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: P63′cm′(e.g.) ↔P63cm↔P63/mcm↔P63/mmc↔P6/mmm. Below the Néel temperature TN≃ 75 K, the structure is antiferromagnetic with the magnetic symmetry not yet determined. Above TN the P63cm phase is ferroelectric with Curie temperature TC≃ 1105 K. The nonpolar paramagnetic phase stable between TC and ∼ 1360 K transforms to a second nonpolar paramagnetic phase stable 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↔Pmm, 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.