Displacive phase transitions and magnetic structures in Nd-substituted BiFeO₃

Neutron powder diffraction was used to determine changes in the nuclear and magnetic structures of Bi_1-xNd_xFeO₃ polymorphs involved in the first-order displacive phase transitions from the high-temperature nonpolar phase to the low temperature polar (x ≥ 0.125) and antipolar (0.125 ≥ x ≥ 0.25) phases, respectively. The high-temperature phase (O₁), which crystallizes with a structure similar to the room-temperature form of NdFeO₃, exhibits Pbnm symmetry and unit cell √2a_c × √2a_c × 2a_c (where a_c ≈ 4 Å is the lattice parameter of an ideal cubic perovskite), determined by a^-a^-c⁺ octahedral tilting. The low-temperature polar structure (R) is similar to the β-phase of BiFeO₃ and features rhombohedral symmetry determined by a ^-a^-a^- octahedral rotations and cation displacements. The recently discovered antipolar phase (O₂) resembles the antiferroelectric Pbam (√2a_c × 2√2a _c × 2a_c) structure of PbZrO₃ but with additional displacements that double the PbZrO₃ unit cell along the c-axis to √2a_c × 2√2a_c × 4a _c and yield Pbnm symmetry. The O₁ ↔ R and O ₁ ↔ O₂ transitions are both accompanied by a large discontinuous expansion of the lattice volume in the low-temperature structures with a contrasting contraction of the [FeO₆] octahedral volume and an abrupt decrease in the magnitude of octahedral rotations. The O₁ ↔ O₂ transition, which occurs in the magnetic state, is accompanied by an abrupt ≈90° reorientation of the magnetic dipoles. This coupling between the nuclear and magnetic structures is manifested in a significant magnetization anomaly. Below 50 K, reverse rotation of magnetic dipoles back to the original orientations in the high-temperature O₁ structure is observed.