| The rare earth manganites RMnO3 for R=Ho, Er, Yb crystallize in hexagonal perovskites type structures with symmetry P6 3cm[#185,( C36v )]. In this work, the structural and magnetic phase transitions are investigated by considering the Landau theory of phase transitions, in which the transition order parameter transforms according to the irreducible representations of the high symmetry space group. The structural phase transitions occurring at the Gamma point for one component order parameters A1, A 2, B1 and B2 lead to symmetries P63cm ( C36v ), P63 ( C66 ), P3c1 ( C33v ) and P31m ( C23v ) respectively. For the two component order parameter E1, the low symmetry phases as a result of structural phase transitions are Pm ( C1s ) and Pc ( C2s ) corresponding to the equilibrium values (eta,0), (0,eta). For E2, the two low symmetry phases correspond to the same symmetry group Cmc21 ( C122v ) with opposite values of equilibrium order parameter i.e., (eta,0), (-eta,0).; The structural changes are also found at the M-point of the hexagonal Brillouin zone. The three-dimensional space group representations at the M-point are M1, M2, M3 and M4. The low symmetry phases appearing at M1 are P63cm ( C36v ), Cmc21 ( C122v ) and Pmc21 ( C12v ). For M2, the low symmetry phases are P63 ( C66 ), Cmc21 ( C122v ) and Pmn21 ( C72v ). For M3, the low symmetry phases are P3c1 ( C33v ), Cc ( C4s ) and Pc ( C2s ). For M4, the low symmetry phases are P31m ( C23v ), Cm ( C3s ) and Pm ( C1s ).; The magnetic symmetry of RMnO3 as a result of magnetic ordering in R3+ ions is supposed to be Pc for HoMnO3 and Pc&barbelow; for ErMnO3, YbMnO3. The irreducible representation E1 at the Gamma point or M3 representation at the M-point of the hexagonal Brillouin zone are proposed to be related to this symmetry for HoMnO3. |
