopies can verify our theoretical results.
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