Atomic displacements at and order of all phase transitions in multiferroic YMnO3 and BaTiO3

Coordinate analysis of the multiple phase transitions in hexagonal YMnO3 leads to the prediction of a previously unknown aristotype phase, with the resulting phase-transition sequence: P6(3)'cm'(e.g.) <-> P6(3)cm <-> P6(3)/mcm <-> P6(3)/mmc <-> P6/mmm. Below the Neel temperature T-N similar or equal to 75 K, the structure is antiferromagnetic with the magnetic symmetry not yet determined. Above T-N the P63cm phase is ferroelectric with Curie temperature T-C similar or equal to 1105 K. The nonpolar paramagnetic phase stable between T-C and similar to 1360 K transforms to a second nonpolar paramagnetic phase stable to similar to 1600 K, with unit-cell volume one-third that below 1360 K. The predicted aristotype phase at the highest temperature is nonpolar and paramagnetic, with unit-cell volume reduced by a further factor of 2. Coordinate analysis of the three well known phase transitions undergone by tetragonal BaTiO3, with space-group sequence R3m <-> Amm2 <-> P4mm <-> Pm (3) over barm, provides a basis for deriving the aristotype phase in YMnO3. Landau theory allows the I <-> II, III <-> IV and IV <-> V phase transitions in YMnO3, and also the I <-> II phase transition in BaTiO3, to be continuous; all four, however, unambiguously exhibit first-order characteristics. The origin of phase transitions, permitted by theory to be second order, that are first order instead have not yet been thoroughly investigated; several possibilities are briefly considered.